Project_1_Model_2_(6).ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "Project_1_Model_2 (5).ipynb",
      "provenance": [],
      "collapsed_sections": [],
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/ctandrewtran/andrewtran/blob/master/Project_1_Model_2_(6).ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "4OucTA3kEJlo"
      },
      "source": [
        "# Winerschniztal Diet! \n",
        "\n",
        "By Andrew Tran, Josh Allen, Ryan Bilas, Matt Mester, and Elizabeth Gurry"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "wbjgTbpkEIjG",
        "outputId": "f79ee0a2-ce0c-4baf-e2d5-42ec12f7d1e9",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "source": [
        "#Installing num2words for use\n",
        "!pip install num2words"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "fRequirement already satisfied: num2words in /usr/local/lib/python3.6/dist-packages (0.5.10)\n",
            "Requirement already satisfied: docopt>=0.6.2 in /usr/local/lib/python3.6/dist-packages (from num2words) (0.6.2)\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "VABxlYoEUTQ1"
      },
      "source": [
        "# Importing Appropriate Programs\n",
        "%matplotlib inline\n",
        "from pylab import *\n",
        "\n",
        "import shutil\n",
        "import sys\n",
        "import os.path\n",
        "\n",
        "if not shutil.which(\"pyomo\"):\n",
        "    !pip install -q pyomo\n",
        "    assert(shutil.which(\"pyomo\"))\n",
        "\n",
        "if not (shutil.which(\"glpsol\") or os.path.isfile(\"glpsol\")):\n",
        "    if \"google.colab\" in sys.modules:\n",
        "        !apt-get install -y -qq glpk-utils\n",
        "    else:\n",
        "        try:\n",
        "            !conda install -c conda-forge ipopt\n",
        "        except:\n",
        "            pass\n",
        "\n",
        "assert(shutil.which(\"glpsol\") or os.path.isfile(\"glpsol\"))\n",
        "\n",
        "from pyomo.environ import *\n",
        "\n",
        "SOLVER = 'glpk'\n",
        "EXECUTABLE = '/usr/bin/glpsol'"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "xLhfnHcsEELM"
      },
      "source": [
        "#importing pandas for use\n",
        "import pandas as pd\n",
        "\n",
        "#used later on to capture variable results from pyomo\n",
        "import sys\n",
        "import io\n",
        "\n",
        "from num2words import num2words # Installed at the top\n",
        "\n",
        "#data stored on uconn's github; query parama raw=true needed to retrieve data properly\n",
        "url = 'https://github.uconn.edu/Ant16112/opim3803/blob/master/GP_data.csv?raw=true'\n",
        "\n",
        "#Reading in the same csv data as Model 1\n",
        "df = pd.read_csv(url)\n",
        "\n",
        "#making sugar calorie column for later calculation\n",
        "df['Sugar_Calories'] = df['Sugar'] * 4\n",
        "\n",
        "#replacing food or drink with integer id to avoid data cleaning manually\n",
        "#there were some issues with the text; num2words was fastest solution\n",
        "df['food_drink_id'] = df.index\n",
        "df['food_drink_id'] = df['food_drink_id'].apply(num2words)\n",
        "df['food_drink_id']  = df['food_drink_id'].str.replace(\" \", '')\n",
        "df['food_drink_id']  = df['food_drink_id'].str.replace(\"and\", '')\n",
        "df['food_drink_id']  = df['food_drink_id'].str.replace(\"-\", '')"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "rGYZhpcMD6WW",
        "outputId": "77d6aeb2-b765-4fc7-e8c1-77bc1f95afe6",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "source": [
        "#Loop we used to automate the writing of the hard code for the constraint\n",
        "\n",
        "constraint_list = list()\n",
        "for x in df.values:\n",
        "  hard_coded_constraint = \"model.\" + str(x[8]) + \"*\" + str(x[2]) + \" + \"\n",
        "  constraint_list.append(hard_coded_constraint)\n",
        "\n",
        "for x in constraint_list:\n",
        "    con = x.replace(\"'\", \"\")\n",
        "    print(con)\n",
        "    break"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "model.zero*15 + \n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "AWI2OpQwEtsY",
        "outputId": "547435b2-537c-444b-82a7-0b81732bb31f",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 602
        }
      },
      "source": [
        "df.head() #Showing me the first 5 rows of the data set"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>Food or Drink</th>\n",
              "      <th>Calories</th>\n",
              "      <th>Protein</th>\n",
              "      <th>Carb</th>\n",
              "      <th>Sodium</th>\n",
              "      <th>Sugar</th>\n",
              "      <th>Weight Watchers Points</th>\n",
              "      <th>Sugar_Calories</th>\n",
              "      <th>food_drink_id</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>Original Chili Cheese Dog, standard bun</td>\n",
              "      <td>320</td>\n",
              "      <td>15</td>\n",
              "      <td>31</td>\n",
              "      <td>1410</td>\n",
              "      <td>4</td>\n",
              "      <td>9</td>\n",
              "      <td>16</td>\n",
              "      <td>zero</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>Original Chili Dog, standard bun</td>\n",
              "      <td>270</td>\n",
              "      <td>12</td>\n",
              "      <td>31</td>\n",
              "      <td>1160</td>\n",
              "      <td>4</td>\n",
              "      <td>8</td>\n",
              "      <td>16</td>\n",
              "      <td>one</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>Original Mustard Dog, standard bun</td>\n",
              "      <td>240</td>\n",
              "      <td>10</td>\n",
              "      <td>27</td>\n",
              "      <td>810</td>\n",
              "      <td>4</td>\n",
              "      <td>7</td>\n",
              "      <td>16</td>\n",
              "      <td>two</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>Original Relish Dog, standard bun</td>\n",
              "      <td>250</td>\n",
              "      <td>10</td>\n",
              "      <td>30</td>\n",
              "      <td>870</td>\n",
              "      <td>6</td>\n",
              "      <td>7</td>\n",
              "      <td>24</td>\n",
              "      <td>three</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>Original Kraut Dog, standard bun</td>\n",
              "      <td>240</td>\n",
              "      <td>10</td>\n",
              "      <td>28</td>\n",
              "      <td>1040</td>\n",
              "      <td>5</td>\n",
              "      <td>7</td>\n",
              "      <td>20</td>\n",
              "      <td>four</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "                             Food or Drink  ...  food_drink_id\n",
              "0  Original Chili Cheese Dog, standard bun  ...           zero\n",
              "1         Original Chili Dog, standard bun  ...            one\n",
              "2       Original Mustard Dog, standard bun  ...            two\n",
              "3        Original Relish Dog, standard bun  ...          three\n",
              "4         Original Kraut Dog, standard bun  ...           four\n",
              "\n",
              "[5 rows x 9 columns]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 13
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "87VPkKFEDOqV"
      },
      "source": [
        "# The Diet: IIFYM\n",
        "\n",
        "Called \"if it fits your macros,\" it is a diet where you simply calculate the calories you burn per day and eat under that threshold alongside protein/fat macro requirements. Any food or drink goes!\n",
        "\n",
        "## IIFYM Guidlines\n",
        "* Calculate basal metabolic rate (BMR) adjusted with total daily energy expenditure (TDEE) and eat 10%-15% calories below that to achieve weightloss\n",
        "* Protein intake is between .7-1 grams per lb of bodyweight\n",
        "* Remaining calories filled by carbs/fats\n",
        "\n",
        "https://www.healthline.com/nutrition/iifym-guide#meeting-your-macros \n",
        "\n",
        "\n",
        "## CDC Health Guidelines\n",
        "Added this in to make sure the diet is more healthy\n",
        "* Sodium must be less than or equal to 2300 mg\n",
        "* Sugar must bes less than 10% of calories for the day\n",
        "\n",
        "https://www.cdc.gov/salt/pdfs/sodium_dietary_guidelines.pdf\n",
        "\n",
        "https://www.cdc.gov/nutrition/data-statistics/know-your-limit-for-added-sugars.html#:~:text=Americans%20should%20keep%20their%20intake,part%20of%20a%20healthy%20diet.&text=For%20example%2C%20in%20a%202%2C000,should%20come%20from%20added%20sugars. \n",
        "\n",
        "\n",
        "## Calculate BMR below using the Original Harris-Benedict Equation\n",
        "https://www.k-state.edu/paccats/Contents/PA/PDF/Physical%20Activity%20and%20Controlling%20Weight.pdf\n",
        "https://bmi-calories.com/bmr-calculator.html"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "EYNidbKPE8ME",
        "outputId": "b8603d12-7f4d-48a1-ea06-9ae7280a2fd0",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "source": [
        "#gathering neccesary inputs for basal metabolic rate calculation\n",
        "print(\"Are you male or female; input m for male and f for female\")\n",
        "gender = input()\n",
        "\n",
        "print(\"Input height in inches\")\n",
        "height = input()\n",
        "height = float(height)\n",
        "\n",
        "print(\"Input age in years\")\n",
        "age = input()\n",
        "age = float(age)\n",
        "\n",
        "print(\"Input weight in lbs\")\n",
        "weight = input()\n",
        "weight = float(weight)\n",
        "\n",
        "def bmr_calc(gender, height, age, weight):\n",
        "  if gender == 'm':\n",
        "    bmr = 66.4730 + (13.7516 * (weight * .45)) + (5.0033 * (height * 2.54)) - (6.7550 * age)\n",
        "    return bmr\n",
        "  elif gender == 'f':\n",
        "    bmr = 655.0955 + (9.5634 * (weight * .45)) + (1.8496 * (height * 2.54)) - (4.6756  * age)\n",
        "    return bmr\n",
        "  else:\n",
        "    print('Wrong info entered, try again.')\n",
        "\n",
        "bmr = bmr_calc(gender,height,age,weight)\n",
        "print(\"Basal Metabolic Rate is: \" + str(bmr))"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Are you male or female; input m for male and f for female\n",
            "f\n",
            "Input height in inches\n",
            "50\n",
            "Input age in years\n",
            "21\n",
            "Input weight in lbs\n",
            "120\n",
            "Basal Metabolic Rate is: 1308.2307\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "aTA9-KflDduW"
      },
      "source": [
        "## BMR Adjustment for activity level\n",
        "\n",
        "We now adjust BMR by TDEE; essentially adjusting per our exercise level\n",
        "\n",
        "Encode by inputting Sedentary, Lightly Active, etc as outlined below. it is case sensitive.\n",
        "\n",
        "*   Sedentary (desk job, little excercise)\n",
        "*   Lightly Active (light excercise/sports 1-3 days a week)\n",
        "*   Moderately Active (moderate excercise/sports 6-7 days a week)\n",
        "*   Very Active (hard excercise every day, or 2x a day excercise)\n",
        "*   Extra Active (hard exercise 2+ times a day, or marathon training)"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "U-kt7xpVFMAs",
        "outputId": "2e7e105b-aafa-435d-8aad-c276d251bd56",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "source": [
        "print(\"How active are you? Input activity rate.\")\n",
        "activity_rate = input()\n",
        "#Multipliers can be found in the K-State article\n",
        "if activity_rate == 'Sedentary':\n",
        "  adj_bmr = bmr * 1.2\n",
        "  print(\"Adjusted BMR is now: \" + str(adj_bmr))\n",
        "elif activity_rate == 'Lightly Active':\n",
        "  adj_bmr = bmr * 1.375\n",
        "  print(\"Adjusted BMR is now: \" + str(adj_bmr))\n",
        "elif activity_rate == 'Moderately Active':\n",
        "  adj_bmr = bmr * 1.55\n",
        "  print(\"Adjusted BMR is now: \" + str(adj_bmr))\n",
        "elif activity_rate == 'Very Active':\n",
        "  adj_bmr = bmr * 1.725\n",
        "  print(\"Adjusted BMR is now: \" + str(adj_bmr))\n",
        "elif activity_rate == 'Extra Active':\n",
        "  adj_bmr = bmr * 1.9\n",
        "  print(\"Adjusted BMR is now: \" + str(adj_bmr))\n",
        "else:\n",
        "  print('Wrong input. Try again.')"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "How active are you? Input activity rate.\n",
            "Lightly Active\n",
            "Adjusted BMR is now: 1798.8172125\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "X07vCLz3DhFi"
      },
      "source": [
        "## Other Constraint Calculations\n",
        "\n",
        "Here are the other constraints that require calculations due to it being dependant on changing variables like weight or BMR.\n",
        "\n",
        "We adjusted the Healthline article suggestion for protein by removing the \"1 gram per lb of bodyweight\" limit and instead only have the requirement to get >= .7 grams of protein per lb of body weight as protein is the most satiating thing to ingest, which aids weightloss.\n",
        "\n",
        "https://academic.oup.com/ajcn/article/87/5/1558S/4650426"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "1ayXWoVGFVJC",
        "outputId": "6eada549-e3b0-4fe9-99b1-16062328197b",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "source": [
        "#calculating out the bounds \n",
        "\n",
        "#calories lowered by ~12% to achieve weightloss\n",
        "adj_bmr = adj_bmr * .875\n",
        "\n",
        "#protein has to be this many grams per lb of body weight\n",
        "protein_lb = weight * .7\n",
        "\n",
        "#sugar has to be less than 10% of your daily calories\n",
        "#sodium has to be less than 2300 mg\n",
        "sugar_cal_b = bmr * .1\n",
        "sodium_b = 2300\n",
        "\n",
        "\n",
        "print(\"Protein lower bound: \" + str(protein_lb))\n",
        "print(\"Sugar calorie  bound is: \" + str(sugar_cal_b))\n",
        "print(\"Sodium lower bound is: \" + str(sodium_b))\n",
        "print(\"Adjusted BMR for Weightloss is: \" + str(adj_bmr))"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Protein lower bound: 84.0\n",
            "Sugar calorie  bound is: 130.82307\n",
            "Sodium lower bound is: 2300\n",
            "Adjusted BMR for Weightloss is: 1373.642235\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "6ad1si7kHQbz"
      },
      "source": [
        "# Model 1\n",
        "This contains our basic model which has the protein, sugar, calorie, and sodium constraints."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "rMOIc6iGH9A3"
      },
      "source": [
        "from pyomo.environ import *\n",
        "\n",
        "SOLVER = 'glpk'\n",
        "EXECUTABLE = '/usr/bin/glpsol'\n",
        "\n",
        "#initialize model\n",
        "model = ConcreteModel()\n",
        "\n",
        "#loop through and create variables\n",
        "for x in df.values:\n",
        "  name = x[8]\n",
        "  model.add_component(name, Var(within=NonNegativeReals))\n",
        "\n",
        "model.cal_const = Constraint(expr = model.zero*320 + \n",
        "model.one*270 + \n",
        "model.two*240 + \n",
        "model.three*250 + \n",
        "model.four*240 + \n",
        "model.five*250 + \n",
        "model.six*240 + \n",
        "model.seven*300 + \n",
        "model.eight*350 + \n",
        "model.nine*340 + \n",
        "model.ten*370 + \n",
        "model.eleven*460 + \n",
        "model.twelve*520 + \n",
        "model.thirteen*460 + \n",
        "model.fourteen*430 + \n",
        "model.fifteen*440 + \n",
        "model.sixteen*430 + \n",
        "model.seventeen*440 + \n",
        "model.eighteen*540 + \n",
        "model.nineteen*430 + \n",
        "model.twenty*440 + \n",
        "model.twentyone*490 + \n",
        "model.twentytwo*550 + \n",
        "model.twentythree*600 + \n",
        "model.twentyfour*370 + \n",
        "model.twentyfive*380 + \n",
        "model.twentysix*370 + \n",
        "model.twentyseven*380 + \n",
        "model.twentyeight*510 + \n",
        "model.twentynine*370 + \n",
        "model.thirty*380 + \n",
        "model.thirtyone*430 + \n",
        "model.thirtytwo*400 + \n",
        "model.thirtythree*450 + \n",
        "model.thirtyfour*600 + \n",
        "model.thirtyfive*540 + \n",
        "model.thirtysix*510 + \n",
        "model.thirtyseven*520 + \n",
        "model.thirtyeight*510 + \n",
        "model.thirtynine*520 + \n",
        "model.forty*620 + \n",
        "model.fortyone*510 + \n",
        "model.fortytwo*520 + \n",
        "model.fortythree*570 + \n",
        "model.fortyfour*620 + \n",
        "model.fortyfive*680 + \n",
        "model.fortysix*510 + \n",
        "model.fortyseven*610 + \n",
        "model.fortyeight*320 + \n",
        "model.fortynine*370 + \n",
        "model.fifty*640 + \n",
        "model.fiftyone*390 + \n",
        "model.fiftytwo*300 + \n",
        "model.fiftythree*470 + \n",
        "model.fiftyfour*350 + \n",
        "model.fiftyfive*570 + \n",
        "model.fiftysix*380 + \n",
        "model.fiftyseven*640 + \n",
        "model.fiftyeight*380 + \n",
        "model.fiftynine*400 + \n",
        "model.sixty*590 + \n",
        "model.sixtyone*510 + \n",
        "model.sixtytwo*350 + \n",
        "model.sixtythree*450 + \n",
        "model.sixtyfour*710 + \n",
        "model.sixtyfive*250 + \n",
        "model.sixtysix*320 + \n",
        "model.sixtyseven*280 + \n",
        "model.sixtyeight*470 + \n",
        "model.sixtynine*490 + \n",
        "model.seventy*410 + \n",
        "model.seventyone*290 + \n",
        "model.seventytwo*360 + \n",
        "model.seventythree*540 + \n",
        "model.seventyfour*1070 + \n",
        "model.seventyfive*150 + \n",
        "model.seventysix*60 + \n",
        "model.seventyseven*25 + \n",
        "model.seventyeight*300 + \n",
        "model.seventynine*430 + \n",
        "model.eighty*790 + \n",
        "model.eightyone*540 + \n",
        "model.eightytwo*370 + \n",
        "model.eightythree*210 + \n",
        "model.eightyfour*420 + \n",
        "model.eightyfive*490 + \n",
        "model.eightysix*590 + \n",
        "model.eightyseven*470 + \n",
        "model.eightyeight*370 + \n",
        "model.eightynine*330 + \n",
        "model.ninety*430 + \n",
        "model.ninetyone*390 + \n",
        "model.ninetytwo*490 + \n",
        "model.ninetythree*440 + \n",
        "model.ninetyfour*540 + \n",
        "model.ninetyfive*520 + \n",
        "model.ninetysix*620 + \n",
        "model.ninetyseven*300 + \n",
        "model.ninetyeight*400 + \n",
        "model.ninetynine*600 + \n",
        "model.onehundred*700 + \n",
        "model.onehundredone*640 + \n",
        "model.onehundredtwo*260 + \n",
        "model.onehundredthree*320 + \n",
        "model.onehundredfour*350 + \n",
        "model.onehundredfive*290 + \n",
        "model.onehundredsix*490 + \n",
        "model.onehundredseven*120 + \n",
        "model.onehundredeight*140 + \n",
        "model.onehundrednine*0 + \n",
        "model.onehundredten*0 + \n",
        "model.onehundredeleven*130 + \n",
        "model.onehundredtwelve*110 + \n",
        "model.onehundredthirteen*160 + \n",
        "model.onehundredfourteen*200 + \n",
        "model.onehundredfifteen*150 + \n",
        "model.onehundredsixteen*0 + \n",
        "model.onehundredseventeen*170 + \n",
        "model.onehundredeighteen*140 + \n",
        "model.onehundrednineteen*160 + \n",
        "model.onehundredtwenty*140 + \n",
        "model.onehundredtwentyone*140 + \n",
        "model.onehundredtwentytwo*150 + \n",
        "model.onehundredtwentythree*200 + \n",
        "model.onehundredtwentyfour*0 + \n",
        "model.onehundredtwentyfive*230 + \n",
        "model.onehundredtwentysix*190 + \n",
        "model.onehundredtwentyseven*210 + \n",
        "model.onehundredtwentyeight*180 + \n",
        "model.onehundredtwentynine*180 + \n",
        "model.onehundredthirty*200 + \n",
        "model.onehundredthirtyone*250 + \n",
        "model.onehundredthirtytwo*0 + \n",
        "model.onehundredthirtythree*280 + \n",
        "model.onehundredthirtyfour*230 + \n",
        "model.onehundredthirtyfive*270 + \n",
        "model.onehundredthirtysix*230 + \n",
        "model.onehundredthirtyseven*230 + \n",
        "model.onehundredthirtyeight*250 + \n",
        "model.onehundredthirtynine*320 + \n",
        "model.onehundredforty*310 + \n",
        "model.onehundredfortyone*370 + \n",
        "model.onehundredfortytwo*0 + \n",
        "model.onehundredfortythree*420 + \n",
        "model.onehundredfortyfour*350 + \n",
        "model.onehundredfortyfive*400 + \n",
        "model.onehundredfortysix*340 + \n",
        "model.onehundredfortyseven*340 + \n",
        "model.onehundredfortyeight*375 + \n",
        "model.onehundredfortynine*500 + \n",
        "model.onehundredfifty*0 + \n",
        "model.onehundredfiftyone*570 + \n",
        "model.onehundredfiftytwo*470 + \n",
        "model.onehundredfiftythree*530 + \n",
        "model.onehundredfiftyfour*450 + \n",
        "model.onehundredfiftyfive*450 + \n",
        "model.onehundredfiftysix*490 + \n",
        "model.onehundredfiftyseven*400 + \n",
        "model.onehundredfiftyeight*390 + \n",
        "model.onehundredfiftynine*370 + \n",
        "model.onehundredsixty*400 + \n",
        "model.onehundredsixtyone*370 + \n",
        "model.onehundredsixtytwo*250 + \n",
        "model.onehundredsixtythree*450 + \n",
        "model.onehundredsixtyfour*160 + \n",
        "model.onehundredsixtyfive*360 + \n",
        "model.onehundredsixtysix*820 + \n",
        "model.onehundredsixtyseven*650 + \n",
        "model.onehundredsixtyeight*650 + \n",
        "model.onehundredsixtynine*650 + \n",
        "model.onehundredseventy*630 + \n",
        "model.onehundredseventyone*630 + \n",
        "model.onehundredseventytwo*620 + \n",
        "model.onehundredseventythree*630 + \n",
        "model.onehundredseventyfour*940 + \n",
        "model.onehundredseventyfive*440 + \n",
        "model.onehundredseventysix*200 + \n",
        "model.onehundredseventyseven*180 + \n",
        "model.onehundredseventyeight*170 + \n",
        "model.onehundredseventynine*200  == adj_bmr)\n",
        "\n",
        "model.proteinlb = Constraint(expr = model.zero*15 + \n",
        "model.one*12 + \n",
        "model.two*10 + \n",
        "model.three*10 + \n",
        "model.four*10 + \n",
        "model.five*10 + \n",
        "model.six*10 + \n",
        "model.seven*11 + \n",
        "model.eight*17 + \n",
        "model.nine*12 + \n",
        "model.ten*12 + \n",
        "model.eleven*19 + \n",
        "model.twelve*22 + \n",
        "model.thirteen*19 + \n",
        "model.fourteen*17 + \n",
        "model.fifteen*17 + \n",
        "model.sixteen*17 + \n",
        "model.seventeen*17 + \n",
        "model.eighteen*22 + \n",
        "model.nineteen*17 + \n",
        "model.twenty*17 + \n",
        "model.twentyone*18 + \n",
        "model.twentytwo*25 + \n",
        "model.twentythree*23 + \n",
        "model.twentyfour*13 + \n",
        "model.twentyfive*13 + \n",
        "model.twentysix*13 + \n",
        "model.twentyseven*13 + \n",
        "model.twentyeight*17 + \n",
        "model.twentynine*13 + \n",
        "model.thirty*13 + \n",
        "model.thirtyone*14 + \n",
        "model.thirtytwo*15 + \n",
        "model.thirtythree*18 + \n",
        "model.thirtyfour*21 + \n",
        "model.thirtyfive*18 + \n",
        "model.thirtysix*16 + \n",
        "model.thirtyseven*16 + \n",
        "model.thirtyeight*16 + \n",
        "model.thirtynine*16 + \n",
        "model.forty*21 + \n",
        "model.fortyone*16 + \n",
        "model.fortytwo*16 + \n",
        "model.fortythree*17 + \n",
        "model.fortyfour*23 + \n",
        "model.fortyfive*22 + \n",
        "model.fortysix*34 + \n",
        "model.fortyseven*39 + \n",
        "model.fortyeight*21 + \n",
        "model.fortynine*24 + \n",
        "model.fifty*43 + \n",
        "model.fiftyone*27 + \n",
        "model.fiftytwo*19 + \n",
        "model.fiftythree*33 + \n",
        "model.fiftyfour*22 + \n",
        "model.fiftyfive*38 + \n",
        "model.fiftysix*24 + \n",
        "model.fiftyseven*42 + \n",
        "model.fiftyeight*22 + \n",
        "model.fiftynine*23 + \n",
        "model.sixty*29 + \n",
        "model.sixtyone*24 + \n",
        "model.sixtytwo*11 + \n",
        "model.sixtythree*12 + \n",
        "model.sixtyfour*16 + \n",
        "model.sixtyfive*7 + \n",
        "model.sixtysix*8 + \n",
        "model.sixtyseven*12 + \n",
        "model.sixtyeight*25 + \n",
        "model.sixtynine*22 + \n",
        "model.seventy*12 + \n",
        "model.seventyone*16 + \n",
        "model.seventytwo*23 + \n",
        "model.seventythree*34 + \n",
        "model.seventyfour*69 + \n",
        "model.seventyfive*0 + \n",
        "model.seventysix*0 + \n",
        "model.seventyseven*0 + \n",
        "model.seventyeight*2 + \n",
        "model.seventynine*3 + \n",
        "model.eighty*6 + \n",
        "model.eightyone*12 + \n",
        "model.eightytwo*8 + \n",
        "model.eightythree*6 + \n",
        "model.eightyfour*13 + \n",
        "model.eightyfive*24 + \n",
        "model.eightysix*25 + \n",
        "model.eightyseven*25 + \n",
        "model.eightyeight*17 + \n",
        "model.eightynine*10 + \n",
        "model.ninety*11 + \n",
        "model.ninetyone*16 + \n",
        "model.ninetytwo*17 + \n",
        "model.ninetythree*18 + \n",
        "model.ninetyfour*19 + \n",
        "model.ninetyfive*19 + \n",
        "model.ninetysix*20 + \n",
        "model.ninetyseven*16 + \n",
        "model.ninetyeight*17 + \n",
        "model.ninetynine*20 + \n",
        "model.onehundred*21 + \n",
        "model.onehundredone*24 + \n",
        "model.onehundredtwo*6 + \n",
        "model.onehundredthree*12 + \n",
        "model.onehundredfour*8 + \n",
        "model.onehundredfive*1 + \n",
        "model.onehundredsix*6 + \n",
        "model.onehundredseven*0 + \n",
        "model.onehundredeight*0 + \n",
        "model.onehundrednine*0 + \n",
        "model.onehundredten*0 + \n",
        "model.onehundredeleven*10 + \n",
        "model.onehundredtwelve*9 + \n",
        "model.onehundredthirteen*8 + \n",
        "model.onehundredfourteen*11 + \n",
        "model.onehundredfifteen*0 + \n",
        "model.onehundredsixteen*0 + \n",
        "model.onehundredseventeen*0 + \n",
        "model.onehundredeighteen*0 + \n",
        "model.onehundrednineteen*0 + \n",
        "model.onehundredtwenty*0 + \n",
        "model.onehundredtwentyone*0 + \n",
        "model.onehundredtwentytwo*0 + \n",
        "model.onehundredtwentythree*0 + \n",
        "model.onehundredtwentyfour*0 + \n",
        "model.onehundredtwentyfive*0 + \n",
        "model.onehundredtwentysix*0 + \n",
        "model.onehundredtwentyseven*0 + \n",
        "model.onehundredtwentyeight*0 + \n",
        "model.onehundredtwentynine*0 + \n",
        "model.onehundredthirty*0 + \n",
        "model.onehundredthirtyone*0 + \n",
        "model.onehundredthirtytwo*0 + \n",
        "model.onehundredthirtythree*0 + \n",
        "model.onehundredthirtyfour*0 + \n",
        "model.onehundredthirtyfive*0 + \n",
        "model.onehundredthirtysix*0 + \n",
        "model.onehundredthirtyseven*0 + \n",
        "model.onehundredthirtyeight*0 + \n",
        "model.onehundredthirtynine*0 + \n",
        "model.onehundredforty*0 + \n",
        "model.onehundredfortyone*0 + \n",
        "model.onehundredfortytwo*0 + \n",
        "model.onehundredfortythree*0 + \n",
        "model.onehundredfortyfour*0 + \n",
        "model.onehundredfortyfive*0 + \n",
        "model.onehundredfortysix*0 + \n",
        "model.onehundredfortyseven*0 + \n",
        "model.onehundredfortyeight*0 + \n",
        "model.onehundredfortynine*0 + \n",
        "model.onehundredfifty*0 + \n",
        "model.onehundredfiftyone*0 + \n",
        "model.onehundredfiftytwo*0 + \n",
        "model.onehundredfiftythree*0 + \n",
        "model.onehundredfiftyfour*0 + \n",
        "model.onehundredfiftyfive*0 + \n",
        "model.onehundredfiftysix*0 + \n",
        "model.onehundredfiftyseven*7 + \n",
        "model.onehundredfiftyeight*7 + \n",
        "model.onehundredfiftynine*7 + \n",
        "model.onehundredsixty*7 + \n",
        "model.onehundredsixtyone*7 + \n",
        "model.onehundredsixtytwo*5 + \n",
        "model.onehundredsixtythree*6 + \n",
        "model.onehundredsixtyfour*3 + \n",
        "model.onehundredsixtyfive*4 + \n",
        "model.onehundredsixtysix*13 + \n",
        "model.onehundredsixtyseven*13 + \n",
        "model.onehundredsixtyeight*13 + \n",
        "model.onehundredsixtynine*13 + \n",
        "model.onehundredseventy*13 + \n",
        "model.onehundredseventyone*13 + \n",
        "model.onehundredseventytwo*13 + \n",
        "model.onehundredseventythree*14 + \n",
        "model.onehundredseventyfour*14 + \n",
        "model.onehundredseventyfive*7 + \n",
        "model.onehundredseventysix*3 + \n",
        "model.onehundredseventyseven*3 + \n",
        "model.onehundredseventyeight*3 + \n",
        "model.onehundredseventynine*3 >= protein_lb)\n",
        "\n",
        "model.sugar = Constraint(expr = model.zero*4 + \n",
        "model.one*4 + \n",
        "model.two*4 + \n",
        "model.three*6 + \n",
        "model.four*5 + \n",
        "model.five*6 + \n",
        "model.six*4 + \n",
        "model.seven*14 + \n",
        "model.eight*5 + \n",
        "model.nine*4 + \n",
        "model.ten*6 + \n",
        "model.eleven*4 + \n",
        "model.twelve*5 + \n",
        "model.thirteen*4 + \n",
        "model.fourteen*4 + \n",
        "model.fifteen*6 + \n",
        "model.sixteen*4 + \n",
        "model.seventeen*6 + \n",
        "model.eighteen*9 + \n",
        "model.nineteen*4 + \n",
        "model.twenty*7 + \n",
        "model.twentyone*14 + \n",
        "model.twentytwo*5 + \n",
        "model.twentythree*5 + \n",
        "model.twentyfour*7 + \n",
        "model.twentyfive*9 + \n",
        "model.twentysix*8 + \n",
        "model.twentyseven*9 + \n",
        "model.twentyeight*12 + \n",
        "model.twentynine*7 + \n",
        "model.thirty*10 + \n",
        "model.thirtyone*17 + \n",
        "model.thirtytwo*7 + \n",
        "model.thirtythree*7 + \n",
        "model.thirtyfour*9 + \n",
        "model.thirtyfive*8 + \n",
        "model.thirtysix*8 + \n",
        "model.thirtyseven*10 + \n",
        "model.thirtyeight*8 + \n",
        "model.thirtynine*10 + \n",
        "model.forty*13 + \n",
        "model.fortyone*8 + \n",
        "model.fortytwo*11 + \n",
        "model.fortythree*18 + \n",
        "model.fortyfour*9 + \n",
        "model.fortyfive*9 + \n",
        "model.fortysix*6 + \n",
        "model.fortyseven*6 + \n",
        "model.fortyeight*3 + \n",
        "model.fortynine*3 + \n",
        "model.fifty*4 + \n",
        "model.fiftyone*3 + \n",
        "model.fiftytwo*5 + \n",
        "model.fiftythree*5 + \n",
        "model.fiftyfour*5 + \n",
        "model.fiftyfive*5 + \n",
        "model.fiftysix*5 + \n",
        "model.fiftyseven*5 + \n",
        "model.fiftyeight*6 + \n",
        "model.fiftynine*4 + \n",
        "model.sixty*6 + \n",
        "model.sixtyone*3 + \n",
        "model.sixtytwo*5 + \n",
        "model.sixtythree*1 + \n",
        "model.sixtyfour*9 + \n",
        "model.sixtyfive*1 + \n",
        "model.sixtysix*1 + \n",
        "model.sixtyseven*6 + \n",
        "model.sixtyeight*2 + \n",
        "model.sixtynine*4 + \n",
        "model.seventy*1 + \n",
        "model.seventyone*2 + \n",
        "model.seventytwo*1 + \n",
        "model.seventythree*2 + \n",
        "model.seventyfour*4 + \n",
        "model.seventyfive*1 + \n",
        "model.seventysix*12 + \n",
        "model.seventyseven*2 + \n",
        "model.seventyeight*0 + \n",
        "model.seventynine*0 + \n",
        "model.eighty*18 + \n",
        "model.eightyone*1 + \n",
        "model.eightytwo*1 + \n",
        "model.eightythree*3 + \n",
        "model.eightyfour*7 + \n",
        "model.eightyfive*3 + \n",
        "model.eightysix*3 + \n",
        "model.eightyseven*2 + \n",
        "model.eightyeight*1 + \n",
        "model.eightynine*4 + \n",
        "model.ninety*4 + \n",
        "model.ninetyone*4 + \n",
        "model.ninetytwo*4 + \n",
        "model.ninetythree*4 + \n",
        "model.ninetyfour*4 + \n",
        "model.ninetyfive*8 + \n",
        "model.ninetysix*8 + \n",
        "model.ninetyseven*1 + \n",
        "model.ninetyeight*1 + \n",
        "model.ninetynine*1 + \n",
        "model.onehundred*1 + \n",
        "model.onehundredone*4 + \n",
        "model.onehundredtwo*4 + \n",
        "model.onehundredthree*4 + \n",
        "model.onehundredfour*4 + \n",
        "model.onehundredfive*0 + \n",
        "model.onehundredsix*11 + \n",
        "model.onehundredseven*21 + \n",
        "model.onehundredeight*28 + \n",
        "model.onehundrednine*0 + \n",
        "model.onehundredten*0 + \n",
        "model.onehundredeleven*13 + \n",
        "model.onehundredtwelve*12 + \n",
        "model.onehundredthirteen*25 + \n",
        "model.onehundredfourteen*33 + \n",
        "model.onehundredfifteen*41 + \n",
        "model.onehundredsixteen*0 + \n",
        "model.onehundredseventeen*46 + \n",
        "model.onehundredeighteen*39 + \n",
        "model.onehundrednineteen*43 + \n",
        "model.onehundredtwenty*39 + \n",
        "model.onehundredtwentyone*35 + \n",
        "model.onehundredtwentytwo*41 + \n",
        "model.onehundredtwentythree*55 + \n",
        "model.onehundredtwentyfour*0 + \n",
        "model.onehundredtwentyfive*61 + \n",
        "model.onehundredtwentysix*52 + \n",
        "model.onehundredtwentyseven*57 + \n",
        "model.onehundredtwentyeight*52 + \n",
        "model.onehundredtwentynine*45 + \n",
        "model.onehundredthirty*54 + \n",
        "model.onehundredthirtyone*68 + \n",
        "model.onehundredthirtytwo*0 + \n",
        "model.onehundredthirtythree*77 + \n",
        "model.onehundredthirtyfour*65 + \n",
        "model.onehundredthirtyfive*72 + \n",
        "model.onehundredthirtysix*65 + \n",
        "model.onehundredthirtyseven*58 + \n",
        "model.onehundredthirtyeight*68 + \n",
        "model.onehundredthirtynine*84 + \n",
        "model.onehundredforty*81 + \n",
        "model.onehundredfortyone*103 + \n",
        "model.onehundredfortytwo*0 + \n",
        "model.onehundredfortythree*115 + \n",
        "model.onehundredfortyfour*97 + \n",
        "model.onehundredfortyfive*107 + \n",
        "model.onehundredfortysix*97 + \n",
        "model.onehundredfortyseven*86 + \n",
        "model.onehundredfortyeight*101 + \n",
        "model.onehundredfortynine*137 + \n",
        "model.onehundredfifty*0 + \n",
        "model.onehundredfiftyone*153 + \n",
        "model.onehundredfiftytwo*130 + \n",
        "model.onehundredfiftythree*143 + \n",
        "model.onehundredfiftyfour*130 + \n",
        "model.onehundredfiftyfive*115 + \n",
        "model.onehundredfiftysix*133 + \n",
        "model.onehundredfiftyseven*50 + \n",
        "model.onehundredfiftyeight*51 + \n",
        "model.onehundredfiftynine*48 + \n",
        "model.onehundredsixty*53 + \n",
        "model.onehundredsixtyone*49 + \n",
        "model.onehundredsixtytwo*30 + \n",
        "model.onehundredsixtythree*37 + \n",
        "model.onehundredsixtyfour*18 + \n",
        "model.onehundredsixtyfive*25 + \n",
        "model.onehundredsixtysix*122 + \n",
        "model.onehundredsixtyseven*91 + \n",
        "model.onehundredsixtyeight*91 + \n",
        "model.onehundredsixtynine*92 + \n",
        "model.onehundredseventy*76 + \n",
        "model.onehundredseventyone*80 + \n",
        "model.onehundredseventytwo*78 + \n",
        "model.onehundredseventythree*78 + \n",
        "model.onehundredseventyfour*87 + \n",
        "model.onehundredseventyfive*73 + \n",
        "model.onehundredseventysix*26 + \n",
        "model.onehundredseventyseven*28 + \n",
        "model.onehundredseventyeight*25 + \n",
        "model.onehundredseventynine*30 <= sugar_cal_b)\n",
        "\n",
        "model.sodium = Constraint(expr = model.zero*1410 + \n",
        "model.one*1160 + \n",
        "model.two*810 + \n",
        "model.three*870 + \n",
        "model.four*1040 + \n",
        "model.five*1230 + \n",
        "model.six*760 + \n",
        "model.seven*2060 + \n",
        "model.eight*1670 + \n",
        "model.nine*880 + \n",
        "model.ten*970 + \n",
        "model.eleven*1720 + \n",
        "model.twelve*1440 + \n",
        "model.thirteen*1350 + \n",
        "model.fourteen*1000 + \n",
        "model.fifteen*1060 + \n",
        "model.sixteen*1230 + \n",
        "model.seventeen*1420 + \n",
        "model.eighteen*1310 + \n",
        "model.nineteen*950 + \n",
        "model.twenty*1100 + \n",
        "model.twentyone*2250 + \n",
        "model.twentytwo*1720 + \n",
        "model.twentythree*1800 + \n",
        "model.twentyfour*880 + \n",
        "model.twentyfive*930 + \n",
        "model.twentysix*1100 + \n",
        "model.twentyseven*1300 + \n",
        "model.twentyeight*1170 + \n",
        "model.twentynine*830 + \n",
        "model.thirty*970 + \n",
        "model.thirtyone*2120 + \n",
        "model.thirtytwo*1220 + \n",
        "model.thirtythree*1480 + \n",
        "model.thirtyfour*1420 + \n",
        "model.thirtyfive*1330 + \n",
        "model.thirtysix*990 + \n",
        "model.thirtyseven*1040 + \n",
        "model.thirtyeight*1210 + \n",
        "model.thirtynine*1410 + \n",
        "model.forty*1300 + \n",
        "model.fortyone*940 + \n",
        "model.fortytwo*1080 + \n",
        "model.fortythree*2230 + \n",
        "model.fortyfour*1850 + \n",
        "model.fortyfive*1780 + \n",
        "model.fortysix*870 + \n",
        "model.fortyseven*1380 + \n",
        "model.fortyeight*870 + \n",
        "model.fortynine*1130 + \n",
        "model.fifty*1940 + \n",
        "model.fiftyone*980 + \n",
        "model.fiftytwo*650 + \n",
        "model.fiftythree*810 + \n",
        "model.fiftyfour*910 + \n",
        "model.fiftyfive*1320 + \n",
        "model.fiftysix*1020 + \n",
        "model.fiftyseven*1550 + \n",
        "model.fiftyeight*970 + \n",
        "model.fiftynine*1480 + \n",
        "model.sixty*1810 + \n",
        "model.sixtyone*1400 + \n",
        "model.sixtytwo*640 + \n",
        "model.sixtythree*860 + \n",
        "model.sixtyfour*1820 + \n",
        "model.sixtyfive*490 + \n",
        "model.sixtysix*540 + \n",
        "model.sixtyseven*1180 + \n",
        "model.sixtyeight*1880 + \n",
        "model.sixtynine*1870 + \n",
        "model.seventy*1200 + \n",
        "model.seventyone*690 + \n",
        "model.seventytwo*1100 + \n",
        "model.seventythree*1640 + \n",
        "model.seventyfour*3290 + \n",
        "model.seventyfive*140 + \n",
        "model.seventysix*220 + \n",
        "model.seventyseven*1590 + \n",
        "model.seventyeight*400 + \n",
        "model.seventynine*630 + \n",
        "model.eighty*3600 + \n",
        "model.eightyone*1380 + \n",
        "model.eightytwo*800 + \n",
        "model.eightythree*670 + \n",
        "model.eightyfour*1340 + \n",
        "model.eightyfive*1380 + \n",
        "model.eightysix*1500 + \n",
        "model.eightyseven*1720 + \n",
        "model.eightyeight*1180 + \n",
        "model.eightynine*1120 + \n",
        "model.ninety*1240 + \n",
        "model.ninetyone*1270 + \n",
        "model.ninetytwo*1390 + \n",
        "model.ninetythree*1520 + \n",
        "model.ninetyfour*1640 + \n",
        "model.ninetyfive*990 + \n",
        "model.ninetysix*1110 + \n",
        "model.ninetyseven*830 + \n",
        "model.ninetyeight*950 + \n",
        "model.ninetynine*960 + \n",
        "model.onehundred*1080 + \n",
        "model.onehundredone*1820 + \n",
        "model.onehundredtwo*890 + \n",
        "model.onehundredthree*1040 + \n",
        "model.onehundredfour*1180 + \n",
        "model.onehundredfive*240 + \n",
        "model.onehundredsix*460 + \n",
        "model.onehundredseven*25 + \n",
        "model.onehundredeight*0 + \n",
        "model.onehundrednine*0 + \n",
        "model.onehundredten*0 + \n",
        "model.onehundredeleven*130 + \n",
        "model.onehundredtwelve*130 + \n",
        "model.onehundredthirteen*210 + \n",
        "model.onehundredfourteen*230 + \n",
        "model.onehundredfifteen*35 + \n",
        "model.onehundredsixteen*35 + \n",
        "model.onehundredseventeen*70 + \n",
        "model.onehundredeighteen*35 + \n",
        "model.onehundrednineteen*65 + \n",
        "model.onehundredtwenty*45 + \n",
        "model.onehundredtwentyone*75 + \n",
        "model.onehundredtwentytwo*160 + \n",
        "model.onehundredtwentythree*45 + \n",
        "model.onehundredtwentyfour*45 + \n",
        "model.onehundredtwentyfive*95 + \n",
        "model.onehundredtwentysix*45 + \n",
        "model.onehundredtwentyseven*85 + \n",
        "model.onehundredtwentyeight*60 + \n",
        "model.onehundredtwentynine*100 + \n",
        "model.onehundredthirty*210 + \n",
        "model.onehundredthirtyone*60 + \n",
        "model.onehundredthirtytwo*60 + \n",
        "model.onehundredthirtythree*115 + \n",
        "model.onehundredthirtyfour*60 + \n",
        "model.onehundredthirtyfive*110 + \n",
        "model.onehundredthirtysix*75 + \n",
        "model.onehundredthirtyseven*125 + \n",
        "model.onehundredthirtyeight*260 + \n",
        "model.onehundredthirtynine*250 + \n",
        "model.onehundredforty*260 + \n",
        "model.onehundredfortyone*90 + \n",
        "model.onehundredfortytwo*90 + \n",
        "model.onehundredfortythree*170 + \n",
        "model.onehundredfortyfour*85 + \n",
        "model.onehundredfortyfive*160 + \n",
        "model.onehundredfortysix*110 + \n",
        "model.onehundredfortyseven*190 + \n",
        "model.onehundredfortyeight*390 + \n",
        "model.onehundredfortynine*115 + \n",
        "model.onehundredfifty*115 + \n",
        "model.onehundredfiftyone*230 + \n",
        "model.onehundredfiftytwo*115 + \n",
        "model.onehundredfiftythree*220 + \n",
        "model.onehundredfiftyfour*150 + \n",
        "model.onehundredfiftyfive*250 + \n",
        "model.onehundredfiftysix*520 + \n",
        "model.onehundredfiftyseven*250 + \n",
        "model.onehundredfiftyeight*250 + \n",
        "model.onehundredfiftynine*220 + \n",
        "model.onehundredsixty*250 + \n",
        "model.onehundredsixtyone*230 + \n",
        "model.onehundredsixtytwo*180 + \n",
        "model.onehundredsixtythree*200 + \n",
        "model.onehundredsixtyfour*115 + \n",
        "model.onehundredsixtyfive*135 + \n",
        "model.onehundredsixtysix*340 + \n",
        "model.onehundredsixtyseven*440 + \n",
        "model.onehundredsixtyeight*480 + \n",
        "model.onehundredsixtynine*440 + \n",
        "model.onehundredseventy*410 + \n",
        "model.onehundredseventyone*420 + \n",
        "model.onehundredseventytwo*440 + \n",
        "model.onehundredseventythree*460 + \n",
        "model.onehundredseventyfour*540 + \n",
        "model.onehundredseventyfive*290 + \n",
        "model.onehundredseventysix*130 + \n",
        "model.onehundredseventyseven*135 + \n",
        "model.onehundredseventyeight*105 + \n",
        "model.onehundredseventynine*135 <= sodium_b)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "24NsRNUiIFKg"
      },
      "source": [
        "#creating objective function to minimize weight watchers points\n",
        "model.points = Objective(\n",
        "    expr = model.zero*9 + \n",
        "model.one*8 + \n",
        "model.two*7 + \n",
        "model.three*7 + \n",
        "model.four*7 + \n",
        "model.five*7 + \n",
        "model.six*7 + \n",
        "model.seven*8 + \n",
        "model.eight*10 + \n",
        "model.nine*9 + \n",
        "model.ten*10 + \n",
        "model.eleven*13 + \n",
        "model.twelve*14 + \n",
        "model.thirteen*12 + \n",
        "model.fourteen*12 + \n",
        "model.fifteen*12 + \n",
        "model.sixteen*12 + \n",
        "model.seventeen*12 + \n",
        "model.eighteen*15 + \n",
        "model.nineteen*12 + \n",
        "model.twenty*12 + \n",
        "model.twentyone*14 + \n",
        "model.twentytwo*15 + \n",
        "model.twentythree*17 + \n",
        "model.twentyfour*10 + \n",
        "model.twentyfive*11 + \n",
        "model.twentysix*10 + \n",
        "model.twentyseven*11 + \n",
        "model.twentyeight*14 + \n",
        "model.twentynine*10 + \n",
        "model.thirty*11 + \n",
        "model.thirtyone*12 + \n",
        "model.thirtytwo*11 + \n",
        "model.thirtythree*13 + \n",
        "model.thirtyfour*16 + \n",
        "model.thirtyfive*15 + \n",
        "model.thirtysix*14 + \n",
        "model.thirtyseven*14 + \n",
        "model.thirtyeight*14 + \n",
        "model.thirtynine*14 + \n",
        "model.forty*17 + \n",
        "model.fortyone*14 + \n",
        "model.fortytwo*14 + \n",
        "model.fortythree*16 + \n",
        "model.fortyfour*17 + \n",
        "model.fortyfive*19 + \n",
        "model.fortysix*15 + \n",
        "model.fortyseven*18 + \n",
        "model.fortyeight*9 + \n",
        "model.fortynine*10 + \n",
        "model.fifty*19 + \n",
        "model.fiftyone*10 + \n",
        "model.fiftytwo*8 + \n",
        "model.fiftythree*14 + \n",
        "model.fiftyfour*9 + \n",
        "model.fiftyfive*17 + \n",
        "model.fiftysix*10 + \n",
        "model.fiftyseven*19 + \n",
        "model.fiftyeight*10 + \n",
        "model.fiftynine*10 + \n",
        "model.sixty*16 + \n",
        "model.sixtyone*14 + \n",
        "model.sixtytwo*10 + \n",
        "model.sixtythree*12 + \n",
        "model.sixtyfour*20 + \n",
        "model.sixtyfive*7 + \n",
        "model.sixtysix*9 + \n",
        "model.sixtyseven*7 + \n",
        "model.sixtyeight*12 + \n",
        "model.sixtynine*14 + \n",
        "model.seventy*11 + \n",
        "model.seventyone*8 + \n",
        "model.seventytwo*10 + \n",
        "model.seventythree*14 + \n",
        "model.seventyfour*29 + \n",
        "model.seventyfive*4 + \n",
        "model.seventysix*1 + \n",
        "model.seventyseven*1 + \n",
        "model.seventyeight*9 + \n",
        "model.seventynine*12 + \n",
        "model.eighty*22 + \n",
        "model.eightyone*15 + \n",
        "model.eightytwo*11 + \n",
        "model.eightythree*6 + \n",
        "model.eightyfour*11 + \n",
        "model.eightyfive*13 + \n",
        "model.eightysix*16 + \n",
        "model.eightyseven*12 + \n",
        "model.eightyeight*10 + \n",
        "model.eightynine*9 + \n",
        "model.ninety*12 + \n",
        "model.ninetyone*11 + \n",
        "model.ninetytwo*14 + \n",
        "model.ninetythree*12 + \n",
        "model.ninetyfour*15 + \n",
        "model.ninetyfive*14 + \n",
        "model.ninetysix*17 + \n",
        "model.ninetyseven*8 + \n",
        "model.ninetyeight*11 + \n",
        "model.ninetynine*17 + \n",
        "model.onehundred*19 + \n",
        "model.onehundredone*18 + \n",
        "model.onehundredtwo*7 + \n",
        "model.onehundredthree*9 + \n",
        "model.onehundredfour*10 + \n",
        "model.onehundredfive*8 + \n",
        "model.onehundredsix*13 + \n",
        "model.onehundredseven*3 + \n",
        "model.onehundredeight*4 + \n",
        "model.onehundrednine*0 + \n",
        "model.onehundredten*0 + \n",
        "model.onehundredeleven*4 + \n",
        "model.onehundredtwelve*3 + \n",
        "model.onehundredthirteen*4 + \n",
        "model.onehundredfourteen*5 + \n",
        "model.onehundredfifteen*4 + \n",
        "model.onehundredsixteen*0 + \n",
        "model.onehundredseventeen*5 + \n",
        "model.onehundredeighteen*4 + \n",
        "model.onehundrednineteen*5 + \n",
        "model.onehundredtwenty*4 + \n",
        "model.onehundredtwentyone*4 + \n",
        "model.onehundredtwentytwo*4 + \n",
        "model.onehundredtwentythree*6 + \n",
        "model.onehundredtwentyfour*0 + \n",
        "model.onehundredtwentyfive*7 + \n",
        "model.onehundredtwentysix*6 + \n",
        "model.onehundredtwentyseven*6 + \n",
        "model.onehundredtwentyeight*6 + \n",
        "model.onehundredtwentynine*5 + \n",
        "model.onehundredthirty*6 + \n",
        "model.onehundredthirtyone*7 + \n",
        "model.onehundredthirtytwo*0 + \n",
        "model.onehundredthirtythree*8 + \n",
        "model.onehundredthirtyfour*7 + \n",
        "model.onehundredthirtyfive*8 + \n",
        "model.onehundredthirtysix*7 + \n",
        "model.onehundredthirtyseven*6 + \n",
        "model.onehundredthirtyeight*7 + \n",
        "model.onehundredthirtynine*9 + \n",
        "model.onehundredforty*9 + \n",
        "model.onehundredfortyone*11 + \n",
        "model.onehundredfortytwo*0 + \n",
        "model.onehundredfortythree*12 + \n",
        "model.onehundredfortyfour*11 + \n",
        "model.onehundredfortyfive*12 + \n",
        "model.onehundredfortysix*11 + \n",
        "model.onehundredfortyseven*9 + \n",
        "model.onehundredfortyeight*11 + \n",
        "model.onehundredfortynine*15 + \n",
        "model.onehundredfifty*0 + \n",
        "model.onehundredfiftyone*17 + \n",
        "model.onehundredfiftytwo*14 + \n",
        "model.onehundredfiftythree*16 + \n",
        "model.onehundredfiftyfour*14 + \n",
        "model.onehundredfiftyfive*12 + \n",
        "model.onehundredfiftysix*14 + \n",
        "model.onehundredfiftyseven*12 + \n",
        "model.onehundredfiftyeight*11 + \n",
        "model.onehundredfiftynine*11 + \n",
        "model.onehundredsixty*11 + \n",
        "model.onehundredsixtyone*11 + \n",
        "model.onehundredsixtytwo*7 + \n",
        "model.onehundredsixtythree*13 + \n",
        "model.onehundredsixtyfour*5 + \n",
        "model.onehundredsixtyfive*10 + \n",
        "model.onehundredsixtysix*24 + \n",
        "model.onehundredsixtyseven*19 + \n",
        "model.onehundredsixtyeight*19 + \n",
        "model.onehundredsixtynine*19 + \n",
        "model.onehundredseventy*18 + \n",
        "model.onehundredseventyone*18 + \n",
        "model.onehundredseventytwo*18 + \n",
        "model.onehundredseventythree*19 + \n",
        "model.onehundredseventyfour*28 + \n",
        "model.onehundredseventyfive*13 + \n",
        "model.onehundredseventysix*6 + \n",
        "model.onehundredseventyseven*5 + \n",
        "model.onehundredseventyeight*5 + \n",
        "model.onehundredseventynine*6, sense=minimize\n",
        "    )"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "uq3Al1pjIRR6"
      },
      "source": [
        "## Model 1 Results\n",
        "\n",
        "Here, we output the models results and the weight watchers points. It is common to NOT get a result as the model is unable to work; we have a strict sodium limit as per the CDC guidelines and the menu is high in salt. Thus, higher calorie diets typically can't work."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "vJal6AiwIH0F",
        "outputId": "f6adbbd2-f520-442a-8655-bb0f59e19ff4",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "source": [
        "#printing model results and weight watchers points\n",
        "SolverFactory(SOLVER, executable=EXECUTABLE).solve(model).write(num=1)\n",
        "print(\" \")\n",
        "print(\"**       Weight Watchers Points: \" + str(model.points()) + \"       **\")"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "# ==========================================================\n",
            "# = Solver Results                                         =\n",
            "# ==========================================================\n",
            "# ----------------------------------------------------------\n",
            "#   Problem Information\n",
            "# ----------------------------------------------------------\n",
            "Problem: \n",
            "- Name: unknown\n",
            "  Lower bound: 34.9825727668861\n",
            "  Upper bound: 34.9825727668861\n",
            "  Number of objectives: 1\n",
            "  Number of constraints: 5\n",
            "  Number of variables: 179\n",
            "  Number of nonzeros: 652\n",
            "  Sense: minimize\n",
            "# ----------------------------------------------------------\n",
            "#   Solver Information\n",
            "# ----------------------------------------------------------\n",
            "Solver: \n",
            "- Status: ok\n",
            "  Termination condition: optimal\n",
            "  Statistics: \n",
            "    Branch and bound: \n",
            "      Number of bounded subproblems: 0\n",
            "      Number of created subproblems: 0\n",
            "  Error rc: 0\n",
            "  Time: 0.013035297393798828\n",
            "# ----------------------------------------------------------\n",
            "#   Solution Information\n",
            "# ----------------------------------------------------------\n",
            "Solution: \n",
            "- number of solutions: 0\n",
            "  number of solutions displayed: 0\n",
            " \n",
            "**       Weight Watchers Points: 34.98257276688621       **\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "lRfPEUwWUrFx",
        "outputId": "037d8d28-e79e-4fb9-e334-456c5221c9db",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "source": [
        "# Save the model \n",
        "model.write(\"/content/model.lp\", io_options={'symbolic_solver_labels': True})\n",
        "\n",
        "# Generate the file \"sensit.sen\", this contains the report we want to see\n",
        "!/usr/bin/glpsol -m /content/model.lp --lp --ranges sensit.sen"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "GLPSOL: GLPK LP/MIP Solver, v4.65\n",
            "Parameter(s) specified in the command line:\n",
            " -m /content/model.lp --lp --ranges sensit.sen\n",
            "Reading problem data from '/content/model.lp'...\n",
            "5 rows, 179 columns, 652 non-zeros\n",
            "1026 lines were read\n",
            "GLPK Simplex Optimizer, v4.65\n",
            "5 rows, 179 columns, 652 non-zeros\n",
            "Preprocessing...\n",
            "4 rows, 178 columns, 651 non-zeros\n",
            "Scaling...\n",
            " A: min|aij| =  1.000e+00  max|aij| =  3.600e+03  ratio =  3.600e+03\n",
            "GM: min|aij| =  1.560e-01  max|aij| =  6.409e+00  ratio =  4.107e+01\n",
            "EQ: min|aij| =  2.435e-02  max|aij| =  1.000e+00  ratio =  4.107e+01\n",
            "Constructing initial basis...\n",
            "Size of triangular part is 4\n",
            "      0: obj =   3.863368786e+01 inf =   2.123e+00 (2)\n",
            "      2: obj =   4.085266937e+01 inf =   0.000e+00 (0)\n",
            "*     7: obj =   3.498257277e+01 inf =   0.000e+00 (0)\n",
            "OPTIMAL LP SOLUTION FOUND\n",
            "Time used:   0.0 secs\n",
            "Memory used: 0.2 Mb (201752 bytes)\n",
            "Write sensitivity analysis report to 'sensit.sen'...\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "y972qkZyUrwp",
        "outputId": "5da17387-8097-4ec9-ecb3-69a86480acbc",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "source": [
        "# Display the contents of the report: (this shows the sensitivity analysis report)\n",
        "!cat /content/sensit.sen"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "GLPK 4.65 - SENSITIVITY ANALYSIS REPORT                                                                         Page   1\n",
            "\n",
            "Problem:    \n",
            "Objective:  points = 34.98257277 (MINimum)\n",
            "\n",
            "   No. Row name     St      Activity         Slack   Lower bound       Activity      Obj coef  Obj value at Limiting\n",
            "                                          Marginal   Upper bound          range         range   break point variable\n",
            "------ ------------ -- ------------- ------------- -------------  ------------- ------------- ------------- ------------\n",
            "     1 c_e_cal_const_\n",
            "                    NS    1373.64224        .         1373.64224     1345.26973          -Inf      34.16899 onehundredsix\n",
            "                                            .02867    1373.64224     2231.61879          +Inf      59.58500 fiftyone\n",
            "\n",
            "     2 c_l_proteinlb_\n",
            "                    NL      84.00000        .           84.00000       79.99091       -.04461      34.80371 onehundredtwelve\n",
            "                                            .04461          +Inf       89.50310          +Inf      35.22808 onehundredsix\n",
            "\n",
            "     3 c_u_sugar_   NU     130.82307        .               -Inf       66.13227          -Inf      36.31528 onehundredfourteen\n",
            "                                           -.02060     130.82307      141.67645        .02060      34.75898 onehundredsix\n",
            "\n",
            "     4 c_u_sodium_  NU    2300.00000        .               -Inf     1535.53238          -Inf      36.79700 fiftyone\n",
            "                                           -.00237    2300.00000     2404.18436        .00237      34.73530 onehundredtwelve\n",
            "\n",
            "     5 c_e_ONE_VAR_CONSTANT\n",
            "                    NS       1.00000        .            1.00000         .               -Inf      34.98257 ONE_VAR_CONSTANT\n",
            "                                            .            1.00000           +Inf          +Inf      34.98257\n",
            "\n",
            "GLPK 4.65 - SENSITIVITY ANALYSIS REPORT                                                                         Page   2\n",
            "\n",
            "Problem:    \n",
            "Objective:  points = 34.98257277 (MINimum)\n",
            "\n",
            "   No. Column name  St      Activity      Obj coef   Lower bound       Activity      Obj coef  Obj value at Limiting\n",
            "                                          Marginal   Upper bound          range         range   break point variable\n",
            "------ ------------ -- ------------- ------------- -------------  ------------- ------------- ------------- ------------\n",
            "     1 eight        NL        .           10.00000        .             -.10492       6.72798      34.63927 onehundredtwelve\n",
            "                                           3.27202          +Inf         .58358          +Inf      36.89206 fiftyone\n",
            "\n",
            "     2 eighteen     NL        .           15.00000        .             -.27169      13.17133      34.48574 onehundredtwelve\n",
            "                                           1.82867          +Inf         .36243          +Inf      35.64535 onehundredsix\n",
            "\n",
            "     3 eighty       NL        .           22.00000        .             -.03525      14.00563      34.70076 onehundredtwelve\n",
            "                                           7.99437          +Inf         .26656          +Inf      37.11359 fiftyone\n",
            "\n",
            "     4 eightyeight  NL        .           10.00000        .             -.22527       8.54688      34.65523 onehundredtwelve\n",
            "                                           1.45312          +Inf         .94975          +Inf      36.36268 fiftyone\n",
            "\n",
            "     5 eightyfive   NL        .           13.00000        .             -.25934      11.78427      34.66729 onehundredtwelve\n",
            "                                           1.21573          +Inf         .87050          +Inf      36.04087 fiftyone\n",
            "\n",
            "     6 eightyfour   NL        .           11.00000        .             -.14347       9.29881      34.73851 onehundredtwelve\n",
            "                                           1.70119          +Inf         .82491          +Inf      36.38590 fiftyone\n",
            "\n",
            "     7 eightynine   NL        .            9.00000        .             -.16437       7.16819      34.68147 onehundredtwelve\n",
            "                                           1.83181          +Inf         .95932          +Inf      36.73986 fiftyone\n",
            "\n",
            "     8 eightyone    NL        .           15.00000        .             -.15718      12.72386      34.62481 onehundredtwelve\n",
            "                                           2.27614          +Inf         .21269          +Inf      35.46668 onehundredsix\n",
            "\n",
            "     9 eightyseven  NL        .           12.00000        .             -.14377      10.46901      34.76247 onehundredtwelve\n",
            "                                           1.53099          +Inf         .61947          +Inf      35.93097 fiftyone\n",
            "\n",
            "    10 eightysix    NL        .           16.00000        .             -.24834      14.41157      34.58810 onehundredtwelve\n",
            "                                           1.58843          +Inf         .34857          +Inf      35.53625 onehundredsix\n",
            "\n",
            "GLPK 4.65 - SENSITIVITY ANALYSIS REPORT                                                                         Page   3\n",
            "\n",
            "Problem:    \n",
            "Objective:  points = 34.98257277 (MINimum)\n",
            "\n",
            "   No. Column name  St      Activity      Obj coef   Lower bound       Activity      Obj coef  Obj value at Limiting\n",
            "                                          Marginal   Upper bound          range         range   break point variable\n",
            "------ ------------ -- ------------- ------------- -------------  ------------- ------------- ------------- ------------\n",
            "    11 eightythree  NL        .            6.00000        .             -.27936       4.63740      34.60191 onehundredtwelve\n",
            "                                           1.36260          +Inf        1.64393          +Inf      37.22259 fiftyone\n",
            "\n",
            "    12 eightytwo    NL        .           11.00000        .             -.32931       9.04727      34.33952 onehundredtwelve\n",
            "                                           1.95273          +Inf         .22199          +Inf      35.41605 onehundredsix\n",
            "\n",
            "    13 eleven       NL        .           13.00000        .             -.11565       9.87338      34.62098 onehundredtwelve\n",
            "                                           3.12662          +Inf         .60798          +Inf      36.88351 fiftyone\n",
            "\n",
            "    14 fifteen      NL        .           12.00000        .             -.32487      10.73593      34.57191 onehundredtwelve\n",
            "                                           1.26407          +Inf         .38402          +Inf      35.46801 onehundredsix\n",
            "\n",
            "    15 fifty        NL        .           19.00000        .             -.28944      15.58343      33.99368 onehundredtwelve\n",
            "                                           3.41657          +Inf         .60969          +Inf      37.06562 fiftyone\n",
            "\n",
            "    16 fiftyeight   NL        .           10.00000        .             -.71118       9.45211      34.59293 onehundredtwelve\n",
            "                                            .54789          +Inf        1.34262          +Inf      35.71817 fiftyone\n",
            "\n",
            "    17 fiftyfive    NL        .           17.00000        .           -15.22836      14.80406       1.54201 onehundredfourteen\n",
            "                                           2.19594          +Inf         .84020          +Inf      36.82759 onehundredsix\n",
            "\n",
            "    18 fiftyfour    NL        .            9.00000        .            -1.01100       8.75487      34.73475 onehundredtwelve\n",
            "                                            .24513          +Inf        1.42410          +Inf      35.33166 fiftyone\n",
            "\n",
            "    19 fiftynine    NL        .           10.00000        .             -.17288       8.90097      34.79257 onehundredtwelve\n",
            "                                           1.09903          +Inf         .72098          +Inf      35.77495 fiftyone\n",
            "\n",
            "    20 fiftyone     BS       1.36659      10.00000        .             1.44965       9.70444      34.57867 onehundredseven\n",
            "                                            .               +Inf         .53230      10.17281      35.21873 seventysix\n",
            "\n",
            "GLPK 4.65 - SENSITIVITY ANALYSIS REPORT                                                                         Page   4\n",
            "\n",
            "Problem:    \n",
            "Objective:  points = 34.98257277 (MINimum)\n",
            "\n",
            "   No. Column name  St      Activity      Obj coef   Lower bound       Activity      Obj coef  Obj value at Limiting\n",
            "                                          Marginal   Upper bound          range         range   break point variable\n",
            "------ ------------ -- ------------- ------------- -------------  ------------- ------------- ------------- ------------\n",
            "    21 fiftyseven   NL        .           19.00000        .           -46.29355      16.44386     -83.35000 onehundredtwelve\n",
            "                                           2.55614          +Inf         .88296          +Inf      37.23954 fiftyone\n",
            "\n",
            "    22 fiftysix     NL        .           10.00000        .             -.75382       9.44327      34.56290 onehundredtwelve\n",
            "                                            .55673          +Inf        1.24341          +Inf      35.67482 fiftyone\n",
            "\n",
            "    23 fiftythree   NL        .           14.00000        .            -2.88510      12.92396      31.87809 onehundredfourteen\n",
            "                                           1.07604          +Inf         .27836          +Inf      35.28210 onehundredtwelve\n",
            "\n",
            "    24 fiftytwo     NL        .            8.00000        .           -54.20733       7.80439      24.37884 onehundredfourteen\n",
            "                                            .19561          +Inf        1.01956          +Inf      35.18201 onehundredsix\n",
            "\n",
            "    25 five         NL        .            7.00000        .             -.12745       4.57191      34.67311 onehundredtwelve\n",
            "                                           2.42809          +Inf         .78264          +Inf      36.88288 fiftyone\n",
            "\n",
            "    26 forty        NL        .           17.00000        .             -.28644      15.36204      34.51340 onehundredtwelve\n",
            "                                           1.63796          +Inf         .18251          +Inf      35.28151 onehundredsix\n",
            "\n",
            "    27 fortyeight   NL        .            9.00000        .            -1.04938       7.98615      33.91866 onehundredtwelve\n",
            "                                           1.01385          +Inf        1.44908          +Inf      36.45172 fiftyone\n",
            "\n",
            "    28 fortyfive    NL        .           19.00000        .             -.13952      16.07030      34.57383 onehundredtwelve\n",
            "                                           2.92970          +Inf         .27880          +Inf      35.79939 onehundredsix\n",
            "\n",
            "    29 fortyfour    NL        .           17.00000        .             -.12455      14.22827      34.63736 onehundredtwelve\n",
            "                                           2.77173          +Inf         .62110          +Inf      36.70409 fiftyone\n",
            "\n",
            "    30 fortynine    NL        .           10.00000        .             -.42838       8.93664      34.52705 onehundredtwelve\n",
            "                                           1.06336          +Inf        1.03993          +Inf      36.08839 fiftyone\n",
            "\n",
            "GLPK 4.65 - SENSITIVITY ANALYSIS REPORT                                                                         Page   5\n",
            "\n",
            "Problem:    \n",
            "Objective:  points = 34.98257277 (MINimum)\n",
            "\n",
            "   No. Column name  St      Activity      Obj coef   Lower bound       Activity      Obj coef  Obj value at Limiting\n",
            "                                          Marginal   Upper bound          range         range   break point variable\n",
            "------ ------------ -- ------------- ------------- -------------  ------------- ------------- ------------- ------------\n",
            "    31 fortyone     NL        .           14.00000        .             -.56029      12.94218      34.38988 onehundredtwelve\n",
            "                                           1.05782          +Inf         .16347          +Inf      35.15550 onehundredsix\n",
            "\n",
            "    32 fortyseven   NL        .           18.00000        .           -18.52059      15.83266      -5.15779 onehundredfourteen\n",
            "                                           2.16734          +Inf         .55497          +Inf      36.18538 onehundredsix\n",
            "\n",
            "    33 fortysix     NL        .           15.00000        .            -2.98565      13.95256      31.85529 onehundredfourteen\n",
            "                                           1.04744          +Inf         .27456          +Inf      35.27016 onehundredsix\n",
            "\n",
            "    34 fortythree   NL        .           16.00000        .             -.07100      11.43952      34.65877 onehundredtwelve\n",
            "                                           4.56048          +Inf         .45916          +Inf      37.07655 fiftyone\n",
            "\n",
            "    35 fortytwo     NL        .           14.00000        .             -.30891      12.83484      34.62264 onehundredtwelve\n",
            "                                           1.16516          +Inf         .20121          +Inf      35.21702 onehundredsix\n",
            "\n",
            "    36 four         NL        .            7.00000        .             -.16570       4.75672      34.61086 onehundredtwelve\n",
            "                                           2.24328          +Inf         .95992          +Inf      37.13594 fiftyone\n",
            "\n",
            "    37 fourteen     NL        .           12.00000        .             -.40746      10.63279      34.42549 onehundredtwelve\n",
            "                                           1.36721          +Inf         .33783          +Inf      35.44445 onehundredsix\n",
            "\n",
            "    38 nine         NL        .            9.00000        .             -.31171       8.11380      34.70633 onehundredtwelve\n",
            "                                            .88620          +Inf         .57303          +Inf      35.49040 onehundredsix\n",
            "\n",
            "    39 nineteen     NL        .           12.00000        .             -.50651      10.75147      34.35018 onehundredtwelve\n",
            "                                           1.24853          +Inf         .29438          +Inf      35.35012 onehundredsix\n",
            "\n",
            "    40 ninety       NL        .           12.00000        .             -.15989       9.79548      34.63010 onehundredtwelve\n",
            "                                           2.20452          +Inf         .51195          +Inf      36.11117 onehundredsix\n",
            "\n",
            "GLPK 4.65 - SENSITIVITY ANALYSIS REPORT                                                                         Page   6\n",
            "\n",
            "Problem:    \n",
            "Objective:  points = 34.98257277 (MINimum)\n",
            "\n",
            "   No. Column name  St      Activity      Obj coef   Lower bound       Activity      Obj coef  Obj value at Limiting\n",
            "                                          Marginal   Upper bound          range         range   break point variable\n",
            "------ ------------ -- ------------- ------------- -------------  ------------- ------------- ------------- ------------\n",
            "    41 ninetyeight  NL        .           11.00000        .             -.49701       9.95302      34.46221 onehundredtwelve\n",
            "                                           1.04698          +Inf         .38226          +Inf      35.38279 onehundredsix\n",
            "\n",
            "    42 ninetyfive   NL        .           14.00000        .             -.69289      13.24410      34.45882 onehundredtwelve\n",
            "                                            .75590          +Inf         .18223          +Inf      35.12032 onehundredsix\n",
            "\n",
            "    43 ninetyfour   NL        .           15.00000        .             -.13711      12.35725      34.62023 onehundredtwelve\n",
            "                                           2.64275          +Inf         .69114          +Inf      36.80907 fiftyone\n",
            "\n",
            "    44 ninetynine   NL        .           17.00000        .           -10.35401      15.79812      22.53826 onehundredfourteen\n",
            "                                           1.20188          +Inf         .11071          +Inf      35.11563 onehundredsix\n",
            "\n",
            "    45 ninetyone    NL        .           11.00000        .             -.17896       8.80035      34.58893 onehundredtwelve\n",
            "                                           2.19965          +Inf         .87105          +Inf      36.89857 fiftyone\n",
            "\n",
            "    46 ninetyseven  NL        .            8.00000        .             -.54309       7.32573      34.61638 onehundredtwelve\n",
            "                                            .67427          +Inf        1.47037          +Inf      35.97400 fiftyone\n",
            "\n",
            "    47 ninetysix    NL        .           17.00000        .             -.61960      15.87139      34.28329 onehundredtwelve\n",
            "                                           1.12861          +Inf         .12850          +Inf      35.12760 onehundredsix\n",
            "\n",
            "    48 ninetythree  NL        .           12.00000        .             -.14039       9.72996      34.66387 onehundredtwelve\n",
            "                                           2.27004          +Inf         .70926          +Inf      36.59263 fiftyone\n",
            "\n",
            "    49 ninetytwo    NL        .           14.00000        .             -.17365      11.42764      34.53587 onehundredtwelve\n",
            "                                           2.57236          +Inf         .59984          +Inf      36.52559 onehundredsix\n",
            "\n",
            "    50 one          NL        .            8.00000        .             -.15606       5.44198      34.58337 onehundredtwelve\n",
            "                                           2.55802          +Inf         .86372          +Inf      37.19198 fiftyone\n",
            "\n",
            "GLPK 4.65 - SENSITIVITY ANALYSIS REPORT                                                                         Page   7\n",
            "\n",
            "Problem:    \n",
            "Objective:  points = 34.98257277 (MINimum)\n",
            "\n",
            "   No. Column name  St      Activity      Obj coef   Lower bound       Activity      Obj coef  Obj value at Limiting\n",
            "                                          Marginal   Upper bound          range         range   break point variable\n",
            "------ ------------ -- ------------- ------------- -------------  ------------- ------------- ------------- ------------\n",
            "    51 onehundred   NL        .           19.00000        .            -9.89802      18.42541      29.29526 onehundredfourteen\n",
            "                                            .57459          +Inf         .08829          +Inf      35.03330 onehundredsix\n",
            "\n",
            "    52 onehundredeight\n",
            "                    NL        .            4.00000        .            -1.48768       3.43766      34.14599 onehundredtwelve\n",
            "                                            .56234          +Inf         .42472          +Inf      35.22141 onehundredsix\n",
            "\n",
            "    53 onehundredeighteen\n",
            "                    NL        .            4.00000        .             -.59715       3.12797      34.46184 onehundredtwelve\n",
            "                                            .87203          +Inf         .96601          +Inf      35.82496 onehundredsix\n",
            "\n",
            "    54 onehundredeleven\n",
            "                    NL        .            4.00000        .           -36.15594       3.59751      20.43020 fiftyone\n",
            "                                            .40249          +Inf         .70920          +Inf      35.26802 onehundredtwelve\n",
            "\n",
            "    55 onehundredfifteen\n",
            "                    NL        .            4.00000        .             -.58051       3.37352      34.61890 onehundredtwelve\n",
            "                                            .62648          +Inf         .83101          +Inf      35.50318 onehundredsix\n",
            "\n",
            "    56 onehundredfiftyeight\n",
            "                    NL        .           11.00000        .            -1.12339       9.85149      33.69235 onehundredtwelve\n",
            "                                           1.14851          +Inf         .17888          +Inf      35.18802 onehundredsix\n",
            "\n",
            "    57 onehundredfiftyfive\n",
            "                    NL        .           12.00000        .             -.16461       9.94122      34.64367 onehundredtwelve\n",
            "                                           2.05878          +Inf         .32465          +Inf      35.65096 onehundredsix\n",
            "\n",
            "    58 onehundredfiftyfour\n",
            "                    NL        .           14.00000        .             -.16600       9.86954      34.29690 onehundredtwelve\n",
            "                                           4.13046          +Inf         .38881          +Inf      36.58855 onehundredsix\n",
            "\n",
            "    59 onehundredfiftynine\n",
            "                    NL        .           11.00000        .            -1.76438       9.41100      32.17898 onehundredtwelve\n",
            "                                           1.58900          +Inf         .18437          +Inf      35.27553 onehundredsix\n",
            "\n",
            "    60 onehundredfiftyone\n",
            "                    NL        .           17.00000        .             -.13685      12.64683      34.38685 onehundredtwelve\n",
            "                                           4.35317          +Inf         .25105          +Inf      36.07545 onehundredsix\n",
            "\n",
            "GLPK 4.65 - SENSITIVITY ANALYSIS REPORT                                                                         Page   8\n",
            "\n",
            "Problem:    \n",
            "Objective:  points = 34.98257277 (MINimum)\n",
            "\n",
            "   No. Column name  St      Activity      Obj coef   Lower bound       Activity      Obj coef  Obj value at Limiting\n",
            "                                          Marginal   Upper bound          range         range   break point variable\n",
            "------ ------------ -- ------------- ------------- -------------  ------------- ------------- ------------- ------------\n",
            "    61 onehundredfiftyseven\n",
            "                    NL        .           12.00000        .            -1.32205      10.15885      32.54848 onehundredtwelve\n",
            "                                           1.84115          +Inf         .16570          +Inf      35.28766 onehundredsix\n",
            "\n",
            "    62 onehundredfiftysix\n",
            "                    NL        .           14.00000        .             -.10566      10.07656      34.56803 onehundredtwelve\n",
            "                                           3.92344          +Inf         .48090          +Inf      36.86937 onehundredfourteen\n",
            "\n",
            "    63 onehundredfiftythree\n",
            "                    NL        .           16.00000        .             -.14497      11.72958      34.36351 onehundredtwelve\n",
            "                                           4.27042          +Inf         .27916          +Inf      36.17472 onehundredsix\n",
            "\n",
            "    64 onehundredfiftytwo\n",
            "                    NL        .           14.00000        .             -.18045      10.52611      34.35571 onehundredtwelve\n",
            "                                           3.47389          +Inf         .27912          +Inf      35.95221 onehundredsix\n",
            "\n",
            "    65 onehundredfive\n",
            "                    NL        .            8.00000        .           -13.51087       7.79072      32.15499 onehundredfourteen\n",
            "                                            .20928          +Inf         .12591          +Inf      35.00892 onehundredsix\n",
            "\n",
            "    66 onehundredforty\n",
            "                    NL        .            9.00000        .             -.19473       6.60343      34.51588 onehundredtwelve\n",
            "                                           2.39657          +Inf         .83299          +Inf      36.97889 onehundredfourteen\n",
            "\n",
            "    67 onehundredfortyeight\n",
            "                    NL        .           11.00000        .             -.14047       7.74673      34.52560 onehundredtwelve\n",
            "                                           3.25327          +Inf         .63630          +Inf      37.05264 onehundredfourteen\n",
            "\n",
            "    68 onehundredfortyfive\n",
            "                    NL        .           12.00000        .             -.19638       8.88589      34.37103 onehundredtwelve\n",
            "                                           3.11411          +Inf         .35193          +Inf      36.07853 onehundredsix\n",
            "\n",
            "    69 onehundredfortyfour\n",
            "                    NL        .           11.00000        .             -.24200       7.83617      34.21693 onehundredtwelve\n",
            "                                           3.16383          +Inf         .37652          +Inf      36.17383 onehundredsix\n",
            "\n",
            "    70 onehundredfortynine\n",
            "                    NL        .           15.00000        .             -.17403      11.24215      34.32861 onehundredtwelve\n",
            "                                           3.75785          +Inf         .25031          +Inf      35.92320 onehundredsix\n",
            "\n",
            "GLPK 4.65 - SENSITIVITY ANALYSIS REPORT                                                                         Page   9\n",
            "\n",
            "Problem:    \n",
            "Objective:  points = 34.98257277 (MINimum)\n",
            "\n",
            "   No. Column name  St      Activity      Obj coef   Lower bound       Activity      Obj coef  Obj value at Limiting\n",
            "                                          Marginal   Upper bound          range         range   break point variable\n",
            "------ ------------ -- ------------- ------------- -------------  ------------- ------------- ------------- ------------\n",
            "    71 onehundredfortyone\n",
            "                    NL        .           11.00000        .             -.22740       8.27419      34.36271 onehundredtwelve\n",
            "                                           2.72581          +Inf         .36176          +Inf      35.96866 onehundredsix\n",
            "\n",
            "    72 onehundredfortyseven\n",
            "                    NL        .            9.00000        .             -.21994       7.52682      34.65857 onehundredtwelve\n",
            "                                           1.47318          +Inf         .41676          +Inf      35.59654 onehundredsix\n",
            "\n",
            "    73 onehundredfortysix\n",
            "                    NL        .           11.00000        .             -.22495       7.49008      34.19301 onehundredtwelve\n",
            "                                           3.50992          +Inf         .47962          +Inf      36.66601 onehundredsix\n",
            "\n",
            "    74 onehundredfortythree\n",
            "                    NL        .           12.00000        .             -.18094       9.27085      34.48875 onehundredtwelve\n",
            "                                           2.72915          +Inf         .36739          +Inf      35.98525 onehundredsix\n",
            "\n",
            "    75 onehundredfour\n",
            "                    NL        .           10.00000        .             -.14261       7.51006      34.62748 onehundredtwelve\n",
            "                                           2.48994          +Inf         .90541          +Inf      37.23700 fiftyone\n",
            "\n",
            "    76 onehundredfourteen\n",
            "                    BS       3.47189       5.00000        .             3.50424       4.18558      32.15499 onehundredfive\n",
            "                                            .               +Inf       -2.21516       5.04152      35.12674 seventysix\n",
            "\n",
            "    77 onehundrednineteen\n",
            "                    NL        .            5.00000        .             -.48577       3.54786      34.27717 onehundredtwelve\n",
            "                                           1.45214          +Inf         .90138          +Inf      36.29150 onehundredsix\n",
            "\n",
            "    78 onehundredone\n",
            "                    NL        .           18.00000        .             -.14200      15.02059      34.55950 onehundredtwelve\n",
            "                                           2.97941          +Inf         .51957          +Inf      36.53058 onehundredsix\n",
            "\n",
            "    79 onehundredseven\n",
            "                    NL        .            3.00000        .            -1.57642       2.94903      34.90222 onehundredtwelve\n",
            "                                            .05097          +Inf         .48167          +Inf      35.00712 onehundredsix\n",
            "\n",
            "    80 onehundredseventeen\n",
            "                    NL        .            5.00000        .             -.45143       3.76094      34.42323 onehundredtwelve\n",
            "                                           1.23906          +Inf         .87584          +Inf      36.06779 onehundredsix\n",
            "\n",
            "GLPK 4.65 - SENSITIVITY ANALYSIS REPORT                                                                         Page  10\n",
            "\n",
            "Problem:    \n",
            "Objective:  points = 34.98257277 (MINimum)\n",
            "\n",
            "   No. Column name  St      Activity      Obj coef   Lower bound       Activity      Obj coef  Obj value at Limiting\n",
            "                                          Marginal   Upper bound          range         range   break point variable\n",
            "------ ------------ -- ------------- ------------- -------------  ------------- ------------- ------------- ------------\n",
            "    81 onehundredseventy\n",
            "                    NL        .           18.00000        .            -1.45337      16.10638      32.23044 onehundredtwelve\n",
            "                                           1.89362          +Inf         .10802          +Inf      35.18713 onehundredsix\n",
            "\n",
            "    82 onehundredseventyeight\n",
            "                    NL        .            5.00000        .            -1.88519       4.24434      33.55800 onehundredtwelve\n",
            "                                            .75566          +Inf         .44930          +Inf      35.32209 onehundredsix\n",
            "\n",
            "    83 onehundredseventyfive\n",
            "                    NL        .           13.00000        .             -.44618      10.73708      33.97290 onehundredtwelve\n",
            "                                           2.26292          +Inf         .20096          +Inf      35.43734 onehundredsix\n",
            "\n",
            "    84 onehundredseventyfour\n",
            "                    NL        .           28.00000        .            -1.93708      24.50506      28.21259 fiftyone\n",
            "                                           3.49494          +Inf         .05602          +Inf      35.17834 onehundredsix\n",
            "\n",
            "    85 onehundredseventynine\n",
            "                    NL        .            6.00000        .            -1.10883       4.93038      33.79654 onehundredtwelve\n",
            "                                           1.06962          +Inf         .39059          +Inf      35.40036 onehundredsix\n",
            "\n",
            "    86 onehundredseventyone\n",
            "                    NL        .           18.00000        .             -.97428      16.00024      33.03424 onehundredtwelve\n",
            "                                           1.99976          +Inf         .11362          +Inf      35.20978 onehundredsix\n",
            "\n",
            "    87 onehundredseventyseven\n",
            "                    NL        .            5.00000        .            -1.07874       4.39808      34.33325 onehundredtwelve\n",
            "                                            .60192          +Inf         .49029          +Inf      35.27769 onehundredsix\n",
            "\n",
            "    88 onehundredseventysix\n",
            "                    NL        .            6.00000        .            -1.63532       5.02465      33.38756 onehundredtwelve\n",
            "                                            .97535          +Inf         .33642          +Inf      35.31070 onehundredsix\n",
            "\n",
            "    89 onehundredseventythree\n",
            "                    NL        .           19.00000        .             -.96180      15.99112      32.08864 onehundredtwelve\n",
            "                                           3.00888          +Inf         .11828          +Inf      35.33846 onehundredsix\n",
            "\n",
            "    90 onehundredseventytwo\n",
            "                    NL        .           18.00000        .             -.85444      15.70722      33.02352 onehundredtwelve\n",
            "                                           2.29278          +Inf         .11822          +Inf      35.25363 onehundredsix\n",
            "\n",
            "GLPK 4.65 - SENSITIVITY ANALYSIS REPORT                                                                         Page  11\n",
            "\n",
            "Problem:    \n",
            "Objective:  points = 34.98257277 (MINimum)\n",
            "\n",
            "   No. Column name  St      Activity      Obj coef   Lower bound       Activity      Obj coef  Obj value at Limiting\n",
            "                                          Marginal   Upper bound          range         range   break point variable\n",
            "------ ------------ -- ------------- ------------- -------------  ------------- ------------- ------------- ------------\n",
            "    91 onehundredsix\n",
            "                    BS        .08971      13.00000        .              .33135      12.40338      34.92905 seventysix\n",
            "                                            .               +Inf      -48.06908      13.14495      34.99558 seventyfive\n",
            "\n",
            "    92 onehundredsixty\n",
            "                    NL        .           11.00000        .            -1.06590      10.09704      34.02011 onehundredtwelve\n",
            "                                            .90296          +Inf         .17366          +Inf      35.13938 onehundredsix\n",
            "\n",
            "    93 onehundredsixtyeight\n",
            "                    NL        .           19.00000        .             -.47115      16.20472      33.66557 onehundredtwelve\n",
            "                                           2.79528          +Inf         .12549          +Inf      35.33336 onehundredsix\n",
            "\n",
            "    94 onehundredsixtyfive\n",
            "                    NL        .           10.00000        .            -3.57888       9.66599      33.78718 fiftyone\n",
            "                                            .33401          +Inf         .11795          +Inf      35.02197 onehundredsix\n",
            "\n",
            "    95 onehundredsixtyfour\n",
            "                    NL        .            5.00000        .            -3.63015       4.07806      31.63580 onehundredtwelve\n",
            "                                            .92194          +Inf         .41139          +Inf      35.36185 onehundredsix\n",
            "\n",
            "    96 onehundredsixtynine\n",
            "                    NL        .           19.00000        .             -.55583      16.27905      33.47019 onehundredtwelve\n",
            "                                           2.72095          +Inf         .12157          +Inf      35.31335 onehundredsix\n",
            "\n",
            "    97 onehundredsixtyone\n",
            "                    NL        .           11.00000        .            -1.38247       9.36667      32.72454 onehundredtwelve\n",
            "                                           1.63333          +Inf         .19068          +Inf      35.29402 onehundredsix\n",
            "\n",
            "    98 onehundredsixtyseven\n",
            "                    NL        .           19.00000        .             -.57520      16.29965      33.42933 onehundredtwelve\n",
            "                                           2.70035          +Inf         .12022          +Inf      35.30721 onehundredsix\n",
            "\n",
            "    99 onehundredsixtysix\n",
            "                    NL        .           24.00000        .             -.70764      20.77310      32.69908 onehundredtwelve\n",
            "                                           3.22690          +Inf         .08112          +Inf      35.24434 onehundredsix\n",
            "\n",
            "   100 onehundredsixtythree\n",
            "                    NL        .           13.00000        .            -3.15412      11.93447      31.62175 fiftyone\n",
            "                                           1.06553          +Inf         .10402          +Inf      35.09341 onehundredsix\n",
            "\n",
            "GLPK 4.65 - SENSITIVITY ANALYSIS REPORT                                                                         Page  12\n",
            "\n",
            "Problem:    \n",
            "Objective:  points = 34.98257277 (MINimum)\n",
            "\n",
            "   No. Column name  St      Activity      Obj coef   Lower bound       Activity      Obj coef  Obj value at Limiting\n",
            "                                          Marginal   Upper bound          range         range   break point variable\n",
            "------ ------------ -- ------------- ------------- -------------  ------------- ------------- ------------- ------------\n",
            "   101 onehundredsixtytwo\n",
            "                    NL        .            7.00000        .            -2.13183       6.34654      33.58951 onehundredtwelve\n",
            "                                            .65346          +Inf         .28044          +Inf      35.16583 onehundredsix\n",
            "\n",
            "   102 onehundredthirteen\n",
            "                    NL        .            4.00000        .            -2.74515       3.93144      34.79437 onehundredtwelve\n",
            "                                            .06856          +Inf        3.96933          +Inf      35.25470 onehundredfourteen\n",
            "\n",
            "   103 onehundredthirty\n",
            "                    NL        .            6.00000        .             -.26149       4.12410      34.49204 onehundredtwelve\n",
            "                                           1.87590          +Inf        1.18742          +Inf      37.21005 onehundredfourteen\n",
            "\n",
            "   104 onehundredthirtyeight\n",
            "                    NL        .            7.00000        .             -.20892       5.15075      34.59623 onehundredtwelve\n",
            "                                           1.84925          +Inf         .94516          +Inf      36.73040 onehundredfourteen\n",
            "\n",
            "   105 onehundredthirtyfive\n",
            "                    NL        .            8.00000        .             -.29046       5.99786      34.40103 onehundredtwelve\n",
            "                                           2.00214          +Inf         .52050          +Inf      36.02469 onehundredsix\n",
            "\n",
            "   106 onehundredthirtyfour\n",
            "                    NL        .            7.00000        .             -.35318       5.11375      34.31639 onehundredtwelve\n",
            "                                           1.88625          +Inf         .62765          +Inf      36.16647 onehundredsix\n",
            "\n",
            "   107 onehundredthirtynine\n",
            "                    NL        .            9.00000        .             -.19426       6.85211      34.56533 onehundredtwelve\n",
            "                                           2.14789          +Inf         .73824          +Inf      36.56823 onehundredsix\n",
            "\n",
            "   108 onehundredthirtyone\n",
            "                    NL        .            7.00000        .             -.34881       5.62544      34.50311 onehundredtwelve\n",
            "                                           1.37456          +Inf         .49462          +Inf      35.66246 onehundredsix\n",
            "\n",
            "   109 onehundredthirtyseven\n",
            "                    NL        .            6.00000        .             -.32990       5.10368      34.68687 onehundredtwelve\n",
            "                                            .89632          +Inf         .59871          +Inf      35.51920 onehundredsix\n",
            "\n",
            "   110 onehundredthirtysix\n",
            "                    NL        .            7.00000        .             -.33609       5.07815      34.33666 onehundredtwelve\n",
            "                                           1.92185          +Inf         .68391          +Inf      36.29694 onehundredsix\n",
            "\n",
            "GLPK 4.65 - SENSITIVITY ANALYSIS REPORT                                                                         Page  13\n",
            "\n",
            "Problem:    \n",
            "Objective:  points = 34.98257277 (MINimum)\n",
            "\n",
            "   No. Column name  St      Activity      Obj coef   Lower bound       Activity      Obj coef  Obj value at Limiting\n",
            "                                          Marginal   Upper bound          range         range   break point variable\n",
            "------ ------------ -- ------------- ------------- -------------  ------------- ------------- ------------- ------------\n",
            "   111 onehundredthirtythree\n",
            "                    NL        .            8.00000        .             -.26878       6.16974      34.49064 onehundredtwelve\n",
            "                                           1.83026          +Inf         .56519          +Inf      36.01702 onehundredsix\n",
            "\n",
            "   112 onehundredthree\n",
            "                    NL        .            9.00000        .             -.20449       7.16055      34.60642 onehundredtwelve\n",
            "                                           1.83945          +Inf        1.06097          +Inf      36.93418 fiftyone\n",
            "\n",
            "   113 onehundredtwelve\n",
            "                    BS        .93035       3.00000        .             7.51554       2.97811      34.96220 seventysix\n",
            "                                            .               +Inf       -2.11295       3.30681      35.26802 onehundredeleven\n",
            "\n",
            "   114 onehundredtwenty\n",
            "                    NL        .            4.00000        .             -.56478       3.10424      34.47666 onehundredtwelve\n",
            "                                            .89576          +Inf        1.05507          +Inf      35.92766 onehundredsix\n",
            "\n",
            "   115 onehundredtwentyeight\n",
            "                    NL        .            6.00000        .             -.41501       3.94782      34.13090 onehundredtwelve\n",
            "                                           2.05218          +Inf         .97203          +Inf      36.97736 onehundredsix\n",
            "\n",
            "   116 onehundredtwentyfive\n",
            "                    NL        .            7.00000        .             -.34188       5.11308      34.33747 onehundredtwelve\n",
            "                                           1.88692          +Inf         .60387          +Inf      36.12203 onehundredsix\n",
            "\n",
            "   117 onehundredtwentynine\n",
            "                    NL        .            5.00000        .             -.42205       3.99709      34.55929 onehundredtwelve\n",
            "                                           1.00291          +Inf         .75516          +Inf      35.73993 onehundredsix\n",
            "\n",
            "   118 onehundredtwentyone\n",
            "                    NL        .            4.00000        .             -.55060       3.11544      34.49553 onehundredtwelve\n",
            "                                            .88456          +Inf         .94857          +Inf      35.82164 onehundredsix\n",
            "\n",
            "   119 onehundredtwentyseven\n",
            "                    NL        .            6.00000        .             -.36590       4.64572      34.48704 onehundredtwelve\n",
            "                                           1.35428          +Inf         .71073          +Inf      35.94510 onehundredsix\n",
            "\n",
            "   120 onehundredtwentysix\n",
            "                    NL        .            6.00000        .             -.45611       4.27017      34.19357 onehundredtwelve\n",
            "                                           1.72983          +Inf         .66125          +Inf      36.12642 onehundredsix\n",
            "\n",
            "GLPK 4.65 - SENSITIVITY ANALYSIS REPORT                                                                         Page  14\n",
            "\n",
            "Problem:    \n",
            "Objective:  points = 34.98257277 (MINimum)\n",
            "\n",
            "   No. Column name  St      Activity      Obj coef   Lower bound       Activity      Obj coef  Obj value at Limiting\n",
            "                                          Marginal   Upper bound          range         range   break point variable\n",
            "------ ------------ -- ------------- ------------- -------------  ------------- ------------- ------------- ------------\n",
            "   121 onehundredtwentythree\n",
            "                    NL        .            6.00000        .             -.43459       4.49511      34.32857 onehundredtwelve\n",
            "                                           1.50489          +Inf         .62959          +Inf      35.93003 onehundredsix\n",
            "\n",
            "   122 onehundredtwentytwo\n",
            "                    NL        .            4.00000        .             -.34218       3.07684      34.66668 onehundredtwelve\n",
            "                                            .92316          +Inf        1.55821          +Inf      36.42106 onehundredfourteen\n",
            "\n",
            "   123 onehundredtwo\n",
            "                    NL        .            7.00000        .             -.18567       5.52839      34.70934 onehundredtwelve\n",
            "                                           1.47161          +Inf        1.19489          +Inf      36.74099 fiftyone\n",
            "\n",
            "   124 seven        NL        .            8.00000        .             -.06377       3.91550      34.72212 onehundredtwelve\n",
            "                                           4.08450          +Inf         .43583          +Inf      36.76271 fiftyone\n",
            "\n",
            "   125 seventeen    NL        .           12.00000        .             -.15306       9.88149      34.65832 onehundredtwelve\n",
            "                                           2.11851          +Inf         .78080          +Inf      36.63671 fiftyone\n",
            "\n",
            "   126 seventy      NL        .           11.00000        .             -.17903       9.42334      34.70030 onehundredtwelve\n",
            "                                           1.57666          +Inf         .59080          +Inf      35.91406 onehundredsix\n",
            "\n",
            "   127 seventyeight NL        .            9.00000        .             -.87298       7.74233      33.88465 onehundredtwelve\n",
            "                                           1.25767          +Inf         .14892          +Inf      35.16986 onehundredsix\n",
            "\n",
            "   128 seventyfive  NL        .            4.00000        .            -3.25871       3.94836      34.81428 onehundredtwelve\n",
            "                                            .05164          +Inf         .25180          +Inf      34.99558 onehundredsix\n",
            "\n",
            "   129 seventyfour  NL        .           29.00000        .             -.14746      25.86944      34.52093 onehundredtwelve\n",
            "                                           3.13056          +Inf         .35518          +Inf      36.09449 fiftyone\n",
            "\n",
            "   130 seventynine  NL        .           12.00000        .             -.46457      10.96879      34.50350 onehundredtwelve\n",
            "                                           1.03121          +Inf         .10982          +Inf      35.09582 onehundredsix\n",
            "\n",
            "GLPK 4.65 - SENSITIVITY ANALYSIS REPORT                                                                         Page  15\n",
            "\n",
            "Problem:    \n",
            "Objective:  points = 34.98257277 (MINimum)\n",
            "\n",
            "   No. Column name  St      Activity      Obj coef   Lower bound       Activity      Obj coef  Obj value at Limiting\n",
            "                                          Marginal   Upper bound          range         range   break point variable\n",
            "------ ------------ -- ------------- ------------- -------------  ------------- ------------- ------------- ------------\n",
            "   131 seventyone   NL        .            8.00000        .            -1.58401       7.35066      33.95401 onehundredtwelve\n",
            "                                            .64934          +Inf         .90875          +Inf      35.57266 onehundredsix\n",
            "\n",
            "   132 seventyseven NL        .            1.00000        .             -.06579      -3.09812      34.71295 onehundredtwelve\n",
            "                                           4.09812          +Inf         .48806          +Inf      36.98270 fiftyone\n",
            "\n",
            "   133 seventysix   NL        .            1.00000        .             -.41672        .95112      34.96220 onehundredtwelve\n",
            "                                            .04888          +Inf        2.94957          +Inf      35.12674 onehundredfourteen\n",
            "\n",
            "   134 seventythree NL        .           14.00000        .             -.29148      13.06766      34.71082 onehundredtwelve\n",
            "                                            .93234          +Inf         .71578          +Inf      35.64992 fiftyone\n",
            "\n",
            "   135 seventytwo   NL        .           10.00000        .             -.44487       8.71769      34.41211 onehundredtwelve\n",
            "                                           1.28231          +Inf        1.06466          +Inf      36.34780 fiftyone\n",
            "\n",
            "   136 six          NL        .            7.00000        .             -.30425       5.44189      34.50852 onehundredtwelve\n",
            "                                           1.55811          +Inf        1.47843          +Inf      37.28613 fiftyone\n",
            "\n",
            "   137 sixteen      NL        .           12.00000        .             -.21451      10.08690      34.57220 onehundredtwelve\n",
            "                                           1.91310          +Inf         .95633          +Inf      36.81214 fiftyone\n",
            "\n",
            "   138 sixty        NL        .           16.00000        .             -.16165      13.79244      34.62572 onehundredtwelve\n",
            "                                           2.20756          +Inf         .63501          +Inf      36.38440 fiftyone\n",
            "\n",
            "   139 sixtyeight   NL        .           12.00000        .             -.11777      10.08926      34.75755 onehundredtwelve\n",
            "                                           1.91074          +Inf         .54837          +Inf      36.03036 fiftyone\n",
            "\n",
            "   140 sixtyfive    NL        .            7.00000        .             -.84132       6.29744      34.39149 onehundredtwelve\n",
            "                                            .70256          +Inf         .31588          +Inf      35.20450 onehundredsix\n",
            "\n",
            "GLPK 4.65 - SENSITIVITY ANALYSIS REPORT                                                                         Page  16\n",
            "\n",
            "Problem:    \n",
            "Objective:  points = 34.98257277 (MINimum)\n",
            "\n",
            "   No. Column name  St      Activity      Obj coef   Lower bound       Activity      Obj coef  Obj value at Limiting\n",
            "                                          Marginal   Upper bound          range         range   break point variable\n",
            "------ ------------ -- ------------- ------------- -------------  ------------- ------------- ------------- ------------\n",
            "   141 sixtyfour    NL        .           20.00000        .             -.11327      16.56793      34.59383 onehundredtwelve\n",
            "                                           3.43207          +Inf         .18570          +Inf      35.61992 onehundredsix\n",
            "\n",
            "   142 sixtynine    NL        .           14.00000        .             -.10967      10.51145      34.60000 onehundredtwelve\n",
            "                                           3.48855          +Inf         .55688          +Inf      36.92529 fiftyone\n",
            "\n",
            "   143 sixtyone     NL        .           14.00000        .             -.25630      12.31030      34.54950 onehundredtwelve\n",
            "                                           1.68970          +Inf         .86835          +Inf      36.44982 fiftyone\n",
            "\n",
            "   144 sixtyseven   NL        .            7.00000        .             -.15043       5.64006      34.77800 onehundredtwelve\n",
            "                                           1.35994          +Inf         .85435          +Inf      36.14444 fiftyone\n",
            "\n",
            "   145 sixtysix     NL        .            9.00000        .            -1.10262       8.23062      34.13424 onehundredtwelve\n",
            "                                            .76938          +Inf         .19943          +Inf      35.13601 onehundredsix\n",
            "\n",
            "   146 sixtythree   NL        .           12.00000        .             -.49273      11.37731      34.67576 onehundredtwelve\n",
            "                                            .62269          +Inf         .16466          +Inf      35.08510 onehundredsix\n",
            "\n",
            "   147 sixtytwo     NL        .           10.00000        .             -.87617       8.90496      34.02313 onehundredtwelve\n",
            "                                           1.09504          +Inf         .23342          +Inf      35.23817 onehundredsix\n",
            "\n",
            "   148 ten          NL        .           10.00000        .             -.25166       8.71923      34.66025 onehundredtwelve\n",
            "                                           1.28077          +Inf         .54591          +Inf      35.68176 onehundredsix\n",
            "\n",
            "   149 thirteen     NL        .           12.00000        .             -.19626      10.75156      34.73755 onehundredtwelve\n",
            "                                           1.24844          +Inf         .86149          +Inf      36.05809 fiftyone\n",
            "\n",
            "   150 thirty       NL        .           11.00000        .             -.25685       8.96819      34.46071 onehundredtwelve\n",
            "                                           2.03181          +Inf         .61200          +Inf      36.22604 onehundredsix\n",
            "\n",
            "GLPK 4.65 - SENSITIVITY ANALYSIS REPORT                                                                         Page  17\n",
            "\n",
            "Problem:    \n",
            "Objective:  points = 34.98257277 (MINimum)\n",
            "\n",
            "   No. Column name  St      Activity      Obj coef   Lower bound       Activity      Obj coef  Obj value at Limiting\n",
            "                                          Marginal   Upper bound          range         range   break point variable\n",
            "------ ------------ -- ------------- ------------- -------------  ------------- ------------- ------------- ------------\n",
            "   151 thirtyeight  NL        .           14.00000        .             -.22850      12.30135      34.59443 onehundredtwelve\n",
            "                                           1.69865          +Inf         .26610          +Inf      35.43459 onehundredsix\n",
            "\n",
            "   152 thirtyfive   NL        .           15.00000        .             -.20791      12.96601      34.55969 onehundredtwelve\n",
            "                                           2.03399          +Inf         .29383          +Inf      35.58021 onehundredsix\n",
            "\n",
            "   153 thirtyfour   NL        .           16.00000        .             -.21993      14.58613      34.67162 onehundredtwelve\n",
            "                                           1.41387          +Inf         .24424          +Inf      35.32789 onehundredsix\n",
            "\n",
            "   154 thirtynine   NL        .           14.00000        .             -.15763      12.07220      34.67870 onehundredtwelve\n",
            "                                           1.92780          +Inf         .45901          +Inf      35.86745 onehundredsix\n",
            "\n",
            "   155 thirtyone    NL        .           12.00000        .             -.06784       7.57287      34.68223 onehundredtwelve\n",
            "                                           4.42713          +Inf         .45281          +Inf      36.98724 fiftyone\n",
            "\n",
            "   156 thirtyseven  NL        .           14.00000        .             -.35808      12.95038      34.60672 onehundredtwelve\n",
            "                                           1.04962          +Inf         .18479          +Inf      35.17653 onehundredsix\n",
            "\n",
            "   157 thirtysix    NL        .           14.00000        .             -.44156      12.82351      34.46308 onehundredtwelve\n",
            "                                           1.17649          +Inf         .17605          +Inf      35.18969 onehundredsix\n",
            "\n",
            "   158 thirtythree  NL        .           13.00000        .             -.14604      10.04984      34.55173 onehundredtwelve\n",
            "                                           2.95016          +Inf         .74448          +Inf      37.17891 fiftyone\n",
            "\n",
            "   159 thirtytwo    NL        .           11.00000        .             -.18295       9.09936      34.63485 onehundredtwelve\n",
            "                                           1.90064          +Inf         .93309          +Inf      36.75604 fiftyone\n",
            "\n",
            "   160 three        NL        .            7.00000        .             -.22776       5.42636      34.62416 onehundredtwelve\n",
            "                                           1.57364          +Inf        1.23944          +Inf      36.93301 fiftyone\n",
            "\n",
            "GLPK 4.65 - SENSITIVITY ANALYSIS REPORT                                                                         Page  18\n",
            "\n",
            "Problem:    \n",
            "Objective:  points = 34.98257277 (MINimum)\n",
            "\n",
            "   No. Column name  St      Activity      Obj coef   Lower bound       Activity      Obj coef  Obj value at Limiting\n",
            "                                          Marginal   Upper bound          range         range   break point variable\n",
            "------ ------------ -- ------------- ------------- -------------  ------------- ------------- ------------- ------------\n",
            "   161 twelve       NL        .           14.00000        .             -.20693      12.37168      34.64562 onehundredtwelve\n",
            "                                           1.62832          +Inf         .77709          +Inf      36.24792 onehundredsix\n",
            "\n",
            "   162 twenty       NL        .           12.00000        .             -.28388      10.62039      34.59094 onehundredtwelve\n",
            "                                           1.37961          +Inf         .46246          +Inf      35.62058 onehundredsix\n",
            "\n",
            "   163 twentyeight  NL        .           14.00000        .             -.25092      12.35849      34.57069 onehundredtwelve\n",
            "                                           1.64151          +Inf         .28112          +Inf      35.44403 onehundredsix\n",
            "\n",
            "   164 twentyfive   NL        .           11.00000        .             -.28995       9.08373      34.42695 onehundredtwelve\n",
            "                                           1.91627          +Inf         .48178          +Inf      35.90580 onehundredsix\n",
            "\n",
            "   165 twentyfour   NL        .           10.00000        .             -.34236       8.95685      34.62544 onehundredtwelve\n",
            "                                           1.04315          +Inf         .42656          +Inf      35.42754 onehundredsix\n",
            "\n",
            "   166 twentynine   NL        .           10.00000        .             -.40967       9.07553      34.60385 onehundredtwelve\n",
            "                                            .92447          +Inf         .35955          +Inf      35.31497 onehundredsix\n",
            "\n",
            "   167 twentyone    NL        .           14.00000        .             -.06959       9.22507      34.65028 onehundredtwelve\n",
            "                                           4.77493          +Inf         .43526          +Inf      37.06090 fiftyone\n",
            "\n",
            "   168 twentyseven  NL        .           11.00000        .             -.14285       8.20555      34.58338 onehundredtwelve\n",
            "                                           2.79445          +Inf         .83006          +Inf      37.30212 fiftyone\n",
            "\n",
            "   169 twentysix    NL        .           10.00000        .             -.19634       8.41409      34.67119 onehundredtwelve\n",
            "                                           1.58591          +Inf        1.04638          +Inf      36.64203 fiftyone\n",
            "\n",
            "   170 twentythree  NL        .           17.00000        .             -.13417      13.85585      34.56071 onehundredtwelve\n",
            "                                           3.14415          +Inf         .63630          +Inf      36.98320 fiftyone\n",
            "\n",
            "GLPK 4.65 - SENSITIVITY ANALYSIS REPORT                                                                         Page  19\n",
            "\n",
            "Problem:    \n",
            "Objective:  points = 34.98257277 (MINimum)\n",
            "\n",
            "   No. Column name  St      Activity      Obj coef   Lower bound       Activity      Obj coef  Obj value at Limiting\n",
            "                                          Marginal   Upper bound          range         range   break point variable\n",
            "------ ------------ -- ------------- ------------- -------------  ------------- ------------- ------------- ------------\n",
            "   171 twentytwo    NL        .           15.00000        .             -.15262      12.70121      34.63173 onehundredtwelve\n",
            "                                           2.29879          +Inf         .65862          +Inf      36.49660 fiftyone\n",
            "\n",
            "   172 two          NL        .            7.00000        .             -.26548       5.32322      34.53742 onehundredtwelve\n",
            "                                           1.67678          +Inf        1.34808          +Inf      37.24301 fiftyone\n",
            "\n",
            "   173 zero         NL        .            9.00000        .             -.12998       6.41621      34.64672 onehundredtwelve\n",
            "                                           2.58379          +Inf         .70611          +Inf      36.80702 fiftyone\n",
            "\n",
            "   174 onehundredfifty\n",
            "                    NL        .             .             .             -.90595       -.27295      34.73530 onehundredtwelve\n",
            "                                            .27295          +Inf        6.64754          +Inf      36.79700 fiftyone\n",
            "\n",
            "   175 onehundredfortytwo\n",
            "                    NL        .             .             .            -1.15760       -.21361      34.73530 onehundredtwelve\n",
            "                                            .21361          +Inf        8.49408          +Inf      36.79700 fiftyone\n",
            "\n",
            "   176 onehundredsixteen\n",
            "                    NL        .             .             .            -2.97670       -.08307      34.73530 onehundredtwelve\n",
            "                                            .08307          +Inf       21.84193          +Inf      36.79700 fiftyone\n",
            "\n",
            "   177 onehundredthirtytwo\n",
            "                    NL        .             .             .            -1.73641       -.14241      34.73530 onehundredtwelve\n",
            "                                            .14241          +Inf       12.74113          +Inf      36.79700 fiftyone\n",
            "\n",
            "   178 onehundredtwentyfour\n",
            "                    NL        .             .             .            -2.31521       -.10681      34.73530 onehundredtwelve\n",
            "                                            .10681          +Inf       16.98817          +Inf      36.79700 fiftyone\n",
            "\n",
            "   179 ONE_VAR_CONSTANT\n",
            "                    BS       1.00000        .             .             1.00000          -Inf          -Inf\n",
            "                                            .               +Inf        1.00000          +Inf          +Inf\n",
            "\n",
            "End of report\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "aEfo3ituKdN7",
        "outputId": "b9f9f1ef-9a14-4303-9460-834a3b381095",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 166
        }
      },
      "source": [
        "#looping through variable objects in the model and accessing their values\n",
        "\n",
        "#initializing lists\n",
        "product_id_list = []\n",
        "quantity_list = []\n",
        "\n",
        "for v in model.component_objects(Var, active=True):\n",
        "    varobject = getattr(model, str(v))\n",
        "    for index in varobject:\n",
        "        if varobject[index].value == 0:\n",
        "          continue\n",
        "        elif varobject[index].value == None:\n",
        "          continue  \n",
        "        else:\n",
        "#v is a pyomo simplevar type. printing it out then retrieving its contents and input into a list\n",
        "#also gathering the quantity from the model as well into alist\n",
        "          old_stdout = sys.stdout \n",
        "          sys.stdout = buffer = io.StringIO()\n",
        "          print(v)\n",
        "          sys.stdout = old_stdout     \n",
        "          whatWasPrinted = buffer.getvalue()\n",
        "          product_id_list.append(whatWasPrinted.replace(\"\\n\", \"\"))\n",
        "          quantity_list.append(varobject[index].value)\n",
        "  \n",
        "product_dict = {'food_drink_id':product_id_list,\n",
        "                'quantity':quantity_list}\n",
        "\n",
        "#making a dataframe from dict\n",
        "answer_df = pd.DataFrame(product_dict)\n",
        "\n",
        "#merging the original df and the new df for the answer df\n",
        "answer_df2 = answer_df.merge(df, how='left', on = 'food_drink_id')\n",
        "answer_df2 = answer_df2[['Food or Drink', 'quantity']]\n",
        "answer_df2.head()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>Food or Drink</th>\n",
              "      <th>quantity</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>Pastrami Burger</td>\n",
              "      <td>1.366585</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>French Toast Sticks</td>\n",
              "      <td>0.089710</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>1% Low Fat Milk</td>\n",
              "      <td>0.930354</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>Chocolate Milk, Protein Fortified, Low Fat (1%)</td>\n",
              "      <td>3.471887</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "                                     Food or Drink  quantity\n",
              "0                                  Pastrami Burger  1.366585\n",
              "1                              French Toast Sticks  0.089710\n",
              "2                                  1% Low Fat Milk  0.930354\n",
              "3  Chocolate Milk, Protein Fortified, Low Fat (1%)  3.471887"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 22
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "7qpQVK1nFa-1"
      },
      "source": [
        "# Model 2\n",
        "This model tries to make for a more realistic diet, including the above restraints from model 1. \n",
        "\n",
        ".Liquids are generally worse at sateity than solids, thus we are eliminating liquids. You also have a max of only 1 syrup and 1 sauce. We are also forcing atleast 2 breakfast items a day,  3 snack items (meaning non-liquid, non-dessert food that is less than 300 calories) 1 dessert, and 3 appetizers. Its important to eat food throughout the day to stay satisfied and have nice variety to stay on track with the diet. Also- Diet drinks and 0 calorie items can be drinken but can't be used in the model since they contribute nothing. \n",
        "\n",
        "https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2197163/#:~:text=There%20is%20strong%20evidence%20that,return%20of%20hunger%20%5B12%5D."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "NnfVLflpm9Xe"
      },
      "source": [
        "from pyomo.environ import *\n",
        "\n",
        "SOLVER = 'glpk'\n",
        "EXECUTABLE = '/usr/bin/glpsol'\n",
        "\n",
        "#initialize model\n",
        "model = ConcreteModel()\n",
        "\n",
        "#loop through and create variables\n",
        "for x in df.values:\n",
        "  name = x[8]\n",
        "  model.add_component(name, Var(within=NonNegativeReals))\n",
        "\n",
        "#Adding these new constraints which will make the end result much more realistic\n",
        "model.sauce_const = Constraint(expr = model.seventyfive + model.seventysix + model.seventyseven <= 1)\n",
        "\n",
        "model.syrup_const = Constraint(expr = model.onehundredseven <= 1)\n",
        "\n",
        "model.dessert = Constraint(expr= model.onehundredfiftyseven + \n",
        "model.onehundredfiftyeight + \n",
        "model.onehundredfiftynine + \n",
        "model.onehundredsixty + \n",
        "model.onehundredsixtyone + \n",
        "model.onehundredsixtytwo + \n",
        "model.onehundredsixtythree + \n",
        "model.onehundredsixtyfour + \n",
        "model.onehundredsixtyfive + \n",
        "model.onehundredsixtysix + \n",
        "model.onehundredsixtyseven + \n",
        "model.onehundredsixtyeight + \n",
        "model.onehundredsixtynine + \n",
        "model.onehundredseventy + \n",
        "model.onehundredseventyone + \n",
        "model.onehundredseventytwo + \n",
        "model.onehundredseventythree + \n",
        "model.onehundredseventyfour + \n",
        "model.onehundredseventyfive + \n",
        "model.onehundredseventysix + \n",
        "model.onehundredseventyseven + \n",
        "model.onehundredseventyeight == 1 )\n",
        "\n",
        "model.app = Constraint(expr =                        \n",
        "model.seventyeight + \n",
        "model.seventynine + \n",
        "model.eighty + \n",
        "model.eightyone + \n",
        "model.eightytwo + \n",
        "model.eightythree + \n",
        "model.eightyfour == 3)\n",
        "\n",
        "model.snack = Constraint(expr = model.onehundredsixtytwo + \n",
        "model.onehundredsixtyfour + \n",
        "model.onehundredseventysix + \n",
        "model.onehundredseventyseven + \n",
        "model.onehundredseventyeight + \n",
        "model.onehundredseventynine + \n",
        "model.one + \n",
        "model.two + \n",
        "model.three + \n",
        "model.four + \n",
        "model.five + \n",
        "model.six + \n",
        "model.seven + \n",
        "model.fiftytwo + \n",
        "model.sixtyfive + \n",
        "model.sixtyseven + \n",
        "model.seventyone + \n",
        "model.seventyfive + \n",
        "model.seventysix + \n",
        "model.seventyseven + \n",
        "model.seventyeight + \n",
        "model.eightythree + \n",
        "model.ninetyseven == 3)\n",
        "\n",
        "model.break_const = Constraint(expr = \n",
        "model.eightynine + \n",
        "model.ninety + \n",
        "model.ninetyone + \n",
        "model.ninetytwo + \n",
        "model.ninetythree + \n",
        "model.ninetyfour + \n",
        "model.ninetyfive + \n",
        "model.ninetysix + \n",
        "model.ninetyseven + \n",
        "model.ninetyeight + \n",
        "model.ninetynine + \n",
        "model.onehundred + \n",
        "model.onehundredone + \n",
        "model.onehundredtwo + \n",
        "model.onehundredthree + \n",
        "model.onehundredfour + \n",
        "model.onehundredfive + \n",
        "model.onehundredsix >= 2)\n",
        "\n",
        "model.liquid_const = Constraint(expr = model.onehundredeight + \n",
        "model.onehundrednine + \n",
        "model.onehundredten + \n",
        "model.onehundredeleven + \n",
        "model.onehundredtwelve + \n",
        "model.onehundredthirteen + \n",
        "model.onehundredfourteen + \n",
        "model.onehundredfifteen + \n",
        "model.onehundredsixteen + \n",
        "model.onehundredseventeen + \n",
        "model.onehundredeighteen + \n",
        "model.onehundrednineteen + \n",
        "model.onehundredtwenty + \n",
        "model.onehundredtwentyone + \n",
        "model.onehundredtwentytwo + \n",
        "model.onehundredtwentythree + \n",
        "model.onehundredtwentyfour + \n",
        "model.onehundredtwentyfive + \n",
        "model.onehundredtwentysix + \n",
        "model.onehundredtwentyseven + \n",
        "model.onehundredtwentyeight + \n",
        "model.onehundredtwentynine + \n",
        "model.onehundredthirty + \n",
        "model.onehundredthirtyone + \n",
        "model.onehundredthirtytwo + \n",
        "model.onehundredthirtythree + \n",
        "model.onehundredthirtyfour + \n",
        "model.onehundredthirtyfive + \n",
        "model.onehundredthirtysix + \n",
        "model.onehundredthirtyseven + \n",
        "model.onehundredthirtyeight + \n",
        "model.onehundredthirtynine + \n",
        "model.onehundredforty + \n",
        "model.onehundredfortyone + \n",
        "model.onehundredfortytwo + \n",
        "model.onehundredfortythree + \n",
        "model.onehundredfortyfour + \n",
        "model.onehundredfortyfive + \n",
        "model.onehundredfortysix + \n",
        "model.onehundredfortyseven + \n",
        "model.onehundredfortyeight + \n",
        "model.onehundredfortynine + \n",
        "model.onehundredfifty + \n",
        "model.onehundredfiftyone + \n",
        "model.onehundredfiftytwo + \n",
        "model.onehundredfiftythree + \n",
        "model.onehundredfiftyfour + \n",
        "model.onehundredfiftyfive + \n",
        "model.onehundredfiftysix <= 0)\n",
        "\n",
        "model.cal_const = Constraint(expr = model.zero*320 + \n",
        "model.one*270 + \n",
        "model.two*240 + \n",
        "model.three*250 + \n",
        "model.four*240 + \n",
        "model.five*250 + \n",
        "model.six*240 + \n",
        "model.seven*300 + \n",
        "model.eight*350 + \n",
        "model.nine*340 + \n",
        "model.ten*370 + \n",
        "model.eleven*460 + \n",
        "model.twelve*520 + \n",
        "model.thirteen*460 + \n",
        "model.fourteen*430 + \n",
        "model.fifteen*440 + \n",
        "model.sixteen*430 + \n",
        "model.seventeen*440 + \n",
        "model.eighteen*540 + \n",
        "model.nineteen*430 + \n",
        "model.twenty*440 + \n",
        "model.twentyone*490 + \n",
        "model.twentytwo*550 + \n",
        "model.twentythree*600 + \n",
        "model.twentyfour*370 + \n",
        "model.twentyfive*380 + \n",
        "model.twentysix*370 + \n",
        "model.twentyseven*380 + \n",
        "model.twentyeight*510 + \n",
        "model.twentynine*370 + \n",
        "model.thirty*380 + \n",
        "model.thirtyone*430 + \n",
        "model.thirtytwo*400 + \n",
        "model.thirtythree*450 + \n",
        "model.thirtyfour*600 + \n",
        "model.thirtyfive*540 + \n",
        "model.thirtysix*510 + \n",
        "model.thirtyseven*520 + \n",
        "model.thirtyeight*510 + \n",
        "model.thirtynine*520 + \n",
        "model.forty*620 + \n",
        "model.fortyone*510 + \n",
        "model.fortytwo*520 + \n",
        "model.fortythree*570 + \n",
        "model.fortyfour*620 + \n",
        "model.fortyfive*680 + \n",
        "model.fortysix*510 + \n",
        "model.fortyseven*610 + \n",
        "model.fortyeight*320 + \n",
        "model.fortynine*370 + \n",
        "model.fifty*640 + \n",
        "model.fiftyone*390 + \n",
        "model.fiftytwo*300 + \n",
        "model.fiftythree*470 + \n",
        "model.fiftyfour*350 + \n",
        "model.fiftyfive*570 + \n",
        "model.fiftysix*380 + \n",
        "model.fiftyseven*640 + \n",
        "model.fiftyeight*380 + \n",
        "model.fiftynine*400 + \n",
        "model.sixty*590 + \n",
        "model.sixtyone*510 + \n",
        "model.sixtytwo*350 + \n",
        "model.sixtythree*450 + \n",
        "model.sixtyfour*710 + \n",
        "model.sixtyfive*250 + \n",
        "model.sixtysix*320 + \n",
        "model.sixtyseven*280 + \n",
        "model.sixtyeight*470 + \n",
        "model.sixtynine*490 + \n",
        "model.seventy*410 + \n",
        "model.seventyone*290 + \n",
        "model.seventytwo*360 + \n",
        "model.seventythree*540 + \n",
        "model.seventyfour*1070 + \n",
        "model.seventyfive*150 + \n",
        "model.seventysix*60 + \n",
        "model.seventyseven*25 + \n",
        "model.seventyeight*300 + \n",
        "model.seventynine*430 + \n",
        "model.eighty*790 + \n",
        "model.eightyone*540 + \n",
        "model.eightytwo*370 + \n",
        "model.eightythree*210 + \n",
        "model.eightyfour*420 + \n",
        "model.eightyfive*490 + \n",
        "model.eightysix*590 + \n",
        "model.eightyseven*470 + \n",
        "model.eightyeight*370 + \n",
        "model.eightynine*330 + \n",
        "model.ninety*430 + \n",
        "model.ninetyone*390 + \n",
        "model.ninetytwo*490 + \n",
        "model.ninetythree*440 + \n",
        "model.ninetyfour*540 + \n",
        "model.ninetyfive*520 + \n",
        "model.ninetysix*620 + \n",
        "model.ninetyseven*300 + \n",
        "model.ninetyeight*400 + \n",
        "model.ninetynine*600 + \n",
        "model.onehundred*700 + \n",
        "model.onehundredone*640 + \n",
        "model.onehundredtwo*260 + \n",
        "model.onehundredthree*320 + \n",
        "model.onehundredfour*350 + \n",
        "model.onehundredfive*290 + \n",
        "model.onehundredsix*490 + \n",
        "model.onehundredseven*120 + \n",
        "model.onehundredeight*140 + \n",
        "model.onehundrednine*0 + \n",
        "model.onehundredten*0 + \n",
        "model.onehundredeleven*130 + \n",
        "model.onehundredtwelve*110 + \n",
        "model.onehundredthirteen*160 + \n",
        "model.onehundredfourteen*200 + \n",
        "model.onehundredfifteen*150 + \n",
        "model.onehundredsixteen*0 + \n",
        "model.onehundredseventeen*170 + \n",
        "model.onehundredeighteen*140 + \n",
        "model.onehundrednineteen*160 + \n",
        "model.onehundredtwenty*140 + \n",
        "model.onehundredtwentyone*140 + \n",
        "model.onehundredtwentytwo*150 + \n",
        "model.onehundredtwentythree*200 + \n",
        "model.onehundredtwentyfour*0 + \n",
        "model.onehundredtwentyfive*230 + \n",
        "model.onehundredtwentysix*190 + \n",
        "model.onehundredtwentyseven*210 + \n",
        "model.onehundredtwentyeight*180 + \n",
        "model.onehundredtwentynine*180 + \n",
        "model.onehundredthirty*200 + \n",
        "model.onehundredthirtyone*250 + \n",
        "model.onehundredthirtytwo*0 + \n",
        "model.onehundredthirtythree*280 + \n",
        "model.onehundredthirtyfour*230 + \n",
        "model.onehundredthirtyfive*270 + \n",
        "model.onehundredthirtysix*230 + \n",
        "model.onehundredthirtyseven*230 + \n",
        "model.onehundredthirtyeight*250 + \n",
        "model.onehundredthirtynine*320 + \n",
        "model.onehundredforty*310 + \n",
        "model.onehundredfortyone*370 + \n",
        "model.onehundredfortytwo*0 + \n",
        "model.onehundredfortythree*420 + \n",
        "model.onehundredfortyfour*350 + \n",
        "model.onehundredfortyfive*400 + \n",
        "model.onehundredfortysix*340 + \n",
        "model.onehundredfortyseven*340 + \n",
        "model.onehundredfortyeight*375 + \n",
        "model.onehundredfortynine*500 + \n",
        "model.onehundredfifty*0 + \n",
        "model.onehundredfiftyone*570 + \n",
        "model.onehundredfiftytwo*470 + \n",
        "model.onehundredfiftythree*530 + \n",
        "model.onehundredfiftyfour*450 + \n",
        "model.onehundredfiftyfive*450 + \n",
        "model.onehundredfiftysix*490 + \n",
        "model.onehundredfiftyseven*400 + \n",
        "model.onehundredfiftyeight*390 + \n",
        "model.onehundredfiftynine*370 + \n",
        "model.onehundredsixty*400 + \n",
        "model.onehundredsixtyone*370 + \n",
        "model.onehundredsixtytwo*250 + \n",
        "model.onehundredsixtythree*450 + \n",
        "model.onehundredsixtyfour*160 + \n",
        "model.onehundredsixtyfive*360 + \n",
        "model.onehundredsixtysix*820 + \n",
        "model.onehundredsixtyseven*650 + \n",
        "model.onehundredsixtyeight*650 + \n",
        "model.onehundredsixtynine*650 + \n",
        "model.onehundredseventy*630 + \n",
        "model.onehundredseventyone*630 + \n",
        "model.onehundredseventytwo*620 + \n",
        "model.onehundredseventythree*630 + \n",
        "model.onehundredseventyfour*940 + \n",
        "model.onehundredseventyfive*440 + \n",
        "model.onehundredseventysix*200 + \n",
        "model.onehundredseventyseven*180 + \n",
        "model.onehundredseventyeight*170 + \n",
        "model.onehundredseventynine*200  == adj_bmr)\n",
        "\n",
        "model.proteinlb = Constraint(expr = model.zero*15 + \n",
        "model.one*12 + \n",
        "model.two*10 + \n",
        "model.three*10 + \n",
        "model.four*10 + \n",
        "model.five*10 + \n",
        "model.six*10 + \n",
        "model.seven*11 + \n",
        "model.eight*17 + \n",
        "model.nine*12 + \n",
        "model.ten*12 + \n",
        "model.eleven*19 + \n",
        "model.twelve*22 + \n",
        "model.thirteen*19 + \n",
        "model.fourteen*17 + \n",
        "model.fifteen*17 + \n",
        "model.sixteen*17 + \n",
        "model.seventeen*17 + \n",
        "model.eighteen*22 + \n",
        "model.nineteen*17 + \n",
        "model.twenty*17 + \n",
        "model.twentyone*18 + \n",
        "model.twentytwo*25 + \n",
        "model.twentythree*23 + \n",
        "model.twentyfour*13 + \n",
        "model.twentyfive*13 + \n",
        "model.twentysix*13 + \n",
        "model.twentyseven*13 + \n",
        "model.twentyeight*17 + \n",
        "model.twentynine*13 + \n",
        "model.thirty*13 + \n",
        "model.thirtyone*14 + \n",
        "model.thirtytwo*15 + \n",
        "model.thirtythree*18 + \n",
        "model.thirtyfour*21 + \n",
        "model.thirtyfive*18 + \n",
        "model.thirtysix*16 + \n",
        "model.thirtyseven*16 + \n",
        "model.thirtyeight*16 + \n",
        "model.thirtynine*16 + \n",
        "model.forty*21 + \n",
        "model.fortyone*16 + \n",
        "model.fortytwo*16 + \n",
        "model.fortythree*17 + \n",
        "model.fortyfour*23 + \n",
        "model.fortyfive*22 + \n",
        "model.fortysix*34 + \n",
        "model.fortyseven*39 + \n",
        "model.fortyeight*21 + \n",
        "model.fortynine*24 + \n",
        "model.fifty*43 + \n",
        "model.fiftyone*27 + \n",
        "model.fiftytwo*19 + \n",
        "model.fiftythree*33 + \n",
        "model.fiftyfour*22 + \n",
        "model.fiftyfive*38 + \n",
        "model.fiftysix*24 + \n",
        "model.fiftyseven*42 + \n",
        "model.fiftyeight*22 + \n",
        "model.fiftynine*23 + \n",
        "model.sixty*29 + \n",
        "model.sixtyone*24 + \n",
        "model.sixtytwo*11 + \n",
        "model.sixtythree*12 + \n",
        "model.sixtyfour*16 + \n",
        "model.sixtyfive*7 + \n",
        "model.sixtysix*8 + \n",
        "model.sixtyseven*12 + \n",
        "model.sixtyeight*25 + \n",
        "model.sixtynine*22 + \n",
        "model.seventy*12 + \n",
        "model.seventyone*16 + \n",
        "model.seventytwo*23 + \n",
        "model.seventythree*34 + \n",
        "model.seventyfour*69 + \n",
        "model.seventyfive*0 + \n",
        "model.seventysix*0 + \n",
        "model.seventyseven*0 + \n",
        "model.seventyeight*2 + \n",
        "model.seventynine*3 + \n",
        "model.eighty*6 + \n",
        "model.eightyone*12 + \n",
        "model.eightytwo*8 + \n",
        "model.eightythree*6 + \n",
        "model.eightyfour*13 + \n",
        "model.eightyfive*24 + \n",
        "model.eightysix*25 + \n",
        "model.eightyseven*25 + \n",
        "model.eightyeight*17 + \n",
        "model.eightynine*10 + \n",
        "model.ninety*11 + \n",
        "model.ninetyone*16 + \n",
        "model.ninetytwo*17 + \n",
        "model.ninetythree*18 + \n",
        "model.ninetyfour*19 + \n",
        "model.ninetyfive*19 + \n",
        "model.ninetysix*20 + \n",
        "model.ninetyseven*16 + \n",
        "model.ninetyeight*17 + \n",
        "model.ninetynine*20 + \n",
        "model.onehundred*21 + \n",
        "model.onehundredone*24 + \n",
        "model.onehundredtwo*6 + \n",
        "model.onehundredthree*12 + \n",
        "model.onehundredfour*8 + \n",
        "model.onehundredfive*1 + \n",
        "model.onehundredsix*6 + \n",
        "model.onehundredseven*0 + \n",
        "model.onehundredeight*0 + \n",
        "model.onehundrednine*0 + \n",
        "model.onehundredten*0 + \n",
        "model.onehundredeleven*10 + \n",
        "model.onehundredtwelve*9 + \n",
        "model.onehundredthirteen*8 + \n",
        "model.onehundredfourteen*11 + \n",
        "model.onehundredfifteen*0 + \n",
        "model.onehundredsixteen*0 + \n",
        "model.onehundredseventeen*0 + \n",
        "model.onehundredeighteen*0 + \n",
        "model.onehundrednineteen*0 + \n",
        "model.onehundredtwenty*0 + \n",
        "model.onehundredtwentyone*0 + \n",
        "model.onehundredtwentytwo*0 + \n",
        "model.onehundredtwentythree*0 + \n",
        "model.onehundredtwentyfour*0 + \n",
        "model.onehundredtwentyfive*0 + \n",
        "model.onehundredtwentysix*0 + \n",
        "model.onehundredtwentyseven*0 + \n",
        "model.onehundredtwentyeight*0 + \n",
        "model.onehundredtwentynine*0 + \n",
        "model.onehundredthirty*0 + \n",
        "model.onehundredthirtyone*0 + \n",
        "model.onehundredthirtytwo*0 + \n",
        "model.onehundredthirtythree*0 + \n",
        "model.onehundredthirtyfour*0 + \n",
        "model.onehundredthirtyfive*0 + \n",
        "model.onehundredthirtysix*0 + \n",
        "model.onehundredthirtyseven*0 + \n",
        "model.onehundredthirtyeight*0 + \n",
        "model.onehundredthirtynine*0 + \n",
        "model.onehundredforty*0 + \n",
        "model.onehundredfortyone*0 + \n",
        "model.onehundredfortytwo*0 + \n",
        "model.onehundredfortythree*0 + \n",
        "model.onehundredfortyfour*0 + \n",
        "model.onehundredfortyfive*0 + \n",
        "model.onehundredfortysix*0 + \n",
        "model.onehundredfortyseven*0 + \n",
        "model.onehundredfortyeight*0 + \n",
        "model.onehundredfortynine*0 + \n",
        "model.onehundredfifty*0 + \n",
        "model.onehundredfiftyone*0 + \n",
        "model.onehundredfiftytwo*0 + \n",
        "model.onehundredfiftythree*0 + \n",
        "model.onehundredfiftyfour*0 + \n",
        "model.onehundredfiftyfive*0 + \n",
        "model.onehundredfiftysix*0 + \n",
        "model.onehundredfiftyseven*7 + \n",
        "model.onehundredfiftyeight*7 + \n",
        "model.onehundredfiftynine*7 + \n",
        "model.onehundredsixty*7 + \n",
        "model.onehundredsixtyone*7 + \n",
        "model.onehundredsixtytwo*5 + \n",
        "model.onehundredsixtythree*6 + \n",
        "model.onehundredsixtyfour*3 + \n",
        "model.onehundredsixtyfive*4 + \n",
        "model.onehundredsixtysix*13 + \n",
        "model.onehundredsixtyseven*13 + \n",
        "model.onehundredsixtyeight*13 + \n",
        "model.onehundredsixtynine*13 + \n",
        "model.onehundredseventy*13 + \n",
        "model.onehundredseventyone*13 + \n",
        "model.onehundredseventytwo*13 + \n",
        "model.onehundredseventythree*14 + \n",
        "model.onehundredseventyfour*14 + \n",
        "model.onehundredseventyfive*7 + \n",
        "model.onehundredseventysix*3 + \n",
        "model.onehundredseventyseven*3 + \n",
        "model.onehundredseventyeight*3 + \n",
        "model.onehundredseventynine*3 >= protein_lb)\n",
        "\n",
        "model.sugar = Constraint(expr = model.zero*4 + \n",
        "model.one*4 + \n",
        "model.two*4 + \n",
        "model.three*6 + \n",
        "model.four*5 + \n",
        "model.five*6 + \n",
        "model.six*4 + \n",
        "model.seven*14 + \n",
        "model.eight*5 + \n",
        "model.nine*4 + \n",
        "model.ten*6 + \n",
        "model.eleven*4 + \n",
        "model.twelve*5 + \n",
        "model.thirteen*4 + \n",
        "model.fourteen*4 + \n",
        "model.fifteen*6 + \n",
        "model.sixteen*4 + \n",
        "model.seventeen*6 + \n",
        "model.eighteen*9 + \n",
        "model.nineteen*4 + \n",
        "model.twenty*7 + \n",
        "model.twentyone*14 + \n",
        "model.twentytwo*5 + \n",
        "model.twentythree*5 + \n",
        "model.twentyfour*7 + \n",
        "model.twentyfive*9 + \n",
        "model.twentysix*8 + \n",
        "model.twentyseven*9 + \n",
        "model.twentyeight*12 + \n",
        "model.twentynine*7 + \n",
        "model.thirty*10 + \n",
        "model.thirtyone*17 + \n",
        "model.thirtytwo*7 + \n",
        "model.thirtythree*7 + \n",
        "model.thirtyfour*9 + \n",
        "model.thirtyfive*8 + \n",
        "model.thirtysix*8 + \n",
        "model.thirtyseven*10 + \n",
        "model.thirtyeight*8 + \n",
        "model.thirtynine*10 + \n",
        "model.forty*13 + \n",
        "model.fortyone*8 + \n",
        "model.fortytwo*11 + \n",
        "model.fortythree*18 + \n",
        "model.fortyfour*9 + \n",
        "model.fortyfive*9 + \n",
        "model.fortysix*6 + \n",
        "model.fortyseven*6 + \n",
        "model.fortyeight*3 + \n",
        "model.fortynine*3 + \n",
        "model.fifty*4 + \n",
        "model.fiftyone*3 + \n",
        "model.fiftytwo*5 + \n",
        "model.fiftythree*5 + \n",
        "model.fiftyfour*5 + \n",
        "model.fiftyfive*5 + \n",
        "model.fiftysix*5 + \n",
        "model.fiftyseven*5 + \n",
        "model.fiftyeight*6 + \n",
        "model.fiftynine*4 + \n",
        "model.sixty*6 + \n",
        "model.sixtyone*3 + \n",
        "model.sixtytwo*5 + \n",
        "model.sixtythree*1 + \n",
        "model.sixtyfour*9 + \n",
        "model.sixtyfive*1 + \n",
        "model.sixtysix*1 + \n",
        "model.sixtyseven*6 + \n",
        "model.sixtyeight*2 + \n",
        "model.sixtynine*4 + \n",
        "model.seventy*1 + \n",
        "model.seventyone*2 + \n",
        "model.seventytwo*1 + \n",
        "model.seventythree*2 + \n",
        "model.seventyfour*4 + \n",
        "model.seventyfive*1 + \n",
        "model.seventysix*12 + \n",
        "model.seventyseven*2 + \n",
        "model.seventyeight*0 + \n",
        "model.seventynine*0 + \n",
        "model.eighty*18 + \n",
        "model.eightyone*1 + \n",
        "model.eightytwo*1 + \n",
        "model.eightythree*3 + \n",
        "model.eightyfour*7 + \n",
        "model.eightyfive*3 + \n",
        "model.eightysix*3 + \n",
        "model.eightyseven*2 + \n",
        "model.eightyeight*1 + \n",
        "model.eightynine*4 + \n",
        "model.ninety*4 + \n",
        "model.ninetyone*4 + \n",
        "model.ninetytwo*4 + \n",
        "model.ninetythree*4 + \n",
        "model.ninetyfour*4 + \n",
        "model.ninetyfive*8 + \n",
        "model.ninetysix*8 + \n",
        "model.ninetyseven*1 + \n",
        "model.ninetyeight*1 + \n",
        "model.ninetynine*1 + \n",
        "model.onehundred*1 + \n",
        "model.onehundredone*4 + \n",
        "model.onehundredtwo*4 + \n",
        "model.onehundredthree*4 + \n",
        "model.onehundredfour*4 + \n",
        "model.onehundredfive*0 + \n",
        "model.onehundredsix*11 + \n",
        "model.onehundredseven*21 + \n",
        "model.onehundredeight*28 + \n",
        "model.onehundrednine*0 + \n",
        "model.onehundredten*0 + \n",
        "model.onehundredeleven*13 + \n",
        "model.onehundredtwelve*12 + \n",
        "model.onehundredthirteen*25 + \n",
        "model.onehundredfourteen*33 + \n",
        "model.onehundredfifteen*41 + \n",
        "model.onehundredsixteen*0 + \n",
        "model.onehundredseventeen*46 + \n",
        "model.onehundredeighteen*39 + \n",
        "model.onehundrednineteen*43 + \n",
        "model.onehundredtwenty*39 + \n",
        "model.onehundredtwentyone*35 + \n",
        "model.onehundredtwentytwo*41 + \n",
        "model.onehundredtwentythree*55 + \n",
        "model.onehundredtwentyfour*0 + \n",
        "model.onehundredtwentyfive*61 + \n",
        "model.onehundredtwentysix*52 + \n",
        "model.onehundredtwentyseven*57 + \n",
        "model.onehundredtwentyeight*52 + \n",
        "model.onehundredtwentynine*45 + \n",
        "model.onehundredthirty*54 + \n",
        "model.onehundredthirtyone*68 + \n",
        "model.onehundredthirtytwo*0 + \n",
        "model.onehundredthirtythree*77 + \n",
        "model.onehundredthirtyfour*65 + \n",
        "model.onehundredthirtyfive*72 + \n",
        "model.onehundredthirtysix*65 + \n",
        "model.onehundredthirtyseven*58 + \n",
        "model.onehundredthirtyeight*68 + \n",
        "model.onehundredthirtynine*84 + \n",
        "model.onehundredforty*81 + \n",
        "model.onehundredfortyone*103 + \n",
        "model.onehundredfortytwo*0 + \n",
        "model.onehundredfortythree*115 + \n",
        "model.onehundredfortyfour*97 + \n",
        "model.onehundredfortyfive*107 + \n",
        "model.onehundredfortysix*97 + \n",
        "model.onehundredfortyseven*86 + \n",
        "model.onehundredfortyeight*101 + \n",
        "model.onehundredfortynine*137 + \n",
        "model.onehundredfifty*0 + \n",
        "model.onehundredfiftyone*153 + \n",
        "model.onehundredfiftytwo*130 + \n",
        "model.onehundredfiftythree*143 + \n",
        "model.onehundredfiftyfour*130 + \n",
        "model.onehundredfiftyfive*115 + \n",
        "model.onehundredfiftysix*133 + \n",
        "model.onehundredfiftyseven*50 + \n",
        "model.onehundredfiftyeight*51 + \n",
        "model.onehundredfiftynine*48 + \n",
        "model.onehundredsixty*53 + \n",
        "model.onehundredsixtyone*49 + \n",
        "model.onehundredsixtytwo*30 + \n",
        "model.onehundredsixtythree*37 + \n",
        "model.onehundredsixtyfour*18 + \n",
        "model.onehundredsixtyfive*25 + \n",
        "model.onehundredsixtysix*122 + \n",
        "model.onehundredsixtyseven*91 + \n",
        "model.onehundredsixtyeight*91 + \n",
        "model.onehundredsixtynine*92 + \n",
        "model.onehundredseventy*76 + \n",
        "model.onehundredseventyone*80 + \n",
        "model.onehundredseventytwo*78 + \n",
        "model.onehundredseventythree*78 + \n",
        "model.onehundredseventyfour*87 + \n",
        "model.onehundredseventyfive*73 + \n",
        "model.onehundredseventysix*26 + \n",
        "model.onehundredseventyseven*28 + \n",
        "model.onehundredseventyeight*25 + \n",
        "model.onehundredseventynine*30 <= sugar_cal_b)\n",
        "\n",
        "model.sodium = Constraint(expr = model.zero*1410 + \n",
        "model.one*1160 + \n",
        "model.two*810 + \n",
        "model.three*870 + \n",
        "model.four*1040 + \n",
        "model.five*1230 + \n",
        "model.six*760 + \n",
        "model.seven*2060 + \n",
        "model.eight*1670 + \n",
        "model.nine*880 + \n",
        "model.ten*970 + \n",
        "model.eleven*1720 + \n",
        "model.twelve*1440 + \n",
        "model.thirteen*1350 + \n",
        "model.fourteen*1000 + \n",
        "model.fifteen*1060 + \n",
        "model.sixteen*1230 + \n",
        "model.seventeen*1420 + \n",
        "model.eighteen*1310 + \n",
        "model.nineteen*950 + \n",
        "model.twenty*1100 + \n",
        "model.twentyone*2250 + \n",
        "model.twentytwo*1720 + \n",
        "model.twentythree*1800 + \n",
        "model.twentyfour*880 + \n",
        "model.twentyfive*930 + \n",
        "model.twentysix*1100 + \n",
        "model.twentyseven*1300 + \n",
        "model.twentyeight*1170 + \n",
        "model.twentynine*830 + \n",
        "model.thirty*970 + \n",
        "model.thirtyone*2120 + \n",
        "model.thirtytwo*1220 + \n",
        "model.thirtythree*1480 + \n",
        "model.thirtyfour*1420 + \n",
        "model.thirtyfive*1330 + \n",
        "model.thirtysix*990 + \n",
        "model.thirtyseven*1040 + \n",
        "model.thirtyeight*1210 + \n",
        "model.thirtynine*1410 + \n",
        "model.forty*1300 + \n",
        "model.fortyone*940 + \n",
        "model.fortytwo*1080 + \n",
        "model.fortythree*2230 + \n",
        "model.fortyfour*1850 + \n",
        "model.fortyfive*1780 + \n",
        "model.fortysix*870 + \n",
        "model.fortyseven*1380 + \n",
        "model.fortyeight*870 + \n",
        "model.fortynine*1130 + \n",
        "model.fifty*1940 + \n",
        "model.fiftyone*980 + \n",
        "model.fiftytwo*650 + \n",
        "model.fiftythree*810 + \n",
        "model.fiftyfour*910 + \n",
        "model.fiftyfive*1320 + \n",
        "model.fiftysix*1020 + \n",
        "model.fiftyseven*1550 + \n",
        "model.fiftyeight*970 + \n",
        "model.fiftynine*1480 + \n",
        "model.sixty*1810 + \n",
        "model.sixtyone*1400 + \n",
        "model.sixtytwo*640 + \n",
        "model.sixtythree*860 + \n",
        "model.sixtyfour*1820 + \n",
        "model.sixtyfive*490 + \n",
        "model.sixtysix*540 + \n",
        "model.sixtyseven*1180 + \n",
        "model.sixtyeight*1880 + \n",
        "model.sixtynine*1870 + \n",
        "model.seventy*1200 + \n",
        "model.seventyone*690 + \n",
        "model.seventytwo*1100 + \n",
        "model.seventythree*1640 + \n",
        "model.seventyfour*3290 + \n",
        "model.seventyfive*140 + \n",
        "model.seventysix*220 + \n",
        "model.seventyseven*1590 + \n",
        "model.seventyeight*400 + \n",
        "model.seventynine*630 + \n",
        "model.eighty*3600 + \n",
        "model.eightyone*1380 + \n",
        "model.eightytwo*800 + \n",
        "model.eightythree*670 + \n",
        "model.eightyfour*1340 + \n",
        "model.eightyfive*1380 + \n",
        "model.eightysix*1500 + \n",
        "model.eightyseven*1720 + \n",
        "model.eightyeight*1180 + \n",
        "model.eightynine*1120 + \n",
        "model.ninety*1240 + \n",
        "model.ninetyone*1270 + \n",
        "model.ninetytwo*1390 + \n",
        "model.ninetythree*1520 + \n",
        "model.ninetyfour*1640 + \n",
        "model.ninetyfive*990 + \n",
        "model.ninetysix*1110 + \n",
        "model.ninetyseven*830 + \n",
        "model.ninetyeight*950 + \n",
        "model.ninetynine*960 + \n",
        "model.onehundred*1080 + \n",
        "model.onehundredone*1820 + \n",
        "model.onehundredtwo*890 + \n",
        "model.onehundredthree*1040 + \n",
        "model.onehundredfour*1180 + \n",
        "model.onehundredfive*240 + \n",
        "model.onehundredsix*460 + \n",
        "model.onehundredseven*25 + \n",
        "model.onehundredeight*0 + \n",
        "model.onehundrednine*0 + \n",
        "model.onehundredten*0 + \n",
        "model.onehundredeleven*130 + \n",
        "model.onehundredtwelve*130 + \n",
        "model.onehundredthirteen*210 + \n",
        "model.onehundredfourteen*230 + \n",
        "model.onehundredfifteen*35 + \n",
        "model.onehundredsixteen*35 + \n",
        "model.onehundredseventeen*70 + \n",
        "model.onehundredeighteen*35 + \n",
        "model.onehundrednineteen*65 + \n",
        "model.onehundredtwenty*45 + \n",
        "model.onehundredtwentyone*75 + \n",
        "model.onehundredtwentytwo*160 + \n",
        "model.onehundredtwentythree*45 + \n",
        "model.onehundredtwentyfour*45 + \n",
        "model.onehundredtwentyfive*95 + \n",
        "model.onehundredtwentysix*45 + \n",
        "model.onehundredtwentyseven*85 + \n",
        "model.onehundredtwentyeight*60 + \n",
        "model.onehundredtwentynine*100 + \n",
        "model.onehundredthirty*210 + \n",
        "model.onehundredthirtyone*60 + \n",
        "model.onehundredthirtytwo*60 + \n",
        "model.onehundredthirtythree*115 + \n",
        "model.onehundredthirtyfour*60 + \n",
        "model.onehundredthirtyfive*110 + \n",
        "model.onehundredthirtysix*75 + \n",
        "model.onehundredthirtyseven*125 + \n",
        "model.onehundredthirtyeight*260 + \n",
        "model.onehundredthirtynine*250 + \n",
        "model.onehundredforty*260 + \n",
        "model.onehundredfortyone*90 + \n",
        "model.onehundredfortytwo*90 + \n",
        "model.onehundredfortythree*170 + \n",
        "model.onehundredfortyfour*85 + \n",
        "model.onehundredfortyfive*160 + \n",
        "model.onehundredfortysix*110 + \n",
        "model.onehundredfortyseven*190 + \n",
        "model.onehundredfortyeight*390 + \n",
        "model.onehundredfortynine*115 + \n",
        "model.onehundredfifty*115 + \n",
        "model.onehundredfiftyone*230 + \n",
        "model.onehundredfiftytwo*115 + \n",
        "model.onehundredfiftythree*220 + \n",
        "model.onehundredfiftyfour*150 + \n",
        "model.onehundredfiftyfive*250 + \n",
        "model.onehundredfiftysix*520 + \n",
        "model.onehundredfiftyseven*250 + \n",
        "model.onehundredfiftyeight*250 + \n",
        "model.onehundredfiftynine*220 + \n",
        "model.onehundredsixty*250 + \n",
        "model.onehundredsixtyone*230 + \n",
        "model.onehundredsixtytwo*180 + \n",
        "model.onehundredsixtythree*200 + \n",
        "model.onehundredsixtyfour*115 + \n",
        "model.onehundredsixtyfive*135 + \n",
        "model.onehundredsixtysix*340 + \n",
        "model.onehundredsixtyseven*440 + \n",
        "model.onehundredsixtyeight*480 + \n",
        "model.onehundredsixtynine*440 + \n",
        "model.onehundredseventy*410 + \n",
        "model.onehundredseventyone*420 + \n",
        "model.onehundredseventytwo*440 + \n",
        "model.onehundredseventythree*460 + \n",
        "model.onehundredseventyfour*540 + \n",
        "model.onehundredseventyfive*290 + \n",
        "model.onehundredseventysix*130 + \n",
        "model.onehundredseventyseven*135 + \n",
        "model.onehundredseventyeight*105 + \n",
        "model.onehundredseventynine*135 <= sodium_b)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "v8hXsuKvnz48",
        "outputId": "3e816247-3e77-4af7-a1f7-ab14b4bfbf8b",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "source": [
        "from pyomo.environ import *\n",
        "\n",
        "#objective function\n",
        "model.points = Objective(\n",
        "    expr = model.zero*9 + \n",
        "model.one*8 + \n",
        "model.two*7 + \n",
        "model.three*7 + \n",
        "model.four*7 + \n",
        "model.five*7 + \n",
        "model.six*7 + \n",
        "model.seven*8 + \n",
        "model.eight*10 + \n",
        "model.nine*9 + \n",
        "model.ten*10 + \n",
        "model.eleven*13 + \n",
        "model.twelve*14 + \n",
        "model.thirteen*12 + \n",
        "model.fourteen*12 + \n",
        "model.fifteen*12 + \n",
        "model.sixteen*12 + \n",
        "model.seventeen*12 + \n",
        "model.eighteen*15 + \n",
        "model.nineteen*12 + \n",
        "model.twenty*12 + \n",
        "model.twentyone*14 + \n",
        "model.twentytwo*15 + \n",
        "model.twentythree*17 + \n",
        "model.twentyfour*10 + \n",
        "model.twentyfive*11 + \n",
        "model.twentysix*10 + \n",
        "model.twentyseven*11 + \n",
        "model.twentyeight*14 + \n",
        "model.twentynine*10 + \n",
        "model.thirty*11 + \n",
        "model.thirtyone*12 + \n",
        "model.thirtytwo*11 + \n",
        "model.thirtythree*13 + \n",
        "model.thirtyfour*16 + \n",
        "model.thirtyfive*15 + \n",
        "model.thirtysix*14 + \n",
        "model.thirtyseven*14 + \n",
        "model.thirtyeight*14 + \n",
        "model.thirtynine*14 + \n",
        "model.forty*17 + \n",
        "model.fortyone*14 + \n",
        "model.fortytwo*14 + \n",
        "model.fortythree*16 + \n",
        "model.fortyfour*17 + \n",
        "model.fortyfive*19 + \n",
        "model.fortysix*15 + \n",
        "model.fortyseven*18 + \n",
        "model.fortyeight*9 + \n",
        "model.fortynine*10 + \n",
        "model.fifty*19 + \n",
        "model.fiftyone*10 + \n",
        "model.fiftytwo*8 + \n",
        "model.fiftythree*14 + \n",
        "model.fiftyfour*9 + \n",
        "model.fiftyfive*17 + \n",
        "model.fiftysix*10 + \n",
        "model.fiftyseven*19 + \n",
        "model.fiftyeight*10 + \n",
        "model.fiftynine*10 + \n",
        "model.sixty*16 + \n",
        "model.sixtyone*14 + \n",
        "model.sixtytwo*10 + \n",
        "model.sixtythree*12 + \n",
        "model.sixtyfour*20 + \n",
        "model.sixtyfive*7 + \n",
        "model.sixtysix*9 + \n",
        "model.sixtyseven*7 + \n",
        "model.sixtyeight*12 + \n",
        "model.sixtynine*14 + \n",
        "model.seventy*11 + \n",
        "model.seventyone*8 + \n",
        "model.seventytwo*10 + \n",
        "model.seventythree*14 + \n",
        "model.seventyfour*29 + \n",
        "model.seventyfive*4 + \n",
        "model.seventysix*1 + \n",
        "model.seventyseven*1 + \n",
        "model.seventyeight*9 + \n",
        "model.seventynine*12 + \n",
        "model.eighty*22 + \n",
        "model.eightyone*15 + \n",
        "model.eightytwo*11 + \n",
        "model.eightythree*6 + \n",
        "model.eightyfour*11 + \n",
        "model.eightyfive*13 + \n",
        "model.eightysix*16 + \n",
        "model.eightyseven*12 + \n",
        "model.eightyeight*10 + \n",
        "model.eightynine*9 + \n",
        "model.ninety*12 + \n",
        "model.ninetyone*11 + \n",
        "model.ninetytwo*14 + \n",
        "model.ninetythree*12 + \n",
        "model.ninetyfour*15 + \n",
        "model.ninetyfive*14 + \n",
        "model.ninetysix*17 + \n",
        "model.ninetyseven*8 + \n",
        "model.ninetyeight*11 + \n",
        "model.ninetynine*17 + \n",
        "model.onehundred*19 + \n",
        "model.onehundredone*18 + \n",
        "model.onehundredtwo*7 + \n",
        "model.onehundredthree*9 + \n",
        "model.onehundredfour*10 + \n",
        "model.onehundredfive*8 + \n",
        "model.onehundredsix*13 + \n",
        "model.onehundredseven*3 + \n",
        "model.onehundredeight*4 + \n",
        "model.onehundrednine*0 + \n",
        "model.onehundredten*0 + \n",
        "model.onehundredeleven*4 + \n",
        "model.onehundredtwelve*3 + \n",
        "model.onehundredthirteen*4 + \n",
        "model.onehundredfourteen*5 + \n",
        "model.onehundredfifteen*4 + \n",
        "model.onehundredsixteen*0 + \n",
        "model.onehundredseventeen*5 + \n",
        "model.onehundredeighteen*4 + \n",
        "model.onehundrednineteen*5 + \n",
        "model.onehundredtwenty*4 + \n",
        "model.onehundredtwentyone*4 + \n",
        "model.onehundredtwentytwo*4 + \n",
        "model.onehundredtwentythree*6 + \n",
        "model.onehundredtwentyfour*0 + \n",
        "model.onehundredtwentyfive*7 + \n",
        "model.onehundredtwentysix*6 + \n",
        "model.onehundredtwentyseven*6 + \n",
        "model.onehundredtwentyeight*6 + \n",
        "model.onehundredtwentynine*5 + \n",
        "model.onehundredthirty*6 + \n",
        "model.onehundredthirtyone*7 + \n",
        "model.onehundredthirtytwo*0 + \n",
        "model.onehundredthirtythree*8 + \n",
        "model.onehundredthirtyfour*7 + \n",
        "model.onehundredthirtyfive*8 + \n",
        "model.onehundredthirtysix*7 + \n",
        "model.onehundredthirtyseven*6 + \n",
        "model.onehundredthirtyeight*7 + \n",
        "model.onehundredthirtynine*9 + \n",
        "model.onehundredforty*9 + \n",
        "model.onehundredfortyone*11 + \n",
        "model.onehundredfortytwo*0 + \n",
        "model.onehundredfortythree*12 + \n",
        "model.onehundredfortyfour*11 + \n",
        "model.onehundredfortyfive*12 + \n",
        "model.onehundredfortysix*11 + \n",
        "model.onehundredfortyseven*9 + \n",
        "model.onehundredfortyeight*11 + \n",
        "model.onehundredfortynine*15 + \n",
        "model.onehundredfifty*0 + \n",
        "model.onehundredfiftyone*17 + \n",
        "model.onehundredfiftytwo*14 + \n",
        "model.onehundredfiftythree*16 + \n",
        "model.onehundredfiftyfour*14 + \n",
        "model.onehundredfiftyfive*12 + \n",
        "model.onehundredfiftysix*14 + \n",
        "model.onehundredfiftyseven*12 + \n",
        "model.onehundredfiftyeight*11 + \n",
        "model.onehundredfiftynine*11 + \n",
        "model.onehundredsixty*11 + \n",
        "model.onehundredsixtyone*11 + \n",
        "model.onehundredsixtytwo*7 + \n",
        "model.onehundredsixtythree*13 + \n",
        "model.onehundredsixtyfour*5 + \n",
        "model.onehundredsixtyfive*10 + \n",
        "model.onehundredsixtysix*24 + \n",
        "model.onehundredsixtyseven*19 + \n",
        "model.onehundredsixtyeight*19 + \n",
        "model.onehundredsixtynine*19 + \n",
        "model.onehundredseventy*18 + \n",
        "model.onehundredseventyone*18 + \n",
        "model.onehundredseventytwo*18 + \n",
        "model.onehundredseventythree*19 + \n",
        "model.onehundredseventyfour*28 + \n",
        "model.onehundredseventyfive*13 + \n",
        "model.onehundredseventysix*6 + \n",
        "model.onehundredseventyseven*5 + \n",
        "model.onehundredseventyeight*5 + \n",
        "model.onehundredseventynine*6, sense=minimize\n",
        "    )\n",
        "\n",
        "#took out the .write to get more room on my screen\n",
        "SolverFactory(SOLVER, executable=EXECUTABLE).solve(model)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "{'Problem': [{'Name': 'unknown', 'Lower bound': -inf, 'Upper bound': inf, 'Number of objectives': 1, 'Number of constraints': 12, 'Number of variables': 181, 'Number of nonzeros': 775, 'Sense': 'minimize'}], 'Solver': [{'Status': 'ok', 'Termination condition': 'other', 'Statistics': {'Branch and bound': {'Number of bounded subproblems': 0, 'Number of created subproblems': 0}}, 'Error rc': 0, 'Time': 0.012289047241210938}]}"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 32
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "a3J5GkL-GuX-"
      },
      "source": [
        "## Model 2 Results\n",
        "\n",
        "Here, we output the models results and the weight watchers points. It is common to NOT get a result as the model is unable to work; we have a strict sodium limit as per the CDC guidelines and the menu is high in salt. Thus, higher calorie diets typically can't work. This is especially true when we make the diet more realistic and require dinner/breakfast items."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "aUMF4JlS_G3U",
        "outputId": "14a27086-cf95-47f5-b2ef-fe04d2e90e1e",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 992
        }
      },
      "source": [
        "#printing model results and weight watchers points\n",
        "SolverFactory(SOLVER, executable=EXECUTABLE).solve(model).write()\n",
        "print(\" \")\n",
        "print(\"Weight Watchers Points: \" + str(model.points()))"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "# ==========================================================\n",
            "# = Solver Results                                         =\n",
            "# ==========================================================\n",
            "# ----------------------------------------------------------\n",
            "#   Problem Information\n",
            "# ----------------------------------------------------------\n",
            "Problem: \n",
            "- Name: unknown\n",
            "  Lower bound: -inf\n",
            "  Upper bound: inf\n",
            "  Number of objectives: 1\n",
            "  Number of constraints: 12\n",
            "  Number of variables: 181\n",
            "  Number of nonzeros: 775\n",
            "  Sense: minimize\n",
            "# ----------------------------------------------------------\n",
            "#   Solver Information\n",
            "# ----------------------------------------------------------\n",
            "Solver: \n",
            "- Status: ok\n",
            "  Termination condition: other\n",
            "  Statistics: \n",
            "    Branch and bound: \n",
            "      Number of bounded subproblems: 0\n",
            "      Number of created subproblems: 0\n",
            "  Error rc: 0\n",
            "  Time: 0.011943578720092773\n",
            " \n",
            "ERROR: evaluating object as numeric value: zero\n",
            "        (object: <class 'pyomo.core.base.var.SimpleVar'>)\n",
            "    No value for uninitialized NumericValue object zero\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "error",
          "ename": "ValueError",
          "evalue": "ignored",
          "traceback": [
            "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
            "\u001b[0;31mValueError\u001b[0m                                Traceback (most recent call last)",
            "\u001b[0;32m<ipython-input-33-672d6ef87eca>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[1;32m      2\u001b[0m \u001b[0mSolverFactory\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mSOLVER\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mexecutable\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mEXECUTABLE\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msolve\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mmodel\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mwrite\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      3\u001b[0m \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\" \"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 4\u001b[0;31m \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"Weight Watchers Points: \"\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0mstr\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mmodel\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mpoints\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
            "\u001b[0;32m/usr/local/lib/python3.6/dist-packages/pyomo/core/base/expression.py\u001b[0m in \u001b[0;36m__call__\u001b[0;34m(self, exception)\u001b[0m\n\u001b[1;32m     52\u001b[0m         \u001b[0;32mif\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mexpr\u001b[0m \u001b[0;32mis\u001b[0m \u001b[0;32mNone\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     53\u001b[0m             \u001b[0;32mreturn\u001b[0m \u001b[0;32mNone\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 54\u001b[0;31m         \u001b[0;32mreturn\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mexpr\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mexception\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mexception\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     55\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     56\u001b[0m     \u001b[0;32mdef\u001b[0m \u001b[0mis_named_expression_type\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;32mpyomo/core/expr/numeric_expr.pyx\u001b[0m in \u001b[0;36mpyomo.core.expr.numeric_expr.ExpressionBase.__call__\u001b[0;34m()\u001b[0m\n",
            "\u001b[0;32m/usr/local/lib/python3.6/dist-packages/pyomo/core/expr/visitor.py\u001b[0m in \u001b[0;36mevaluate_expression\u001b[0;34m(exp, exception, constant)\u001b[0m\n\u001b[1;32m   1055\u001b[0m         \u001b[0mvisitor\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0m_EvaluationVisitor\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1056\u001b[0m     \u001b[0;32mtry\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 1057\u001b[0;31m         \u001b[0;32mreturn\u001b[0m \u001b[0mvisitor\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdfs_postorder_stack\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mexp\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   1058\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1059\u001b[0m     except ( TemplateExpressionError, ValueError, TypeError,\n",
            "\u001b[0;32m/usr/local/lib/python3.6/dist-packages/pyomo/core/expr/visitor.py\u001b[0m in \u001b[0;36mdfs_postorder_stack\u001b[0;34m(self, node)\u001b[0m\n\u001b[1;32m    585\u001b[0m                 \u001b[0m_sub\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0m_argList\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0m_idx\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    586\u001b[0m                 \u001b[0m_idx\u001b[0m \u001b[0;34m+=\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 587\u001b[0;31m                 \u001b[0mflag\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mvalue\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mvisiting_potential_leaf\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0m_sub\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    588\u001b[0m                 \u001b[0;32mif\u001b[0m \u001b[0mflag\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    589\u001b[0m                     \u001b[0m_result\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mappend\u001b[0m\u001b[0;34m(\u001b[0m \u001b[0mvalue\u001b[0m \u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;32m/usr/local/lib/python3.6/dist-packages/pyomo/core/expr/visitor.py\u001b[0m in \u001b[0;36mvisiting_potential_leaf\u001b[0;34m(self, node)\u001b[0m\n\u001b[1;32m    963\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    964\u001b[0m         \u001b[0;32mif\u001b[0m \u001b[0mnode\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mis_numeric_type\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 965\u001b[0;31m             \u001b[0;32mreturn\u001b[0m \u001b[0;32mTrue\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mvalue\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mnode\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    966\u001b[0m         \u001b[0;32melif\u001b[0m \u001b[0mnode\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mis_logical_type\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    967\u001b[0m             \u001b[0;32mreturn\u001b[0m \u001b[0;32mTrue\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mvalue\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mnode\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;32mpyomo/core/expr/numvalue.pyx\u001b[0m in \u001b[0;36mpyomo.core.expr.numvalue.value\u001b[0;34m()\u001b[0m\n",
            "\u001b[0;32mpyomo/core/expr/numvalue.pyx\u001b[0m in \u001b[0;36mpyomo.core.expr.numvalue.value\u001b[0;34m()\u001b[0m\n",
            "\u001b[0;31mValueError\u001b[0m: No value for uninitialized NumericValue object zero"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "UBC0o82oWN1z"
      },
      "source": [
        "# Save the model \n",
        "model.write(\"/content/model.lp\", io_options={'symbolic_solver_labels': True})\n",
        "\n",
        "# Generate the file \"sensit.sen\", this contains the report we want to see\n",
        "!/usr/bin/glpsol -m /content/model.lp --lp --ranges sensit.sen"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "3mCgL6W-WOff"
      },
      "source": [
        "# Display the contents of the report: (this shows the sensitivity analysis report)\n",
        "!cat /content/sensit.sen"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "4nG2kCOOVb18"
      },
      "source": [
        "#looping through variable objects in the model and accessing their values\n",
        "\n",
        "#initializing lists\n",
        "product_id_list = []\n",
        "quantity_list = []\n",
        "\n",
        "for v in model.component_objects(Var, active=True):\n",
        "    varobject = getattr(model, str(v))\n",
        "    for index in varobject:\n",
        "        if varobject[index].value == 0:\n",
        "          continue\n",
        "        elif varobject[index].value == None:\n",
        "          continue  \n",
        "        else:\n",
        "#v is a pyomo simplevar type. printing it out then retrieving its contents and input into a list\n",
        "#also gathering the quantity from the model as well into alist\n",
        "          old_stdout = sys.stdout \n",
        "          sys.stdout = buffer = io.StringIO()\n",
        "          print(v)\n",
        "          sys.stdout = old_stdout     \n",
        "          whatWasPrinted = buffer.getvalue()\n",
        "          product_id_list.append(whatWasPrinted.replace(\"\\n\", \"\"))\n",
        "          quantity_list.append(varobject[index].value)\n",
        "  \n",
        "product_dict = {'food_drink_id':product_id_list,\n",
        "                'quantity':quantity_list}\n",
        "\n",
        "#making a dataframe from dict\n",
        "answer_df = pd.DataFrame(product_dict)\n",
        "\n",
        "#merging the original df and the new df for the answer df\n",
        "answer_df2 = answer_df.merge(df, how='inner', on = 'food_drink_id')\n",
        "answer_df2 = answer_df2[['Food or Drink', 'quantity']]\n",
        "answer_df2.head(100)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "NslhzhEibyBP"
      },
      "source": [
        "# Conclusion\n",
        "\n",
        "There is a huge difference between the two models. The second model is much more realistic as it allows for an actual dinner/breakfast and limits rediculous items like syrup. This allows for a more controlled chaos instead of the amalganation of random offerings from the first model. Whats great is that we didn't make our diet unhealthier with these adjustments aswell. Furthermore, we learned that not everyone can benefit from eating only Wienersschniztel whilst doing our Healthy-IIFYM due to the sodium constraint; sometimes its impossible to balance the protein and sodium constraint! \n",
        "\n",
        "Overall, we were pleased with our blended IIFYM + CDC Health Guidlines as it allows for one to still be healthy and lose weight with this diet!\n",
        "\n",
        "# Learnings\n",
        "\n",
        "*   Diets don't have to be insanely restrictive like cutting out carbs as long as they are data driven! With our diet, they are free to eat whatever they wanted as long as its within their calorie goals and their gurenteed to lose weight!\n",
        "*   Wienerschniztal (and fast food) is insanely unhealthy! Our model failed plenty of times.\n",
        "*   We should pay attention to \"micros\" as well! Things like sodium are important to keep an eye on to maintain good health; not many diets in our research payed attention to micros\n",
        "*I would suggest inputting all fast food menus alongside a column indicating the fast food place. Run the model and output the resulting answer dataframe; would be interesting to see which fast food place has the best items\n",
        "*Perhaps eliminate usage of Weight Watchers points and instead focus on minimizing price; realistically, people take price into consideration as well for their purchases\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Yt7OI3R4dtFG"
      },
      "source": [
        "model.break_const = Constraint(expr = \n",
        "model.eightynine + \n",
        "model.ninety + \n",
        "model.ninetyone + \n",
        "model.ninetytwo + \n",
        "model.ninetythree + \n",
        "model.ninetyfour + \n",
        "model.ninetyfive + \n",
        "model.ninetysix + \n",
        "model.ninetyseven + \n",
        "model.ninetyeight + \n",
        "model.ninetynine + \n",
        "model.onehundred + \n",
        "model.onehundredone + \n",
        "model.onehundredtwo + \n",
        "model.onehundredthree + \n",
        "model.onehundredfour + \n",
        "model.onehundredfive + \n",
        "model.onehundredsix >= 1)\n",
        "\n",
        "model.din_const = Constraint(expr = \n",
        "model.zero +\n",
        "model.one + \n",
        "model.two + \n",
        "model.three + \n",
        "model.four + \n",
        "model.five + \n",
        "model.six + \n",
        "model.seven + \n",
        "model.eight + \n",
        "model.nine + \n",
        "model.ten + \n",
        "model.eleven + \n",
        "model.twelve + \n",
        "model.thirteen + \n",
        "model.fourteen + \n",
        "model.fifteen + \n",
        "model.sixteen + \n",
        "model.seventeen + \n",
        "model.eighteen + \n",
        "model.nineteen + \n",
        "model.twenty + \n",
        "model.twentyone + \n",
        "model.twentytwo + \n",
        "model.twentythree + \n",
        "model.twentyfour + \n",
        "model.twentyfive + \n",
        "model.twentysix + \n",
        "model.twentyseven + \n",
        "model.twentyeight + \n",
        "model.twentynine + \n",
        "model.thirty + \n",
        "model.thirtyone + \n",
        "model.thirtytwo + \n",
        "model.thirtythree + \n",
        "model.thirtyfour + \n",
        "model.thirtyfive + \n",
        "model.thirtysix + \n",
        "model.thirtyseven + \n",
        "model.thirtyeight + \n",
        "model.thirtynine + \n",
        "model.forty + \n",
        "model.fortyone + \n",
        "model.fortytwo + \n",
        "model.fortythree + \n",
        "model.fortyfour + \n",
        "model.fortyfive + \n",
        "model.fortysix + \n",
        "model.fortyseven + \n",
        "model.fortyeight + \n",
        "model.fortynine + \n",
        "model.fifty + \n",
        "model.fiftyone + \n",
        "model.fiftytwo + \n",
        "model.fiftythree + \n",
        "model.fiftyfour + \n",
        "model.fiftyfive + \n",
        "model.fiftysix + \n",
        "model.fiftyseven + \n",
        "model.fiftyeight + \n",
        "model.fiftynine + \n",
        "model.sixty + \n",
        "model.sixtyone + \n",
        "model.sixtytwo + \n",
        "model.sixtythree + \n",
        "model.sixtyfour + \n",
        "model.sixtyfive + \n",
        "model.sixtysix + \n",
        "model.sixtyseven + \n",
        "model.sixtyeight + \n",
        "model.sixtynine + \n",
        "model.seventy + \n",
        "model.seventyone + \n",
        "model.seventytwo + \n",
        "model.seventythree + \n",
        "model.seventyfour >= 1)\n",
        "\n",
        "#dataframe of just foods, no liquid\n",
        "#all liquids are 108+ so its an easy cut\n",
        "new_df = df.copy()\n",
        "new_df['row_id'] = df.index\n",
        "new_df = new_df[(new_df.row_id >= 157)]\n",
        "#new_df2 = new_df[(new_df.row_id <= 107)]\n",
        "\n",
        "#new_df = pd.concat([new_df1, new_df2])\n",
        "\n",
        "#new_df = new_df[(new_df.Calories <= 300)]\n",
        "\n",
        "len(new_df)\n",
        "\n",
        "#Loop we used to automate the writing of the hard code for the constraint\n",
        "#borrowing aboves loop to rewrite constraint; below is an example\n",
        "\n",
        "constraint_list = list()\n",
        "for x in new_df.values:\n",
        "  hard_coded_constraint = \"model.\" + str(x[8]) + \" + \" \n",
        "  constraint_list.append(hard_coded_constraint)\n",
        "\n",
        "for x in constraint_list:\n",
        "    con = x.replace(\"'\", \"\")\n",
        "    print(con)\n",
        "    #break"
      ],
      "execution_count": null,
      "outputs": []
    }
  ]
}