@@ -1494,33 +1494,27 @@ u_1 = 0, leading to v_1 = 12, u_2 = 6, v_2 = 18, u_3 = -3, and v_3 = 37.
1494
1494
1495
1495
### - ** Updated solution** :
1496
1496
1497
- - $x_ {31} = 10$, $x_ {21} = 10$, $x_ {22} = 130$, $x_ {32} = 0$.
1497
+ ### - $x_ {31} = 10$, $x_ {21} = 10$, $x_ {22} = 130$, $x_ {32} = 0$.
1498
1498
1499
- - Total cost increases to ** 9820** due to an incorrect loop adjustment in manual calculations.
1499
+ ### - Total cost increases to [ ** 9820** ] ( ) due to an incorrect loop adjustment in manual calculations.
1500
1500
1501
1501
<br >
1502
1502
1503
1503
### [ Step 3] ( ) : Rechecking Optimality:
1504
1504
1505
1505
### - ** Recalculated multipliers** (after correction)
1506
1506
1507
- - $u =$, $v =$.
1507
+ ### - $u =$, $v =$.
1508
1508
1509
1509
### - ** New reduced costs** :
1510
1510
1511
- - $\bar{c} _ {12} = -4$, $\bar{c} _ {13} = -6$, $\bar{c} _ {23} = -2$, $\bar{c} _ {31} = 0$.
1511
+ ### - c̄₁₂ = -4, c̄₁₃ = -6, c̄₂₃ = -2, c̄₃₁ = 0
1512
1512
1513
- - $ \bar{c}_ {12} = -4$, $\bar{c}_ {13} = -6$, $\bar{c}_ {23} = -2$, $\bar{c}_ {31} = 0$
1513
+ $$ \bar{c}_{12} = -4 $$ , $$ \bar{c}_{13} = -6 $$ , $$ \bar{c}_{23} = -2 $$ , $$ \bar{c}_{31} = 0 $$ .
1514
1514
1515
- - ![ equation ] ( https://latex.codecogs.com/png.image?\bar{c}_{12}=-4,\ \bar{c} _ {13}=-6,\ \bar{c} _ {23}=-2,\ \bar{c} _ {31}=0)
1515
+ - Remaining negative reduced costs necessitate further iterations.
1516
1516
1517
- c̄₁₂ = -4, c̄₁₃ = -6, c̄₂₃ = -2, c̄₃₁ = 0
1518
1517
1519
- \bar{c}_ {12} = -4,\quad \bar{c}_ {13} = -6,\quad \bar{c}_ {23} = -2,\quad \bar{c}_ {31} = 0
1520
-
1521
- $$ \bar{c}_{12} = -4,\quad \bar{c}_{13} = -6,\quad \bar{c}_{23} = -2,\quad \bar{c}_{31} = 0 $$
1522
-
1523
- $\bar{c}_ {12} = -4,\quad \bar{c}_ {13} = -6,\quad \bar{c}_ {23} = -2,\quad \bar{c}_ {31} = 0$
1524
1518
1525
1519
1526
1520
0 commit comments