@@ -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.
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14951495### - ** Updated solution** :
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1497- - $x_ {31} = 10$, $x_ {21} = 10$, $x_ {22} = 130$, $x_ {32} = 0$.
1497+ ### - $x_ {31} = 10$, $x_ {21} = 10$, $x_ {22} = 130$, $x_ {32} = 0$.
14981498
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.
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15031503### [ Step 3] ( ) : Rechecking Optimality:
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15051505### - ** Recalculated multipliers** (after correction)
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1507- - $u =$, $v =$.
1507+ ### - $u =$, $v =$.
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15091509### - ** New reduced costs** :
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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
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1513- - $ \bar{c}_ {12} = -4$, $\bar{c}_ {13} = -6$, $\bar{c}_ {23} = -2$, $\bar{c}_ {31} = 0$
1513+ $$ \bar{c}_{12} = -4 $$ , $$ \bar{c}_{13} = -6 $$ , $$ \bar{c}_{23} = -2 $$ , $$ \bar{c}_{31} = 0 $$ .
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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.
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1517- c̄₁₂ = -4, c̄₁₃ = -6, c̄₂₃ = -2, c̄₃₁ = 0
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1519- \bar{c}_ {12} = -4,\quad \bar{c}_ {13} = -6,\quad \bar{c}_ {23} = -2,\quad \bar{c}_ {31} = 0
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1521- $$ \bar{c}_{12} = -4,\quad \bar{c}_{13} = -6,\quad \bar{c}_{23} = -2,\quad \bar{c}_{31} = 0 $$
1522-
1523- $\bar{c}_ {12} = -4,\quad \bar{c}_ {13} = -6,\quad \bar{c}_ {23} = -2,\quad \bar{c}_ {31} = 0$
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