MAXIMIZE: Z = 3 X1 + 1 X2 + 3 X3 + X4 + X5 + X6 |
MAXIMIZE: Z = 3 X1 + 1 X2 + 3 X3 + 0 X4 + 0 X5 + 0 X6 + 0 X7 + 0 X8 + 0 X9 |
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subject to 2 X1 + 1 X2 + 1 X3 + 1 X4 + 0 X5 + 0 X6 = 2 |
subject to 2 X1 + 1 X2 + 1 X3 + 1 X4 + 1 X9 = 2 |
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X1, X2, X3, X4, X5, X6 ≥ 0 |
X1, X2, X3, X4, X5, X6, X7, X8, X9 ≥ 0 |
Tableau 1 |
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-1 |
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P7 |
-1 |
6 |
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Z |
-13 |
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-5 |
-5 |
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Tableau 2 |
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0.5 |
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0.5 |
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0.5 |
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1.5 |
2.5 |
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P7 |
-1 |
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Z |
-8 |
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1.5 |
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2.5 |
Tableau 3 |
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0.5 |
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P8 |
-1 |
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1.5 |
2.5 |
-0.5 |
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-0.5 |
P6 |
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1.33 |
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0.333 |
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-0.333 |
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0.333 |
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-0.333 |
Z |
-4 |
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-1.5 |
-2.5 |
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1.5 |
Tableau 4 |
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1 |
0.2 |
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0.6 |
-0.4 |
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-0.2 |
0.6 |
P3 |
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1.6 |
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0.6 |
1 |
-0.2 |
0.8 |
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0.4 |
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P6 |
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1.333 |
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0.333 |
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0.333 |
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-0.333 |
Z |
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Tableau 1 |
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0.6 |
-0.4 |
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P3 |
3 |
1.6 |
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0.6 |
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-0.2 |
0.8 |
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P6 |
0 |
1.333 |
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0.333 |
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-0.333 |
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1 |
Z |
5.4 |
0 |
1.4 |
0 |
1.2 |
1.2 |
0 |
The optimal solution value is Z = 5.4
X1 = 0.2
X2 = 0
X3 = 1.6
X4 = 0
X5 = 0
X6 = 1.3333333333333
Herein I used simplex method to derive optimal solution, I am not 100% sure whether this optimum solution is right but I did my best.
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