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# duality - Diet problem Plan a minimum cost menu using only...

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Diet problem: Plan a minimum cost menu using only milk, chicken and bread to satisfy minimum daily requirements for calcium and iron: Calcium Iron cost Milk 23 2 86 Chicken 0 24 109 Bread 5 11 60 min daily req. 10 12 min z = 86 m + 109 c + 60 b s . t . 23 m + 5 b 1 10 2 m + 24 c + 11 b 12 m,c,b 0 Pill manufacturer problem? 1

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min 86 M + 109 C + 60 B s . t . 2) 23 M + 5 B 10 3) 2 M + 24 C + 11 B 12 objective function value 80 . 90535 variable value reduced cost M 0 . 205761 0 C 0 15 . 17284 B 1 . 053498 0 row slack or surplus dual prices 2) 0 - 3 . 399177 3) 0 - 3 . 909465 max 10 X 1 + 12 X 2 s . t . 2) 23 X 1 + 2 X 2 86 3) 24 X 2 109 4) 5 X 1 + 11 X 2 60 objective function value 80 . 90535 variable value reduced cost X 1 3 . 399177 0 X 2 3 . 909465 0 row slack or surplus dual prices 2) 0 . 205761 3) 15 . 17284 0 4) 0 1 . 053498 2
Dakota example (6.5-6.6) x 1 = desks, x 2 = tables, x 3 = chairs. max z = 60 x 1 + 30 x 2 + 20 x 3 s . t . 8 x 1 + 6 x 2 + x 3 48 lumber 4 x 1 + 2 x 2 + 1 . 5 x 3 20 finishing 2 x 1 + 1 . 5 x 2 + 0 . 5 x 3 8 carpentry x 1 ,x 2 ,x 3 0 3

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Dakota example (6.5-6.6): max z = 60 x 1 + 30 x 2 + 20 x 3 s . t . 8 x 1 + 6 x 2 + x 3 48 4 x 1 + 2 x 2 + 1 . 5 x 3 20 2 x 1 + 1 . 5 x 2 + 0 . 5 x 3 8 x 1 ,x 2
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duality - Diet problem Plan a minimum cost menu using only...

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