ISYE 3133 Homework2sol

ISYE 3133 Homework2sol - Engineering Optimization ISYE3133C...

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Engineering Optimization ISYE3133C Homework assignment # 2: Solutions 1. a) 0 1 2 3 4 0 1 2 3 4 5 x2 x1 x1>=0 x2>=0 2x1-x2<=2 -x1-5x2<=-3 b) min s . t . 2 y 1 3 y 2 (1) (2) (3) 2 y 1 y 2 3 y 1 5 y 2 1 y 1 , y 2 0
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c) The dual is infeasible hence the original is unbounded or is infeasible. Then as the original is feasible it is also unbounded. 0 1 2 3 4 0 1 2 3 4 5 y2 y1 y1>=0 y2>=0 2y1-y2>=3 -y1-5y2>=1
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2. a) First convert the problem to the dual of a normal max problem by multiplying the last 3 constraints by -1. You obtain: min z = 5 x 1 +4 x 2 +3 x 3 s.t. 0 . 4 x 1 +0 . 3 x 2 +0 . 2 x 3 500 (Buy enough large valves) 0 . 4 x 1 +0 . 35 x 2 +0 . 2 x 3 300 (Buy enough medium valves) 0 . 2 x 1 +0 . 35 x 2 +0 . 6 x 3 300 (Buy enough small valves) - x 1 ≥ - 700 (Supplier limits) - x 2 ≥ - 700 - x 3 ≥ - 700 x 1 , x 2 , x 3 0 We then obtain that its dual is: max w = 500 y 1 +300 y 2 +300 y 3 - 700 y 4 - 700 y 5 - 700 y 6 s.t. 0 . 4 y 1 +0 . 4 y 2 +0 . 2 y 3 - y 4 5 0 . 3
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ISYE 3133 Homework2sol - Engineering Optimization ISYE3133C...

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