hw2 ISYE 3133 - Engineering Optimization ISYE3133C Homework...

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Engineering Optimization ISYE3133C Homework assignment # 2: (due Monday February 18th at the beginning of the class, which means electronic submission will be automatically closed at 10:05AM and you should hand in the handwritten part at the beginning of the class) Remember that you are allowed to work with others, just let me know who you worked with. 1. a) Draw the feasible region of the following LP. max s . t . 3 x 1 + x 2 (1) (2) (3) 2 x 1 x 2 2 x 1 5 x 2 ≤ − 3 x 1 , x 2 0 b) Write the dual of the previous LP and draw the feasible region of the dual LP c) Indicate if the original problem or its dual are infeasible or unbounded. 2. Consider the following formulation for the heart valve problem (pg. 71 # 2): Variables: x i = amount of valves ordered from supplier i per month 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 a) Write the dual of the heart valve problem formulated above. (Hint: remember that is equivalent to b) The optimal (to the primal) is: with z = $6450. Use this optimal x j 700 x j ≥ − 700 x 1 = 700, x 2 = 700, x 3 = 50,
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solution to the primal and the rules of complementary slackness to solve the dual problem. (Find the optimal values of the dual variables and the objective function value.) c)
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hw2 ISYE 3133 - Engineering Optimization ISYE3133C Homework...

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