# hw4 - IE521 Advanced Optimization HW4 Due December 28(8:00...

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IE521 Advanced Optimization HW4 Due December 28 (8:00 AM) 1. (20 points) Consider the following LP. max 6 x 1 + 10 x 2 + 9 x 3 + 20 x 4 s.t. 4 x 1 + 9 x 2 + 7 x 3 + 10 x 4 600 x 1 + x 2 + 3 x 3 + 40 x 4 400 3 x 1 + 4 x 2 + 2 x 3 + x 4 500 x 1 ,x 2 ,x 3 ,x 4 0 Optimal solution to this LP is z = 2800 / 3 ,x 1 = 400 / 3 ,x 4 = 20 / 3 ,x 2 = x 3 = 0 and s 1 = s 2 = 0 ,s 3 = 280 / 3. (a) Write the dual of the LP. (b) Using complimentary slackness and the given optimal primal solution, ﬁnd the optimal dual solution. 2. (20 points) Consider the following LP: max 5 x 1 + 3 x 2 + x 3 s.t. 2 x 1 + x 2 + x 3 6 x 1 + 2 x 2 + x 3 7 x 1 ,x 2 ,x 3 0 Graphically solve the dual of this LP. Then use complementary slackness to solve this maxi- mization problem. 3. (20 points) Zales Jewelers uses rubies and sapphires to produce two types of rings. A type 1 ring requires 2 rubies, 3 sapphires, and 1 hour of jewelers labor. A type 2 ring requires 3 rubies, 2 sapphires, and 2 hours of jewelers labor. Each type 1 ring sells for \$400; type 2 sells for \$500.

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## This note was uploaded on 01/09/2012 for the course IE 521 taught by Professor Zelihaakça during the Fall '11 term at Fatih Üniversitesi.

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hw4 - IE521 Advanced Optimization HW4 Due December 28(8:00...

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