Carrington_hw9.docx - Nichelle\u2019Le Carrington IE 534 Linear Programming Homework 9 \u2022 Assigned on Friday \u2022 Due by 10:00 AM(CST on Friday \u2022

Carrington_hw9.docx - Nichelle’Le Carrington IE 534...

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Nichelle’Le Carrington IE 534 Linear Programming Homework 9 Assigned on Friday 11/06/2015. Due by 10:00 AM (CST) on Friday 11/20/2015. Homework submitted at 10:01 AM or later will not be accepted. Submission can be in hard copy or by email as a single pdf document to lzw [email protected] 1. (10 points) Use the algorithm described in Lecture 20 to find the Pareto frontier for the following LP. Plot the Pareto frontier on the ( ζ c , ζ d ) space. max ζ c = 53 x 1 + 22 x 2 92 x 3 217 x 4 6 x 5 max ζ d = 101 x 1 61 x 2 + 51 x 3 169 x 4 + 59 x 5 s . t . 86 x 1 + 57 x 2 + 71 x 3 120 x 4 + 26 x 5 89 125 x 1 40 x 2 + 129 x 3 2 x 4 106 x 5 76 159 x 1 + 69 x 2 + 67 x 3 16 x 4 + 142 x 5 46 144 x 1 + 82 x 2 + 119 x 3 160 x 4 81 x 5 2 x 1 , x 2 , x 3 , x 4 , x 5 0 . Matrix notation for program: 1 2 3 4 5 x x x x x x 89 76 46 2 b 53 22 92 217 6 T c 101 61 51 169 59 T d   86 57 71 120 26 125 40 129 2 106 159 69 67 16 142 144 82 119 160 81 A
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Step 0: Find the optimal solution for both objective functions separately. Matlab code for c   c = -[53,22,-92,-217,-6]'; A = [86,57,71,-120,26;125,-40,129,-2,-106;-159,69,67,-16,142;-144,82,119,-160,-81]; b = [89;76;46;2]; Aeq = []; beq = []; lx = [0,0,0,0,0]; ux = []; [x, zeta, flag] = linprog(c, A, b, Aeq, beq, lx, ux) Optimal Solution for c   x = 0.7470 0.4344 0.0000 0.0000 0.0000 zeta = -49.1466 flag = 1 Optimal solution for c * 49.1466 c ; 1 * 0.7470 x ; 2 * 0.4344 x ; 3 * 0.0000 x ; 4 * 0.0000 x ; 5 * 0.0000 x Matlab code for d   d = -[-101,-61,51,-169,59]’; A = [86,57,71,-120,26;125,-40,129,-2,-106;-159,69,67,-16,142;-144,82,119,-160,-81]; b = [89;76;46;2]; Aeq = []; beq = []; lx = [0,0,0,0,0]; ux = []; [x, zeta, flag] = linprog(d, A, b, Aeq, beq, lx, ux) Solution for d   x = 0.0000 0.0000 0.1796 0.0000 0.2392 zeta = -23.2730 flag = 1
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Optimal solution for d : * 23.2730 d
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