t2key - MAT419 Linear Optimization Mar. 6, 2008 TEST 2 NAME...

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Unformatted text preview: MAT419 Linear Optimization Mar. 6, 2008 TEST 2 NAME KEY 1. Suppose the following LOP P has the final tableau, as shown. Max . z = 215 x 1 +68 x 2 − 209 x 3 s . t . 2 x 1 − x 3 ≤ 17 − x 1 +4 x 2 − 3 x 3 ≤ − 12 +5 x 2 +6 x 3 ≤ 26 & x 1 , x 2 , x 3 ≥ 7 − 4 0 3 − 1 0 0 63 − 8 7 − 1 − 2 0 0 7 83 0 6 12 7 0 140 0 336 0 854 203 0 7 12082 (a) Use only the final tableau to write the optimal solution x ∗ and corresponding dual optimal solution y ∗ . x = (63 , , 7) / 7 = (9 , , 1) y = (854 , 203 , 0) / 7 = (122 , 29 , 0) . (b) Prove (without solving P ) that your results from part (a) are correct. 2(9) − (1) ≤ 17 , − (9) + 4(0) − 3(1) ≤ − 12 , 5(0) + 6(1) ≤ 26 , and x 1 , x 2 , x 3 ≥ , so x is primal-feasible. 2(122) − (29) ≥ 215 , 4(29) + 5(0) ≥ 68 , − (122) − 3(29) + 6(0) ≥ − 209 , and y 1 , y 2 , y 3 ≥ , so y is dual-feasible....
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This note was uploaded on 02/24/2009 for the course MAT 18600 taught by Professor Hurlbert during the Spring '08 term at ASU.

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t2key - MAT419 Linear Optimization Mar. 6, 2008 TEST 2 NAME...

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