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Unformatted text preview: state how you are using ±arkas’ Lemma, e.g., by giving a statement of the Lemma.) min 6 x 1 +2 x 2 = z subject tox 1x 2 ≤ 3 x 1x 2 ≤ 2 x 1 +2 x 2 ≤ 1 x 1 , x 2 ≥ Brief Solution: This is similar to problem 6 of the in class exercise to Lecture 10. s 5 Q4. For the LP Maximize a + 3 b + 2 c + d subject to a2 b + 3 c + 3 d ≤ 7 2 a + b + c + 4 d ≤ 10 4 a + b + 3 cd ≤ 8 and a, b, c, d ≥ 0. State the dual minimization problem. Suppose you guess ( a, b, c, d ) = (0 , 42 / 5 , , 2 / 5) is optimal. Use complementary slackness to prove your guess and the solution to the dual problem is correct. Brief solution: This is similar to the in class exercise of Lecture 9. s 6 Q5. Prove Farkas’ Lemma from class. Brief solution: See Lecture 11. 7 (This page is intentionally left blank.)...
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 Spring '08
 Staff
 Math, Linear Programming, Optimization, Dual problem, Simplex algorithm, following linear program

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