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**Unformatted text preview: **P is infeasible. Provide a certiFcate that proves that P is infeasible using ±arkas’ lemma. (Be sure to clearly 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 to-x 1-x 2 ≤ -3 x 1-x 2 ≤ -2 x 1 +2 x 2 ≤ 1 x 1 , x 2 ≥ 5 Q4. For the LP Maximize a + 3 b + 2 c + d subject to a-2 b + 3 c + 3 d ≤ 7 2 a + b + c + 4 d ≤ 10 4 a + b + 3 c-d ≤ 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. 6 Q5. Prove Farkas’ Lemma from class. 7 (This page is intentionally left blank.)...

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