This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
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 tox 1x 2 ≤ 3 x 1x 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 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. 6 Q5. Prove Farkas’ Lemma from class. 7 (This page is intentionally left blank.)...
View
Full Document
 Spring '08
 Staff
 Math, Linear Programming, Optimization, Dual problem, Simplex algorithm, following linear program

Click to edit the document details