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assign3 - CO 350 Assignment 3 Winter 2010 Due Friday...

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CO 350 Assignment 3 – Winter 2010 Due: Friday January 29 at 10:25 a.m. Solutions are due in drop box #9 (Section 1 and drop box #10 (Section 2) , outside MC 4066 by the due time. Use the appropriate slot for your section and surname. Please acknowledge all outside sources, as well as all collaboration, discussion, help, etc., in your submission. 0. Begin your assignment with the following: Last Name: (Print your last name.) First Name: (Print your “official” first name. No nicknames.) ID: (Print your UW student ID) Section: (Print your section number) Acknowledgments: 1. Write the dual of the LP problem: Max 2 x 1 + 3 x 2 + 4 x 3 + x 4 x 1 + 2 x 2 + x 3 + 3 x 4 = 3 x 1 x 2 x 3 + 2 x 4 7 x 1 , x 3 , 0 . 2. Prove the following version of the Duality Theorem. Let ( P ) be an LP problem in standard equality form and suppose that ( P ) and its dual both have feasible solutions. Then ( P ) has an optimal solution x * and its dual has an optimal solution y * having equal objective values.
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