Math482Test3Spring2011solns - UIUC MATH 482 Practice Test...

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UIUC MATH 482 Practice Test 3 (Spring 2011) Instructions: This test has 9 pages including this cover sheet. Answer 4 of the 5 problems given below. (I will grade all 5 problems and score you on the best 4.) Each problem is scored out of 5 points. This test is out of 20 points. Justify all of your steps to ensure full credit. No calculators or other aids are permitted. Write your name and ID below and on every page. Make your student ID available. NAME: STUDENT ID: 1
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2 1. Perform one iteration of the primal-dual algorithm on the fol- lowing primal linear program. Start with the dually feasible vector π = [0 , 1 / 4]. min x 1 +3 x 2 + x 3 = z subject to 2 x 1 - 3 x 2 + x 3 = 2 4 x 1 + x 3 = 6 x 1 , x 2 , x 3 0 What is the new π and the new J after the iteration? Solution: The dual linear program D is max 2 π 1 +6 π 2 subject to 2 π 1 +4 π 2 1 - 3 π 1 3 π 1 + π 2 1 π 1 , π 2 0 For the given π , only the first constraint is binding, so J = { 1 } .
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