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lecture 7 practice

# lecture 7 practice - U of Illinois MATH 482 Lecture 7 In...

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U. of Illinois MATH 482 Lecture 7 In class exercises The goal of this worksheet is to supplement the material in Lecture 7 that introduces the simplex method. I hope this will help guide you through some of the Fner points of that lecture. Please feel free to ask questions at any time. 1. Use the two phase simplex method to solve the following problem: minimize z = x 1 - 5 x 3 subject to x 1 + 3 x 2 + 7 x 3 25 - 3 x 1 - 2 x 2 + 7 x 3 = - 5 2 x 1 + x 2 + 4 x 3 10 subject to x 2 , x 3 0 (so x 1 is not constrained). 1

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3 (Page intentionally left blank.) 2. Some general knowledge/sanity check discussion questions about the simplex method: (a) Can the lexicographic tie breaking rule ever fail? That is, can two rows end up being tied? (b) Can you prove that the lexicographic rule makes row 0 lexicograph- ically larger? (c) Can the auxiliary problem to an LP be unbounded? (d) Why is the column corresponding to

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lecture 7 practice - U of Illinois MATH 482 Lecture 7 In...

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