lecture 5 practice - U of Illinois MATH 482 Lecture 5 In...

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U. of Illinois MATH 482 Lecture 5 In class exercises The goal of this worksheet is to supplement the material in Lecture 5 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. Solve the following LP: minimize z = - 6 x 1 + 8 x 3 subject to - 3 x 1 + 3 x 2 + 2 x 3 + x 4 = 7 2 x 1 - x 3 + x 5 = 1 2 x 1 + x 2 - 3 x 3 + x 6 = 0 (a) Write down the tableau (using the obvious basis). (b) What is the basic feasible solution? What is the objective value at this basic feasible solution? (c) There is a column j with c j < 0. What variable x j is that associated to? 1
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2 (Q1 continued) (d) The ratio test says that in this column we look for the smallest positve b r /a rj and use column r to pivot. To explain this rule, note that if we make x j a little bigger than 0, the objective value drops. How big can we make
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lecture 5 practice - U of Illinois MATH 482 Lecture 5 In...

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