hw7 - Math 171A: Linear Programming Instructor: Philip E....

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Math 171A: Linear Programming Instructor: Philip E. Gill Winter Quarter 2011 Homework Assignment #7 Due Friday February 25, 2011 Starred exercises require the use of Matlab . Exercise 7.1. * Consider the linear program of minimizing c T x subject to the general in- equalities Ax b , where A = - 1 - 3 - 1 1 0 - 3 0 1 - 2 - 2 - 3 1 1 5 1 , b = - 3 - 2 - 4 - 2 - 6 and c = - 5 - 5 3 . (a) Verify that x 0 = (1, 1 3 , 1) T is a vertex. What is the active set? (b) Perform one iteration of the simplex method (Algorithm 4.2 in the text) to obtain the next iterate x 1 . Verify that x 1 is feasible and that c T x 1 < c T x 0 . What is the active set at x 1 ? Show your work. Exercise 7.2. * Consider the Diet Problem of Assignment 5.2. Starting at the point x 0 at which constraints 1, 4, 5, 6, 9 and 14 are active, perform one iteration of the simplex method (Algorithm 4.2 in the text) to obtain the next iterate x 1 . Verify that
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hw7 - Math 171A: Linear Programming Instructor: Philip E....

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