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Homework 4

# Homework 4 - that are optimal e Consider the problem of...

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e62 Introduction to Optimization Spring 2008 Prof. Ben Van Roy April 24, 2008 Homework Assignment 4: Due May 2 PART A Consider a polyhedron P = { x | Ax = b, x 0 } . Suppose that the matrix A has dimensions m × n and that its rows are linearly independent. For each one of the following statements, state whether it is True or false. If true, explain why, perhaps using a diagram, else, provide a counterexample: a) If n = m + 1, then P has at most two basic feasible solutions. b) The set of all optimal solutions is bounded. c) At every optimal solution, no more than m variables can be positive. d) If there are several optimal solutions, then there exist at least two basic feasible solutions
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Unformatted text preview: that are optimal. e) Consider the problem of minimizing max { c T x,d T x } over the set P . If this problem has an optimal solution, it must have an optimal solution which is an extreme point of P . PART B Do problems 13, 15, and 16 from Chapter 3. NOTE : Download the necessary data ( Iris.xls ) from the course website. The Excel worksheet for problem 15 is large. Don’t print it out! You only need to answer the questions and provide a brief description of your steps. Grading Basis A(a) A(b) A(c) A(d) A(e) 13(a) 13(b) 15 16 TOTAL 8 8 8 8 8 10 10 20 20 100...
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