Homework 3

# Homework 3 - e62 Introduction to Optimization Prof Ben Van...

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Unformatted text preview: e62 Introduction to Optimization Prof. Ben Van Roy Spring 2008 April 17, 2008 Homework Assignment 3: Due April 25 Part A Consider the following linear program: maximize cT x 2 −1 −3 0 subject to −2 3 ≥ 0 5 x2 3 x1 −3 2 −8 a) Provide a vector c such that this linear program is feasible but has no optimal solution. b) Provide three diﬀerent values of c so that each will lead to a distinct optimal solution. c) Which among the following additional constraints would guarantee that the linear program is feasible and has an optimal solution for all vectors c? (1) x1 ≤ 6 (2) x2 ≥ 7 (3) 3x1 + 2x2 ≤ 20 (4) 3x1 + 2x2 ≥ 20 (5) x1 + 4x2 ≥ 0 d) Which among the following additional constraints would make that the linear program is infeasible? (1) x1 + 3x2 ≤ 2 (2) 2x1 + 3x2 ≤ 17 (3) 2x1 + 3x2 ≥ 17 (4) x1 − 2x2 ≥ 2 (5) x2 ≤ 0 Part B Do problems 11, 12, and 14 from Chapter 3. ...
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