Math364 Homework 5: Optimization Problems - Prof. B. Krishnamoorthy, Assignments of Linear Algebra

Download Math364 Homework 5: Optimization Problems - Prof. B. Krishnamoorthy and more Assignments Linear Algebra in PDF only on Docsity! Math364 - HW 5 Due on Thursday, Feb 24 1 Principles of Optimization — Homework 5 • The total points (given in parentheses) add up to 160. You will be graded for 140 points (with the possibility of getting up to 20 points as extra credit). • This homework is due in class a week from today – on Thursday, Feb 24. 1. (30) This problem illustrates that one could get more than two basic feasible solutions (bfs’s) that are optimal. Use simplex method to describe all the optimal solutions of the following LP. max z = 2x1 + 3x2 + 5x3 + 4x4 s.t. x1 + 2x2 + 3x3 + x4 ≤ 5 x1 + x2 + 2x3 + 3x4 ≤ 3 x1, x2, x3, x4 ≥ 0 2. (20) WV-IMP Problem 3 from page 158. You must not pivot x1 into the basis in order to answer this question. 3. (30) WV-IMP Problem 1 from page 178 4. (30) WV-IMP Problem 5 from page 178. 5. (20) WV-IMP Problem 1 from page 189. 6. (30) WV-IMP Problem 17 from page 214.