LP Homework Set 3: Solving LP Problems with Geometric Approach and Simplex Algorithm, Assignments of Insurance law

Download LP Homework Set 3: Solving LP Problems with Geometric Approach and Simplex Algorithm and more Assignments Insurance law in PDF only on Docsity! MT 435 Homework Set 3 Due Monday, September 29, 2008 1. Consider the linear programming problem: Maximize z = 2x1 − 3x2 + 6x4 subject to : 3x1 +x2 +7x3 = 6 2x1 −3x2 −2x3 +3x4 = 2 where x1, x2, x3, x4 ≥ 0. a. By considering the column vectors and the geometric approach, determine all pairs of variables that can serve as feasible basic variables. b. One of your pairs should be x2, x4; write the problem in canonical form with x2 and x4 as basic variables. Remember to write the objective function in terms of only non-basic variables. c. Find the associated basic solution and the value of the objective function there. 2. Solve the following problem by hand using the simplex algorithm. Use the tableau format for displaying your work and be sure to state the final resolution of the problem. Maximize z = x1 + 3x2 − x3 subject to : x2 +4x3 ≤ 25 5x1 −4x2 +2x3 ≤ 80 3x1 −2x2 +x3 ≤ 52 where x1, x2, x3 ≥ 0. 1