1. Problem Set # 4 Maximize f(x) = 3x1 + 2 x2 subject to x1 ≤ 4 x1 + 3 x2 ≤ 15 2x1 + x2 ≤ 10 Problem 1 Solve these problems using the simplex tableau. Maximize f(x) = x1 - x2 + 2 x3 subject to x1 + x2 + 3x3 ≤ 15 2x1 - x2 + x3 ≤ 2 -x1 + x2 + x3 ≤ 4 Problem 2 1

2. Solve the following problems by the two-phase method: Problem 3 Problem 4  MAX 123 S.T. 123 123 13 fx= -x - 2x + x x + 3x +x 4 x + 2x - x 6 x + x 12     2x xx xxx S.T. x4x3x2 x f MIN 3 21 321 321  2    5     2

3. Problem 5 For the linear program Max f(X) = 3X 1 + 4X 2 S.T. 5X 1 + 4X 2 ≤ 20 3X 1 + 5X 2 ≤ 15 X 1 ≤ 3.5 X 2 ≤ 2 1.Formulate the dual problem and demonstrate that its solution can be read from the final simplex tableau of the primal problem 2.Perform a sensitivity analysis on the optimum solution. 3.Demonstrate complimentary slackness for the optimum solutions to the primal and dual problems 3

4.  2 2 5 432 3 21 321 321      x xx xxx xxxx f S.T. MIN Problem 6 For the linear program Solve using the Dual Simplex algorithm. 4