Question

LECTURE OF THE OPERATIONS RESEARCH I
You will randomly generate a linear programming model.
• Objective function should be a maximization problem.
• Model must have exactly three decision variables.
• Model must have two less-than equality (≤) constraints.
Please answer the following parts:
a) Take the dual of the primal problem you have on hand.
b) Solve the dual problem by using Graphical Solution Procedure. If the dual problem does not have a single optimal solution (or if the dual has unbounded/infeasible/multiple
optimal solution), go back to the starting point and change your initial model until you have one optimal solution for the dual problem.
c) By using the optimal dual solution, find the optimal primal problem by using Complementary Slackness Theorem. (Do not use Simplex Method to solve the primal problem. You must use complementary slackness theorem.)
d) Comment on the optimal solution of the primal problem. Calculate the values of slack variables. Which variables are basic at the optimal solution? Which variables are nonbasic
at the optimal solution?
e) For the basic variables at the optimal solution, create the optimal tableau by using matrix operations.

Answer 1