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. Ifthe dual problem does not have a single optimal solution (or if thedual has unbounded/infeasible/multiple
optimal solution), go back to the starting point and change yourinitial model until you have one optimal solution for the dualproblem.
c) By using the optimal dual solution, find the optimal primalproblem by using Complementary Slackness Theorem. (Do not useSimplex Method to solve the primal problem. You must usecomplementary slackness theorem.)
d) Comment on the optimal solution of the primal problem. Calculatethe values of slack variables. Which variables are basic at theoptimal solution? Which variables are nonbasic
at the optimal solution?
e) For the basic variables at the optimal solution, create theoptimal tableau by using matrix operations.
