OPERATIONS RESEARCH I HOMEWORK You will randomly generate a linear programming model. Each student must have a different model. If two or more students models are the same, the students will get 0 (zero) points form this assignment. The models should not be obtained from another resource. 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. This homework will be done individually. You have to submit two files: A word document which includes your LP model written by using Equation editor. Your hand-written solution files (pdf, jpeg, etc.). If one of the files is missing, your homework will be graded over 50 points.