OPERATIONS RESEARCH I

HOMEWORK

In this homework, you are going to randomly generate a linear programming model. Each group must have a different LP model. If two or more groups provide the same model, they will get 0 (zero) points form this homework. The models should not be obtained from another resource. Turn it in software will be used to check originality of your models.

This model should satisfy the following restrictions :

The objective function can be maximization or minimization.

The LP must have at least three decision variables.

The LP must have at least three constraints.

1. Solve the LP you create by using the Simplex Method. You can use Big-M or Two-Phase Method if needed. Show each iteration in detail. You should have at least 2 iterations and at most five iterations. If your model is not obeying this rule, please change your model and randomly generate a new model. Make sure that you obtain a single optimal solution.

2. Indicate clearly the optimal basic and nonbasic variables and their values and write the reduced cost of each optimal nonbasic variable.

3. Find the dual of the primal problem you have on hand.

4. Find the optimal dual solution by using the two methods you have learned in class.

5. Verify that your primal and dual solutions are indeed optimal using the Complementary Slackness theorem. Show your work clearly.

6. For the basic variables at the optimal solution, create your optimal tableau this time by using matrix operations.

7. Change the right-hand-side value of one of the constraints. Make sure that your current solution becomes infeasible and you apply the Dual Simplex Method to recover feasibility.

8. Change the objective function coefficient of one basic variable and one nonbasic variable if all nonbasic variables are not slack variables. If you do not have a nonbasic variable which is an original variable for your problem, then change the objective function coefficient of two basic variables. Make sure that your current solution becomes nonoptimal and you apply the Primal Simplex Method to recover optimality.

9. Add a new constraint into your model. Make sure that the new constraint is not satisfied by the current optimal solution and you apply the Dual Simplex Method to recover feasibility.

10. Add a new activity (a new decision variable) into your model. Make sure that your current solution becomes non-optimal and you apply the Primal Simplex Method to recover optimality.

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.)