LPP solution using POM

Program the linear programming formulation for the problem below and solve it with the use of POM (software).

A firm uses three machines in the manufacturing of three products:

? Each unit of product 1 requires three hours on machine 1, two hours on machine 2, and one hour on machine 3.

? Each unit of product 2 requires four hours on machine 1, one hour on machine 2, and three hours on machine 3.

? Each unit of product 3 requires two hours on machine 1, two hours on machine 2, and two hours on machine 3.

The contribution margin of the three products is $30, $40, and $35 per unit, respectively.

Available for scheduling are

? 90 hours of machine 1 time;

? 54 hours of machine 2 time; and

? 93 hours of machine 3 time.

The linear programming formulation of this problem is the following:

Maximize Z =30X1 + 40X2 + 35X3

3X1 + 4X2 + 2X3<=90
2X1 + 1X2 + 2X3<=54
X1 + 3X2 + 2X3<=93

With X1, X2, X3>= 0

4. Answer the following questions by looking at the solution

1. What is the optimal production schedule for this firm? What is the profit contribution of each of these products?
2. What is the marginal value of an additional hour of time on machine 1? Over what range of time is this marginal value valid?
3. What is the opportunity cost associated with product 1? What interpretation should be given to this opportunity cost?
4. How many hours are used for machine 3 with the optimal solution?
5. How much can the contribution margin for product 2 change before the current optimal solution is no longer optimal?

For POM software you can download it free from here: http://www.prenhall.com/weiss