The purpose of this simulation project is to provide you with an opportunity to use the POM-QM for Windows software to solve a linear programming problem and perform sensitivity analysis.

POM-QM for Windows software

For this part of this project, you will need to use the POM software:

1. Read Appendix IV of the Operations Management (Heizer & Render, 2011) textbook.
2. Install and launch the POM-QM for Windows software and from the main menu select Module, and then Linear Programming.
   
   Note: You can retrieve the POM-QM for Windows software from either the CD-ROM that accompanied your Heizer and Render (2011) textbook.
3. Program the linear programming formulation for the problem below and solve it with the use of POM. (Refer to Appendix IV from the Heizer and Render (2011) textbook.) 
   
   Note: Do not program the non-negativity constraint, as this is already assumed by the software.

For additional support, please reference the POM-QM for Windows manual provided in this week’s Learning Resources.

Individual Project problem

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 as follows:

Maximise Z = 30X₁ + 40X₂ + 35X₃

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

With X₁, X₂, X₃ >= 0

Answer the following questions by looking at the solution.

What is the optimal production schedule for this firm? What is the profit contribution of each of these products?

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

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Answer: the solution file keeps the solution in Excel only,