##### Reference no: EM13304982

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:

- Read Appendix IV of the
*Operations Management* (Heizer & Render, 2011) textbook.
- 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.
- 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 = 30X_{1} + 40X_{2} + 35X_{3}

3X_{1} + 4X_{2} + 2X_{3} <= 90

2X_{1} + 1X_{2} + 2X_{3} <= 54

X_{1} + 3X_{2} + 2X_{3} <= 93

With X_{1}, X_{2}, X_{3} >= 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?

- What is the marginal value of an additional hour of time on machine 1? Over what range of time is this marginal value valid?
- What is the opportunity cost associated with product 1? What interpretation should be given to this opportunity cost?
- How many hours are used for machine 3 with the optimal solution?
- 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,