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Program the linear programming formulation for the problem below and solve it with the use of POM (software).
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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
- 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?
For POM software you can download it free from here: http://www.prenhall.com/weiss
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Solution Preview
Hi
Please find attached the answers to your questions. Hope you find them useful.
Regards
COMMENT FROM STUDENT:
1) What is S.T. in the solution refer to?
2) What is the minium …
