Problems:
Linear programming : Quantitative Methods for Business
Please provide the problem formulation in standard form along with your solution so I can understand how you did it. (e.g., Max 30x1 + 50x2 +20x3 etc...) with all the constraints also shown in this manner.
Better Products Inc. manufactures three products on two machines. In a typical week, 40 hours are available on each machine. The profit contribution and production time in hours per unit follows:
|
Category
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Product 1
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Product 2
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Product 3
|
|
Profit/unit
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$30
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$50
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$20
|
|
Machine 1 time/unit
|
0.5
|
2.0
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0.75
|
|
Machine 2 time/unit
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1.0
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1.0
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0.5
|
Two operators are required for machine 1; thus, 2 hours of labor must be scheduled for each hour of machine 1 time. Only one operator is required for machine 2. A maximum of 100 labor-hours is available for assignment to the machines during the coming week. Other production requirement are that product 1 cannot account for more than 50% of the units produced and that product 3 must account for at least 20% of the units produced
a. How many units of each product be produced to maximize the total profit contribution? What is the projected weekly profit associated with the solution?
b. How many hours of production time will be scheduled on each machine?
c. What is the value of an additional hour of labor?
d. Assume that labor capacity can be increased to 120 hours. Would you be interested in using the additional 20 hours available for the resource? Develop the optimal product mix assuming the extra hours are made available.