Problem:
The Billings Company makes home consturction products.
The company has 3 plants.
Plant 1 produces metal hardware
Plant 2 produces wood products
Plant 3 produces glass and does assembly for complex products
Billings wants to introduce two new products - a glass door and a bay window assembly.
The door requires plants 1 & 2. The bay window assembly requires plants 2 & 3
Should the company launch these products and if so, what should be the optimum product mix?
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Prduction Times (hrs)
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|
|
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Plants
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Doors
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Windows
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Capacity/wk
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1
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1
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0
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4 hr
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2
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0
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2
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12 hr
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3
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3
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2
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18 hr
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Unit Profit
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$300
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$500
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If D is the number of doors produced and W is the number of windows,
a. What is the equatiion for the total profit?
b. Give equations for the constraints that apply
c. If the constraints were given by
2W<=12
D <=4
3D + 2W <= 18
Graph the feasible region for the LP solution.
d. Describe how you now approach finding the optimum solution.
e. If the 3rd equation above was changed to 3D + 2W <= 17 because of safety constraints, the optimal sollutions obtained will be D = 2.333 and W = 5 Calculate the corresponding profit. Is this solution acceptable? If not how would you change the solution?