Billings Company Linear Programming
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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?
Prduction Times (hrs)
Marginal
Plants Doors Windows Capacity/wk
1 1 0 4 hr
2 0 2 12 hr
3 3 2 18 hr
Unit Profit $300 $500
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 solutions 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?
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Solution Summary
This posting provides solution to problems on optimal product mix for Billings Company and graphical solution to linear programming problem for maximizing total profit.
Solution Preview
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 ...
Purchase this Solution
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