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# Billings Company Linear Programming

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?

#### 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 ...

#### 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.

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