The Bookholder Company manufactures two types of bookcases out of oal and walnut. Model 01 requires 5 board feet of oak and 2 board feet of walnut. Model 02 requires 4 board feet of oak and 3 board feet of walnut. A profit of $75 is made on each Model 01 bookcase and a profit of $125 is made on each Model 02 bookcase. The company has a supply of 1000 board feet of oak and 600 board feet of walnut. The company has orders for 40 Model 01 bookcases and 50 Model 02 bookcases. These order indicate the minimum number the company must manufacture of each model.

a. Write the set of constraints.
b. Write the objective function.
c. Graph the set of constraints.
d. Determine the number of bookcases of each type the company should manufacture in order to maximize profits.
e. Determine the maximum profit.


I will be happy to critique your thinking. Constrants: min number of each, board feet of lumber.
Objective function: I would max profit.

5x + 4y < or = 1000

2x + 3y < or = 600

4x + 5y > or = 9x > or = 40

y > or = 50

I have solve them and graphed them but I am at a loss for the last two questions in the problem. It seems that these only figure out the wood but I need to figure out the profit. That is where it lost me. Can you help me and tell me if I did this wrong? Or what to do?

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