Question B.11

Each coffee table produced by Kevin Watson Designers nets the firm a profit of $9. Each bookcase yields a $12 profit. Watsons firm is small, and its resources limited. During any given production period (of 1 week), 10 gallons of varnish and 12 lengths of high-quality redwood are available. Each coffee table requires approximately 1 gallon of varnish and 1 length of redwood. Each bookcase takes 1 gallon of varnish and 2 lengths of wood.

Formulate Watsons production-mix decision as a linear programming problem and solve. How many tables and bookcases should be produced each week? What will the maximum profit be?

1. Solve

(Show your graph and the process how to get the answers for each question)

2. For problem B.11, if the profit for the coffee table is increased from $ 9 to $ 15, what is the new optimal solution? (also, you should show the process of how to get new optimal solution)

3. For problem B.11, if the lengths of high-quality redwood are increased from 12 to 16, what is the new optimal solution? (also, you should show the process of how to get new optimal solution)

Question B.3

Solve the following linear programming problem graphically:

Maximize profit = X + 10Y

Subject to: = 4X + 3Y less than / equals 36

2X + 4Y less than / equals 40

Y greater than / equals 3

X, Y greater than / equals 0