Firestone, headquartered in Akron, Ohio, has a plant in Florence, South Carolina, that manufactures two types of tires: SUV 225 radials and SUV 205 radials. Demand is high because of the recent recall of tires. Each batch of 100 SUV 225 radial tires requires 100 gal of synthetic plastic and 5 lb of rubber. Each batch of 100 SUV 205 radial tires requires 60 gal of synthetic plastic and 2.5 lb of rubber. Labor costs are $1 per tire for each type of tire. The manufacturer has weekly quantities available of 660 gal of synthetic plastic, $750 in capital, and 300 lb of rubber. The company estimates a profit of $3 on each SUV 225 radial and $2 on each SUV 205 radial.

a. How many of each type of tire should the company manufacture in order to maximize its profits?

b. Assume now that the manufacturer has the opportunity to sign a nice contract with a tire outlet store to deliver at least 500 SUV 225 radial tires and at least 300 SUV 205 radial tires. Should the manufacturer sign the contract? Support your recommendation.

c. If the manufacturer can obtain an additional 1000 gal of synthetic plastic for a total cost of $50, should he? Support your recommendation.