Problem 4 Linear Programming

Lakeside Boatworks is planning to manufacture three types of molded fiberglass recreational boatsa fishing (bass) boat, a ski boat, and a small speedboat. The estimated selling price and variable cost for each type of boat are summarized in the following table:

The company has incurred fixed costs of $2,800,000 to set up its manufacturing operation and begin production. Lakeside has also entered into agreements with several boat dealers in the region to provide a minimum of 70 bass boats, 50 ski boats, and 50 speedboats. Alternatively, the company is unsure of what actual demand will be, so it has decided to limit production to no more than 120 of any one boat. The company wants to determine the number of boats that it must sell to break even while minimizing its total variable cost.

(a) Formulate a linear programming model for this problem.

(b) Solve the model by using the computer.

Boat Variable Cost Selling Price Bass Ski Speed $12,500 8,500 13,700 $23,000 18,000 26,000