Lakeside Boatworks is planning to manufacture three types of molded fiberglass recreational boats – a 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: Boat Variable Cost ($) Selling Price ($) Bass 12,000 22,000 Ski 9,000 18,000 Speed 14,500 28,000 The company has incurred fixed costs of $2,500,000 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 problem by using the computer.
(c) If the agreements were changed to a minimum of 60 bass boats, 60 ski boats, and 60 speedboats, what is the optimal solution?