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3. 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 Bass Ski Speed Variable Cost (8) Selling Price ($) 12,000 24,000 9,000 15,000 15,000 30,000 The company has incurred fixed costs of $3,000,000 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 50 bass boats, 60 ski boats, and 70 speedboats. Alternatively, the company is unsure of what actual demand will be, so it has decided to limit production to no more than 100 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. What are the minimum variable cost and the optimal point? (C) To produce $500,000 profit, how many boats the company needs to produce? (d) If the agreements were changed to a minimum of 40 bass boats, 70 ski boats, and 60 speed- boats, how many boats the company needs to produce? Solution