Question: 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 estimate selling price and variable cost for each type of boat are summarized in the following table.

Boat Variable cost Selling Price

Bass $12,500 $23,000

Ski $8,500 $18,000

Speed $13,700 $26,000

The company has incurred fixed costs of $2,800,000 to set up its manufacturing operations 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 speed boats. Alternatively, the company is unsure of what the actual demand will be, so it has decided to limit production to no more than 120 of any boat. The company wants to determine the number of boats that it must sell to break even while minimizing its total variable cost.

Formulate a linear programming model for this problem and explain.