The Skimmer Boat Company manufactures the Water Skimmers bass fishing boat. The company purchases the engines it installs in its boats from the Margine company, which specializes in marine engines. Skimmer has the following production schedule for April, May, June, and July.
Margine usually manufactures and ships engines to Skimmer during the month the engines are due. However, from April through July Margine has a large order with another boat customer nad it can manufacture only 40 engines in April, 60 in May, 90 in June, and 50 in July. Margine has several alternative ways to meet Skimmer's production schedule. It can produce up to 30 engines in January, February, and March and carry them in inventory at a cost of $50 per engine per month until it ships them to Skimmer. For example, Margine could build an engine in January and ship it to Skimmer in April, incurring $150 in inventory charges. Margine can also manufacture up to 20 engines in the month they are due on a overtime basis with an additional cost of $400 per engine. Margine wants to determine the least costly production schedule that will meet Skimmer's schedule.
Solution formulates a linear programming problem.