The Skimmer Boat Company manufactures the Water Skimmer bass fishing boat. The company purchases the engines it installs in its boats from the Mar-gine Company, which specializes in marine engines. Skimmer has the following production schedule for April, May, June, and July:

April: 60

May: 85

June: 100

July: 120

Mar-gine usually manufactures and ships engines to Skimmer

during the month the engines are due. However, from April through July,

Mar-gine has a large order with another boat customer, and it can manufacture

only 40 engines in April, 60 in May, 90 in June, and 50 in July. Mar-gine 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, Mar-gine could build an engine

in January and ship it to Skimmer in April, incurring $150 in inventory charges.

Mar-gine can also manufacture up to 20 engines in the month they are due on an

overtime basis, with an additional cost of $400 per engine. Mar-gine wants to

determine the least costly production schedule that will meet skimmer's

schedule.

a. Formulate a linear programming model for this problem.

b. Solve this model by using the computer.

c. If Mar-gine were able to increase its production capacity in January, February, and March from 30 to 40 engines, what would the effect be on the optimal solution?