Introduction to Management Science 12th Edition by Bernard Taylor

تمرين 18

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:
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. 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, 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