Problem 29:

AutoIgnite produces electronic ignition systems for automobiles at a plant in

Cleveland, Ohio. Each ignition system is assembled from two components

produced at AutoIgnite's plants in Buffalo, New York, and Dayton, Ohio. The

Buffalo plant can produce 2000 units of component 1, 1000 units of component

2, or any combination of the two components each day. For instance, 60% of

Buffalo's production time could be used to produce component 1 and 40% of

Buffalo's production time could be used to produce component 2; in this case, the

Buffalo plant would be able to produce 0.60(2000) = 1200 units of component 1

each day and 0.40(1000) = 400 units of component 2 each day. The Dayton plant

can produce 600 units of component 1, 1400 units of component 2, or any

combination of the two components each day. At the end of each day, the

component production at Buffalo and Dayton is sent to Cleveland for assembly of

the ignition systems on the following workday.

1. Formulate a linear programming model that can be used to develop a daily

production schedule for the Buffalo and Dayton plants that will maximize daily

production of ignition systems at Cleveland.

2. Find the optimal solution.