A car manufacturer wants to make two types of cars, model A and model B. Each car requires two operations, assembling and finishing. The numbers of hours of each operation used on each car, as well as the profits per car, based on the current price structure, are given in the following tableau:
Products
process Model A Model B Total time required
Assembly 4hours 6hours 720hours
Finishing 6hours Hours 480hours
Profit $400 $300
In a given production period, the manufacturer has available 720 hours of assembly time and 480 hours of finishing time, and, due to differing projected demands, his managers have decided that he should make at least 20 units of model A and at least 30 units of model B. They feel certain that all models made will be sold.
a) Formulate the problem mathematically in order to maximize profit.
b) How many of each should the manufacturer make so that he satisfies the constraints imposed by the managers and at the same time maximizes his profit?
