A manufacturing firm has discontinued production of a certain unprofitable product line. Considerable excess production capacity was

Question:

A manufacturing firm has discontinued production of a certain unprofitable product line. Considerable excess production capacity was created as a result. Management is considering devoting this excess capacity to one or more of three products: X 1, X 2, and X 3. Machine hours required per unit are

The available time in machine hours per week is

The salespeople estimate they can sell all the units of X 1 and X 2 that can be made. But the sales potential of X 3 is 80 units per week maximum. Unit profits for the three products are
Unit Profits
X 1 ......... $ 20
X 2 .......... 6
X 3 .......... 8
a. Set up the equations that can be solved to maximize the profit per week.
b. Solve these equations using the Excel Solver.
c. What is the optimal solution? How many of each product should be made, and what should the resultant profit be?
d. What is this situation with respect to the machine groups? Would they work at capacity, or would there be unused available time? Will X 3 be at maximum sales capacity?
e. Suppose that an additional 200 hours per week can be obtained from the milling ma-chines by using staff overtime. The incremental cost would be $ 1.50 per hour. Would you recommend doing this? Explain how you arrived at youranswer.