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: X1, X2, and X3.
Machine hours required per unit are
PRODUCT
MACHINE TYPE X1 X2 X3
Milling machine 8 2 3
Lathe 4 3 0
Grinder 2 0 1
The available time in machine hours per week is
MACHINE HOURS PER WEEK
Milling machines 800
Lathes 480
Grinders 320
The salespeople estimate that they can sell all the units of X1 and X2 that can be made. But the sales potential of X3 is 80 units per week maximum.
Unit profits for the three products are
UNIT PROFITS
X1 $20
X2 6
X3 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 X3 be at maximum sales capacity?
e. Suppose that an additional 200 hours per week can be obtained from the milling machines by working overtime. The incremental cost would be $1.50 per hour. Would you recommend doing this? Explain how you arrived at your answer.