3 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.

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.

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