A manufacturing firm has discontinued the 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 area

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 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. (Leave no cells blank - be certain to enter "0" wherever required.)

s.t

b. Solve these equations using the Excel Solver. (Round your answers to the nearest whole number.)

c. How much of each constraint or resource is unused? (Leave no cells blank - be certain to enter "0" wherever required. Round your answers to the nearest whole number.)

d-1. Would the machines work at capacity?

d-2. Will X3 be at maximum sales capacity?

multiple choice

Yes

No

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. What would be the allowable increase (from the excel sensitivity report) in overtime when compared to additional hours that can be obtained?