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 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?

• 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?