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	2	3	5
Lathe	5	2	9
Grinder	0	1	0

The available time in machine hours per week is

	MACHINE HOURS PER WEEK
Milling machines	940
Lathes	520
Grinders	310

The salespeople estimate they can sell all the units of X₁ and X₂ that can be made. But the sales potential of X₃ is 130 units per week maximum. Unit profits for the three products are

	UNIT PROFITS
X1	$	12
X2		16
X3		11

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

No

Yes

e. Suppose that an additional 50 hours per week can be obtained from the lathes by working overtime. The incremental cost would be $6.00 per hour. What would be the allowable increase (from the excel sensitivity report) in overtime when compared to additional hours that can be obtained? (Round "shadow price" to 2 decimal places and the rest to the nearest whole number.)