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.)

Maximize Z =

X1 +

X2 +

X3

s.t

Milling X1 + X2 + X3

Lathes X2 + X2 +X3

Grinders X3 + X2 + X3

Sales X4 + X2 + X3

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.)

Decision for X1 =

Decision for X2 =

Decision for X3 =

Total =

Resources used

Milling

Lathes

Grinders

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.)

Slack Variables Hours

S1

S1

S2

S3

d1) Would the machines work at capacity?

Milling Machines

Lathes

Grinders

d2)

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

• 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?

The allowable increase (from the Excel sensitivity report) in overtime is=

The additional hours that can be obtained =

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 235 Lathe 5 2 9 Grinder 0 1 0 The available time in machine hours per week is Milling machines Lathes Grinders MACHINE HOURS PER WEEK 940 520 310 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 $ 12 16