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 4 Lathe 6 8 0 Grinder 8 0 2 The available time in machine hours per week is MACHINE HOURS PER WEEK Milling machines 502 Lathes 552 Grinders 180 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.
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 | 4 |
| Lathe | 6 | 8 | 0 |
| Grinder | 8 | 0 | 2 |
The available time in machine hours per week is
| MACHINE HOURS PER WEEK | |
| Milling machines | 502 |
| Lathes | 552 |
| Grinders | 180 |
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 | $ | 39 | |
| X2 | 31 | ||
| X3 | 29 | ||
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 (Round your answers to the nearest whole number.)
c. How much of each constraint or resource is unused? (Round your answers to the nearest whole number.)
d-1. Would the machines work at capacity?
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 | 4 |
| Lathe | 6 | 8 | 0 |
| Grinder | 8 | 0 | 2 |
The available time in machine hours per week is
| MACHINE HOURS PER WEEK | |
| Milling machines | 502 |
| Lathes | 552 |
| Grinders | 180 |
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 | $ | 39 | |
| X2 | 31 | ||
| X3 | 29 | ||
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 | X1+ | X2+ | X3 | <= | ||||
| Grinders | X1+ | X2+ | X3 | <= | ||||
| X1,X2,X3 | >= |
b. Solve these equations. (Round your answers to the nearest whole number.)
| Decision for X1 | |
| Decision for X2 | |
| Decision for X3 | |
| Total Profit |
| Resources Used | |
| Milling | |
| Lathes | |
| Grinders | |
| Sales |
c. How much of each constraint or resource is unused? (Round your answers to the nearest whole number.)
| Slack Variables | Hours |
| S1 | |
| S2 | |
| S3 | |
| S4 |
d-1. Would the machines work at capacity?
| Milling | |
| Lathes | |
| Grinders |
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