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 1 Lathe 4 1 7 Grinder 2 1 3 The available time in machine hours per week is MACHINE HOURS PER WEEK Milling machines 1,000 Lathes 560 Grinders 270 The salespeople estimate they can sell all the units of X1 and X2that 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 $ 12 X2 9 X3 13 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 150 hours per week can be obtained from the grinders by working overtime. The incremental cost would be $3.50 per hour. What would be the allowable increase (from the excel sensitivity report) in overtime when compared to additional hours that can be obtained? (Round "shadow price" to 2 decimal places and the rest to the nearest whole number.)
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 1 Lathe 4 1 7 Grinder 2 1 3 The available time in machine hours per week is MACHINE HOURS PER WEEK Milling machines 1,000 Lathes 560 Grinders 270 The salespeople estimate they can sell all the units of X1 and X2that 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 $ 12 X2 9 X3 13 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 150 hours per week can be obtained from the grinders by working overtime. The incremental cost would be $3.50 per hour. What would be the allowable increase (from the excel sensitivity report) in overtime when compared to additional hours that can be obtained? (Round "shadow price" to 2 decimal places and the rest to the nearest whole number.)
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter6: Optimization Models With Integer Variables
Section: Chapter Questions
Problem 51P
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Question
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 | 1 |
| Lathe | 4 | 1 | 7 |
| Grinder | 2 | 1 | 3 |
The available time in machine hours per week is
| MACHINE HOURS PER WEEK | |
| Milling machines | 1,000 |
| Lathes | 560 |
| Grinders | 270 |
The salespeople estimate they can sell all the units of X1 and X2that 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 | $ | 12 | |
| X2 | 9 | ||
| X3 | 13 | ||
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 150 hours per week can be obtained from the grinders by working overtime. The incremental cost would be $3.50 per hour. What would be the allowable increase (from the excel sensitivity report) in overtime when compared to additional hours that can be obtained? (Round "shadow price" to 2 decimal places and the rest to the nearest whole number.)
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