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, X3. Machine hours required per unit are: Machine Type X1 X2 X3 Milling machine 3 5 6 Lathe 3 5 4 Grinder 1 3 3 The available time in machine hours per week is: Machine Hours Per week Milling machines 860 Lathes 600 Grinders 210 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, X3.
Machine hours required per unit are:
| Machine Type | X1 | X2 | X3 |
| Milling machine | 3 | 5 | 6 |
| Lathe | 3 | 5 | 4 |
| Grinder | 1 | 3 | 3 |
The available time in machine hours per week is:
| Machine Hours Per week | |
| Milling machines | 860 |
| Lathes | 600 |
| Grinders | 210 |
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 | 12 |
| X2 | 15 |
| X3 | 8 |
a. Set up the equations that can be solved to maximize the profit per week.
| Maximize Z = | X1 + | X2 + | X3 |
| Milling | X1 + | X2+ | X3<_ | ||||
| Lathes | X1+ | X2+ | X3<_ | ||||
| Grinders | X1+ | X2+ | X3<_ | ||||
| Sales | X1+ | X2+ | X3<_ | ||||
b. Solve these equations using the Excel Solver.
| Decision for X1 | |
| Decision for X2 | |
| Decision for X3 | |
| Total profit |
| Resources Used | |
| Milling | |
| Lathes | |
| Grinders | |
| Sales |
c. How much constraint or resource is unused?
| Slack Variables | Hours |
| S1 | |
| S2 | |
| S3 | |
| S4 |
d-1 Would the machines work at capacity?
| Milling Machines | |
| Lathes | |
| Grinders |
d-2 Will X3 be at maximum sales capacity? Yes or no.
e. Suppose that an additional 150 hours per week can be obtained from the lathes by working overtime. The incremental cost would be $5.00 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. |
| Decision for X1 | 200 |
| Decision for X2 | 0 |
| Decision for X3 | 0 |
| decision for X4 | 2400 |
| Resources Used | |
| Milling | 600 |
| Lathes | 600 |
| Grinder | 200 |
| Sales | 0 |
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