Formulate but do not solve the following exercise as a linear programming problem. Custom Office Furniture Company is introducing a new line of executive desks made from a specially selected grade of walnut. Initially, three different models—A, B, and C—are to be marketed. Each model A desk requires 1 1 4 hr for fabrication, 1 hr for assembly
Formulate but do not solve the following exercise as a linear programming problem.
Custom Office Furniture Company is introducing a new line of executive desks made from a specially selected grade of walnut. Initially, three different models—A, B, and C—are to be marketed. Each model A desk requires
| 1 |
| 4 |
hr for fabrication, 1 hr for assembly, and 1 hr for finishing; each model B desk requires
| 1 |
| 2 |
hr for fabrication, 1 hr for assembly and 1 hr for finishing; each model C desk requires
| 1 |
| 2 |
hr,
| 3 |
| 4 |
hr,
| 1 |
| 2 |
hr for fabrication, assembly, and finishing, respectively. The profit on each model A desk is $26, the profit on each model B desk is $28, and the profit on each model C desk is $23. The total time available in the fabrication department, the assembly department, and the finishing department in the first month of production is 305 hr, 210 hr, and 185 hr, respectively. To maximize Custom's profit, P (in dollars), how many desks of each model (x model A desks, y model B desks and z model C desks) should be made in the month?
| Maximize | P | = |
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subject to the constraints | |
| fabrication |
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| assembly |
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| finishing |
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| x ≥ 0 | |||||
| y ≥ 0 | |||||
| z ≥ 0 |
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