question archive Frandec Company manufactures, assembles, and rebuilds material handling equipment used in warehouses and distribution centers
Frandec Company manufactures, assembles, and rebuilds material handling equipment used in warehouses and distribution centers
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Frandec Company manufactures, assembles, and rebuilds material handling equipment used in warehouses and distribution centers. One product, called a Liftmaster, is assembled from four components: a frame, a motor, two supports, and a metal strap. Frandec’s production schedule calls for 4000 Liftmasters to be made next month. Frandec purchases the motors from an outside supplier, but the frames, supports, and straps may be either manufactured by the company or purchased from an outside supplier. Manufacturing and purchase costs per unit are shown.
| Component | Manufacturing Cost | Purchase Cost |
| Frame | $32.00 | $45.00 |
| Support | $9.50 | $13.00 |
| Strap | $6.50 | $7.50 |
Three departments are involved in the production of these components. The time (in minutes per unit) required to process each component in each department and the available capacity (in hours) for the three departments are as follows:
| Department | |||
| Component | Cutting | Milling | Shaping |
| Frame | 2.9 | 1.9 | 2.5 |
| Support | 1.2 | 1.5 | 2 |
| Strap | 0.8 | — | 1.5 |
| Capacity (hours) | 330 | 390 | 640 |
a. Formulate and solve a linear programming model for this make-or-buy application. How many of each component should be manufactured and how many should be purchased?
| Let | |
| FM = number of frames manufactured | |
| FP = number of frames purchased | |
| SM = number of supports manufactured | |
| SP = number of supports purchased | |
| TM = number of straps manufactured | |
| TP = number of straps purchased |
| Min | ___________FM | + | ____________FP | + | ___________SM | + | ___________SP | + | ___________TM | + | ___________TP | ||
| s.t. | |||||||||||||
| 2.9FM | + | ___________SM | + | ___________TM | ≤ | ___________ | |||||||
| ___________FM | + | 1.5SM | ≤ | ___________ | |||||||||
| ___________FM | + | ___________SM | + | 1.5TM | ≤ | ___________ | |||||||
| FM | + | ___________FP | ≥ | ___________ | |||||||||
| SM | + | ___________SP | ≥ | ___________ | |||||||||
| TM | + | ___________TP | ≥ | ___________ | |||||||||
| FM, FP, SM, SP, TM, TP ≥ 0 | |||||||||||||
If required, round your answers to the nearest whole number.
| Manufacture | Purchase | |
|---|---|---|
| Frames | _____?____ | ____?_____ |
| Supports | _____?____ | ____?_____ |
| Straps | _____?____ | ____?_____ |
b. What is the total cost of the manufacturing and purchasing plan? When required, round your answer to the nearest dollar.
$ _______________?
c. How many hours of production time are used in each department? If required, round your answer to two decimal places.
| Department | Hours of production time used |
|---|---|
| Cutting | _________hours |
| Milling | _________hours |
| Shaping | _________hours |
d. How much should Frandec be willing to pay for an additional hour of time in the shaping department? If required, round your answer to two decimal places.
$__________ because there is (slack/ surplus) of __________ hours.
e. Another manufacturer has offered to sell frames to Frandec for $39 each. Could Frandec improve its position by pursuing this opportunity?
(Yes/ No)
Why or why not? If required, round your answers to the nearest cent.
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