Answered Essay: 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 meta

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 5000 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 $40.00 $53.00
Support $13.50 $17.00
Strap $8.50 $9.50

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 3.7 2.4 3.3
Support 1.5 1.9 2.8
Strap 1 1.9
Capacity (hours) 360 420 680

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.
3.7FM + SM + TM
FM + 1.9SM
FM + SM + 1.9TM
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

What is the total cost of the manufacturing and purchasing plan? When required, round your answer to the nearest dollar.

$

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

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 of  hours.

Another manufacturer has offered to sell frames to Frandec for $47 each. Could Frandec improve its position by pursuing this opportunity?

Why or why not? If required, round your answers to the nearest cent.

Because the current purchase price is $  . The reduced cost is $   which means that the solution may be improved if the cost is $   or below.

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