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196 CHAPTER 4 LINEAR PROGRAMMING APPLICATIONS

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
either be manufactured by the company or purchased from an outside supplier.
Manufacturing and purchase costs per unit are shown.

Component Manufacturing Cost Purchase Cost

Frame E38.00 E51.00
Support E11.50 E15.00
Strap E 6.50 E 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 3.5 2.2 3.1
Support 1.3 1.7 2.6
Strap 0.8 — 1.7
Capacity (hours) 350 420 680

a. How many of each component should be manufactured and how many should be
purchased?
b. What is the total cost of the manufacturing and purchasing plan?
c. How many hours of production time are used in each department?
d. How much should Frandec be willing to pay for an additional hour of time in the shaping
department?
e. Another manufacturer has offered to sell frames to Frandec for E45 each. Could
Frandec improve its position by pursuing this opportunity? Why or why not?
13 The Two-Rivers Oil Company near Pittsburgh transports gasoline to its distributors by
truck. The company recently contracted to supply gasoline distributors in southern Ohio,
and it has $600 000 available to spend on the necessary expansion of its fleet of gasoline
tank trucks. Three models of gasoline tank trucks are available.

Capacity Purchase Monthly Operating Cost,
Truck Model (gallons) Cost Including Depreciation
Super Tanker 5 000 $67 000 $550
Regular Line 2 500 $55 000 $425
Econo-Tanker 1 000 $46 000 $350

The company estimates that the monthly demand for the region will be 550 000 gallons
of gasoline. Because of the size and speed differences of the trucks, the number of
deliveries or round trips possible per month for each truck model will vary. Trip
capacities are estimated at 15 trips per month for the Super Tanker, 20 trips per month
for the Regular Line and 25 trips per month for the Econo-Tanker. Based on

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