6 The Universal machine shop has several lines of decorative

6. The Universal machine shop has several lines of decorative and functional metal items. The most recent order has been for 1200 door lock units for an apartment complex developer. The sales and production departments must work together to determine delivery schedules. Each lock unit consists of three components: the knob and faceplate, the actual lock itself, and a set of two keys. Although the processes used in the manufacture of the three components vary, there are three areas where the production manager is concerned about the availability of resources. These three areas, their usage by the three components, and their availability are detailed in the table.

Resource

Knob and Plate

Lock

Key (each)

Available

Brass Alloy

12

  5

  1

15000 units

Machining

18

20

10

36000 minutes

Finishing

15

  5

  1

12000 minutes

A quick look at the amounts available confirms that Universal does not have the resources to fill this contract. A subcontractor, who can make an unlimited number of each of the three components, quotes the prices below.

Component

Subcontractor Cost

Universal Cost

Knob and Plate

10.00

6.00

Lock

9.00

4.00

Keys (set of 2)

1.00

  .50

Develop and discuss a linear programming model that would tell Universal how to fill the order for 1500 lock sets at the minimum cost. Discuss the model

Solution