Question

In: Operations Management

4. (20 pts) GA Industries manufactures handling equipment used in distribution centers. One product, called a...

4. (20 pts) GA Industries manufactures handling equipment used in distribution centers. One product, called a Liftmaster, has three components: a frame with strap, a motor and two supports. The most recent order has been for 4000 Liftmasters for next month. The sales and production departments must work together to determine delivery schedules. 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

Frame

Motor

Support

Available

Steel

32

7

12

54000 units

Cutting

26

15

9

35000 minutes

Shaping

25

11

5

28000 minutes

A quick look at the amounts available confirms that GA 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

GA Cost

Frame

50

36

Motor

16

14

Support

8

6

The subcontractor requires that the minimum purchase of frame is 600. Due to their production capacity onstraint, the subcontractor can only supply up to 2500 motors.

Develop a linear programming model that would tell GA how to fill the order for 4000 Liftmasters at the minimum cost.

Solutions

Expert Solution

Decision Variables:

FM = units of frame manufactured

FP = units of frame procured

SM = units of support manufactured

SP = units of support procured

TM = units of motor manufactured

TP = units of motor procured

Formulation:

Min

$36*FM

+

$50*FP

+

$6*SM

+

$8*SP

+

$14*TM

+

$16*TP

s.t.

Steel required

32*FM

+

12*SM

+

7*TM

≤

54,000

Cutting minutes required

26*FM

+

9*SM

+

15*TM

≤

35000

Shaping minutes required

25*FM

+

5*SM

+

11*TM

≤

28000

Frames required

FM

+

FP

≥

4000

Support required

SM

+

SP

≥

8000

Motor required

TM

+

TP

≥

4000

Minimum purchase of frame

1*FP

>=

600

Maximum purchase of motors

1*TP

<=

2500

FM, FP, SM, SP, TM, TP ≥ 0

Excel Model:

Item

Manufactured

Purchased

Frame

460

3540

Support

0

8000

Motor

1500

2500

Total cost = $318,560

keosha answered 1 hour ago
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