Problem 9-17
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.
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:
(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?
If required, round your answers to one decimal place.
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
s.t.
38
FM
+
51
FP
+
11.5
SM
+
15.0
SP
+
6.5
TM
+
7.5
TP
3.5FM
+
1.3
2.2
+
SM
3.1
TM
+ 1.7SM
FM
0.8
+
FM
FM
+
0
+ 1.7TM
SM
1
FP
SM
+
1
SP
TM
+
1
TP
≤
350
≤
420
≤
680
≥
0
≥
0
≥
0
FM, FP, SM, SP, TM, TP ≥ 0.
Manufacture Purchase
Frames
100
4900
Supports
0
10000
Straps
0
5000
(b) What is the total cost of the manufacturing and purchasing plan?
When required, round your answer to the nearest dollar.
441200
$
(c) How many hours of production time are used in each department?
Department
(d)
Hours of production
time used
Cutting
350
Milling
220
Shaping
3.10
hours
hours
hours
How much should Frandec be willing to pay for an additional hour of time in the shaping
department?
56.00
$
Another manufacturer has offered to sell frames to Frandec for $45 each. Could Frandec
(e)
improve its position by pursuing this opportunity?
Why or why not?
The input in the box below will not be graded, but may be reviewed and considered by your
instructor. The 45.00 will minimize the slack utilizing all the resources for cutting and
shaping and also reduce the cost to 411621 saving 29,579 in cost