Intorduction to management science 13th edition. Chapter 4, question 17. Frandec
ID: 2771956 • Letter: I
Question
Intorduction to management science 13th edition. Chapter 4, question 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 complany or purchased from an outside supplier. Manufacturing and purchase costs per unit are shown.
Component Manufacturing Cost Purchase Cost
Frame $38.00 $51.00
Support $11.50 $15.00
Strap $6.50 $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:
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. 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?
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 $45 each. Could Frandec improve its position by pursuing this opportunity? Why or why not?
I am told to us MS software to solve this problem
Explanation / Answer
Answer:
(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
FM
+
FP
+
SM
+
SP
+
TM
+
TP
s.t.
3.5FM
+
SM
+
TM
FM
+
1.7SM
FM
+
SM
+
1.7TM
FM
+
FP
SM
+
SP
TM
+
TP
FM, FP, SM, SP, TM, TP 0.
Manufacture
Purchase
Frames
Supports
Straps
(b)
What is the total cost of the manufacturing and purchasing plan?
When required, round your answer to the nearest dollar.
$
(c)
How many hours of production time are used in each department?
Department
Hours of production
time used
Cutting
hours
Milling
hours
Shaping
hours
(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 $45 each. Could Frandec 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
(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
FM
+
FP
+
SM
+
SP
+
TM
+
TP
s.t.
3.5FM
+
SM
+
TM
FM
+
1.7SM
FM
+
SM
+
1.7TM
FM
+
FP
SM
+
SP
TM
+
TP
FM, FP, SM, SP, TM, TP 0.
Manufacture
Purchase
Frames
Supports
Straps
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