Problem 4 17 (Algorithmic) 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 Frandecs 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 Component Manufacturing Cost Purchase Cost Frame $40 00 $53 00 Support $13 50 $17 00 Strap $8 50 $9 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 7 2 4 3 3 Support 1 5 1 9 2 8 Strap 1 1 9 Capacity (hours) 360 420 680 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 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 FM SM TM FM SM FM SM TM FM FP SM SP TM TP FM, FP, SM, SP, TM, TP 0 If required, round your answers to the nearest whole number If an amount is zero, enter 0 Manufacture Purchase Frames Supports Straps What is the total cost of the manufacturing and purchasing plan When required, round your answer to the nearest dollar $ How many hours of production time are used in each department If required, round your answer to two decimal places Department Hours of production time used Cutting hours Milling hours Shaping hours How much should Frandec be willing to pay for an additional hour of time in the shaping department If required, round your answers to the nearest whole number If an amount is zero, enter 0 $ Another manufacturer has offered to sell frames to Frandec for $47 each Could Frandec improve its position by pursuing this opportunity Why or why not If required, round your answers to the nearest cent Because the current purchase price is $ The reduced cost is $ which means that the solution may be improved if the cost is $ or below

Question: Problem 4-17 (Algorithmic) Frandec Company manufactures, assembles, and rebuilds material handling equipment used in warehouses and distribution centers. One product, called a Liftmaster, is assembled

Problem 4-17 (Algorithmic)

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. Frandecs 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.


Component	Manufacturing Cost	Purchase Cost
Frame	$40.00	$53.00
Support	$13.50	$17.00
Strap	$8.50	$9.50

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	3.7	2.4	3.3
Support	1.5	1.9	2.8
Strap	1		1.9
Capacity (hours)	360	420	680

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?

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.

FM, FP, SM, SP, TM, TP 0

If required, round your answers to the nearest whole number. If an amount is zero, enter "0"

	Manufacture	Purchase
Frames
Supports
Straps

What is the total cost of the manufacturing and purchasing plan? When required, round your answer to the nearest dollar. $
How many hours of production time are used in each department? If required, round your answer to two decimal places.

Department Hours of production time used

Cutting hours

Milling hours

Shaping hours
How much should Frandec be willing to pay for an additional hour of time in the shaping department? If required, round your answers to the nearest whole number. If an amount is zero, enter "0". $
Another manufacturer has offered to sell frames to Frandec for $47 each. Could Frandec improve its position by pursuing this opportunity? Why or why not? If required, round your answers to the nearest cent. Because the current purchase price is $ . The reduced cost is $ which means that the solution may be improved if the cost is $ or below.

Department	Hours of production time used
Cutting	hours
Milling	hours
Shaping	hours

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