Question

Problem 4-17

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.

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:

	Department
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

1. 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

2. What is the total cost of the manufacturing and purchasing plan? When required, round your answer to the nearest dollar.
   
   $  
   
3. 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

4. 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".
   
   $  
   
5. 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? 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.

Answer 1