A linear programming computer package is needed.

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 5,500Liftmasters 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	$37.00	$50.00
Support	$10.50	$14.00
Strap	$5.50	$6.50

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	Department
	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. (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, and TP = number of straps purchased. Express time in minutes per unit.)

Min

37FM+10.5SM+5.5TM+50FP+14SP+6.5TP

Cutting constraint

3.5FM+1.3SM+0.8TM350

Milling constraint

2.2FM+1.7SM420

Shaping constraint

3.1FM+2.6SM+1.7TM680

Frame constraint

FM+FP5500

Support constraint

SM+SP5500

Strap constraint

TM+TP5500

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

How many of each component should be manufactured and how many should be purchased? (Round your answers to the nearest whole number.)

(FM, FP, SM, SP, TM, TP) =

(b)

What is the total cost (in $) of the manufacturing and purchasing plan?

$

(c)

How many hours of production time are used in each department? (Round your answers to two decimal places.)

Cutting hrs Milling hrsShaping hrs

(d)

How much (in $) should Frandec be willing to pay for an additional hour of time in the shaping department?

$