randec 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:

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 fill in the blank $1$

$38$

FM $+$ fill in the blank $2$

$51$

FP $+$ fill in the blank $3$

$11\mathrm{.}50$

SM $+$ fill in the blank $4$

$15$

SP $+$ fill in the blank $5$

$6\mathrm{.}50$

TM $+$ fill in the blank $6$

$7\mathrm{.}50$

TP

s$.$t$.$

$3\mathrm{.}5$FM $+$ fill in the blank $7$

$11\mathrm{.}50$

SM $+$ fill in the blank $8$

$6\mathrm{.}50$

TM $<=$ fill in the blank $9$

fill in the blank $10$

FM $+1\mathrm{.}7$SM $<=$ fill in the blank $11$

fill in the blank $12$

FM $+$ fill in the blank $13$

SM $+1\mathrm{.}7$TM $<=$ fill in the blank $14$

FM $+$ fill in the blank $15$

FP $>=$ fill in the blank $16$

SM $+$ fill in the blank $17$

SP $>=$ fill in the blank $18$

TM $+$ fill in the blank $19$

TP $>=$ fill in the blank $20$

FM$,$ FP$,$ SM$,$ SP$,$ TM$,$ TP $>=0.$

Manufacture Purchase

Frames fill in the blank $21$

fill in the blank $22$

Supports fill in the blank $23$

fill in the blank $24$

Straps fill in the blank $25$

fill in the blank $26$

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

$ fill in the blank $27$

How many hours of production time are used in each department?

Department Hours of production

time used

Cutting fill in the blank $28$

hours

Milling fill in the blank $29$

hours

Shaping fill in the blank $30$

hours

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

$ fill in the blank $31$

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?

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