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 $5,500$ 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 $$39\mathrm{.}00$ $$52\mathrm{.}00$

Support $$12\mathrm{.}50$ $$16\mathrm{.}00$

Strap $$7\mathrm{.}50$ $$8\mathrm{.}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 $3\mathrm{.}52\mathrm{.}23\mathrm{.}1$

Support $1\mathrm{.}31\mathrm{.}72\mathrm{.}6$

Strap $0\mathrm{.}81\mathrm{.}7$

Capacity $($hours$)350420680$

$($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 $\_\_\_\_\_\_\_\_$

Cutting constraint $\_\_\_\_\_\_\_\_\_$

Milling constraint $\_\_\_\_\_\_\_\_\_$

Shaping constraint $\_\_\_\_\_\_\_\_$

Frame constraint $\_\_\_\_\_\_\_\_\_$

Support constraint $\_\_\_\_\_\_\_\_\_\_$

Strap constraint $\_\_\_\_\_\_\_\_\_\_\_$

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 $\_\_\_\_\_\_\_$hrs

Shaping $\_\_\_\_\_\_\_$hrs

$($d$)$

How much $($in $$)$ 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? $($Round your answer to three decimal places.$)$

$---$Select$---$ Yes or No $.$

The reduced cost of $\_\_\_\_\_\_\_\_\_\_\_$indicates that the solution $---$Select$---$ can or cannot be improved.