$8-13($High$-$tech production problem$)$ Quitmeyer Electronics Incorporated manufactures the following six microcomputer peripheral devices: internal modems, external modems, graphics circuit boards, CD drives, hard disk drives, and memory expansion boards. Each of these technical products requires time, in minutes, on three types of electronic testing devices, as shown in the table on this page.

The first two test devices are available $120$ hours per week. The third $($device $3)$ requires more preventive maintenance and may be used only $100$ hours each week. The market for all six computer components is vast, and Quitmeyer Electronics believes that it can sell as many units of each product as it can manufacture. The table that follows summarizes the revenue and material cost for each product:

Data for Problem $8\mathrm{.}13$

$\backslash$table$[[,$INTERNAL MODEM,EXTERNAL MODEM,CIRCUIT BOARD,CD DRIVE,HARD DRIVE,MEMORY BOARD$],[$Test device $1,7,3,12,6,18,17],[$Test device $2,2,5,3,2,15,17],[$Test device $3,5,1,3,2,9,2]]$

$\backslash$table$[[$DEVICE$,$REVENUE PER UNIT SOLD $($$$),$MATERIAL COST PER UNIT $($$$)],[$Internal modem,$200,35],[$External modem,$120,25]]$

$\backslash$table$[[$DEVICE$,$REVENUE PER UNIT SOLD $($$$),$MATERIAL COST PER UNIT $($$$)],[$Internal modem,$200,35],[$External modem,$120,25],[$Graphics circuit board,$180,40],[$CD drive,$130,45],[$Hard disk drive,$430,170],[$Memory expansion board,$260,60]]$

In addition, variable labor costs are $$15$ per hour for test device $1,$$$12$ per hour for test device $2,$ and $$18$ per hour for test device $3.$ uitmeyer Electronics wants to maximize its profits.

a$.$ Formulate this as an LP model problem.

b$.$ Solve the problem by computer. What is the best product mix?

c$.$ What is the value of an additional minute of time per week on test device $1?$ Test device $2?$ Test device $3?$ Should Quitmeyer Electronics add one or more test devices to make more time available? If so$,$ on which device$($s$)$ should it add?