$7-14$ The Electrocomp Corporation manufactures two electrical products: air conditioners

and large fans. The assembly process for each is similar in that both require a certain

amount of wiring and drilling. Each air conditioner takes $3$ hours of wiring and $2$ hours of

drilling. Each fan must go through $2$ hours of wiring and $1$ hour of drilling. During the

next production period, $240$ hours of wiring time are available, and up to $140$ hours of

drilling time may be used. Each air conditioner sold yields a profit of $$25.$ Each fan

assembled may be sold for a $$15$ profit. Formulate and solve this LP production mix

situation to find the best combination of air conditioners and fans that yields the highest

profit. Use the corner point graphical approach.

$[$QX$]7-15$ Electrocomp's management realizes that it forgot to include two critical

constraints $($see Problem $7-14).$ In particular, management decides that there should be a

minimum number of air conditioners produced in order to fulfill a contract. Also, due to

an oversupply of fans in the preceding period, a limit should be placed on the total

number of fans produced.

$1.$

a$.$ If Electrocomp decides that at least $20$ air conditioners should be produced but no

more than $80$ fans should be produced, what would be the optimal solution? How

much slack or surplus is there for each of the four