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 oversup

ply of fans in the preceding period, a limit should be

placed on the total number of fans produced.

$($a$)$ If Electrocomp decides that at least $20$ air con

ditioners 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 constraints?

$($b$)$ If Electrocomp decides that at least $30$ air con

ditioners should be produced but no more than

$50$ fans should be produced, what would be the

optimal solution? How much slack or surplus is

there for each of the four constraints at the optimal solution?