$2.$ Elctrocomp Corporation manufactures two products: air conditioners and large fans. Each air conditioner takes $3$ hours of wiring and $2$ hours of drilling. Each fan must go through $2$ hours of wiring and $2$ hours 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. Because company incurred an oversupply of fans in the preceding period, management insists that no more than $80$ fans be produced this production period. Each air conditioner yields a profit of $$25,$ and each fan yields a profit of $$15.$ Management wants to find the best combination of these two products that yields the highest profit.

Formulate the linear programming model for this problem.