$($worth $13$ points$)$ A small motor manufacturer makes two types of motor, models A and B$.$ The assembly process for each is similar in that both require a certain amount of wiring, drilling, and assembly. Each model A takes $3$ hours of wiring, $2$ hours of drilling,

and $1\mathrm{.}5$ hours of assembly. Each model B must go through $2$ hours of wiring, $1$ hour of drilling, and $0\mathrm{.}5$ hours of assembly. During the next production period, $240$ hours of wiring time, $210$ hours of drilling time, and $120$ hours of assembly time are available. Each model A sold yields a profit of $$22.$ Each model B can be sold for a $$15$ profit. Assuming that all motors that are assembled can be sold, find the best combination of motors to yield the highest profit. Formulate the LP model.