A friend of yours is considering two cell phone service providers. Provider A charges $100 per month for the service regardless of the number of phone calls made. Provider B does not have a fixed service fee but instead charges $0.5 per minute for calls. Your friend's monthly demand for minutes of calling is given by the equation QD=16080PQD=16080P, where PPis the price of a minute.

With Provider A, the cost of an extra minute is

. With Provider B, the cost of an extra minute is

.

Given your friend's demand for minutes and the cost of an extra minute with each provider, if your friend used Provider A, he would talk for

minutes, and if he used Provider B, he would talk for

minutes.

This means your friend would pay

for service with Provider A and

for service with Provider B.