As Sales Manager for Montevideo Productions, Inc., you are planning to review the prices you charge clients for television advertisement development.

You currently charge each client an hourly development fee of $2,700. With this pricing structure, the demand, measured by the number of contracts Montevideo signs per month, is 3 contracts.

This is down 6 contracts from the figure last year, when your company charged only $2,100.

(a) Construct a linear demand equation giving the number of contracts q as a function of the hourly fee p Montevideo charges for development.

q(p) =

(b) On average, Montevideo bills for 50 hours of production time on each contract. Give a formula for the total revenue obtained by charging $p per hour.

R(p) =

(c) The costs to Montevideo Productions are estimated as follows:

Fixed costs: $100,000 per month
Variable costs: $90,000 per contract
Express Montevideo Productions' monthly cost as a function of the number q of contracts.

C(q) =

Express Montevideo Productions' monthly cost as a function of the hourly production charge p.

C(p) =

(d) Express Montevideo Productions' monthly profit as a function of the hourly development fee p.

P(p) =

Find the price it should charge to maximize the profit.
p = $ per hour