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 $3,000. With this pricing structure, the demand, measured by the number of contracts Montevideo signs per month, is 10 contracts. This is down 5 contracts from the figure last year, when your company charged only $2,500. 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 40 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: $150,000 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 (in dollars per hour).
p = $ per hour