Question

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 $2,900. With this pricing structure, the demand, measured by the number of contracts Montevideo signs per month, is 11 contracts. This is down 7 contracts from the figure last year, when your company charged only $2,200.

(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: $130,000 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

  

Answer 1

Solutions We can write given information om coodinate foom (Pig) where and q no. of contracts. P e is price @) (P cod = $900, 11) and 2200, 18) slope m- Yo-Y R-2, 18-11 7 -700 2200 - 2900 m = -0.01 Equation of line 4- y = m(x-x) y-11= -0.01(x -2900) y-11= -0 ot 29 y = -0.01xt uo Tq (P) = -0. olp+ uo RP) = 9 (P) x 40 p - -• of P + цо) х цор = -0.4p²+ 1600 p

c) fixed cost $ 130000 per month $ 90.000 peo contract Variable cost a cost ca 130 000 + 90000 (9 - As a function p C(P) = 130000 + 90000(-0.014740 190000 900 p + 3600000 T CP = 37300000-900p (d) porfit Revenue - cost function = -0.4p2t + 16oop 37300000+ 900 p = -0.487 2 Boop 37300000 4 from the above ean we conclude that we get profit as a quadratic function It is parabola. They have marimumat vestes pt coefficient is Rrus it is downward - Б - 2500 29 - 2(0.4) tre -$3125