As Sales Manager for Montevideo Productions, Inc., you are planning to review th

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 21 contracts. This is down 8 contracts from the figure last year, when your company charged only $2,100. 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)= 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) = The costs to Montevideo Productions are estimated as follows: Fixed costs: $140,000 per month Variable cost: $80,000 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) = 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

Explanation / Answer

slope = 8(2100-2900) = -8/800 = -0.01

so eq of line is q = -0.01*p+c , but we know (2900,21) is a point so ,

21 = -0.01*2900+c => c = 50 so eq is q = -0.01*p+50 ----ANSWER a

b) Revenue = total contracts *time per each contract *price per each contract

R(p) = ( -0.01*p+50 )*50*p = -0.5p^2+2500p ------ANSWER b

c) Total cost = Fixed + variable per contract*no of contracts (q)

C(q) = 140000+80000*q ----ANSWER c (first part)

C(p) = 140000+80000*(-0.01*p+50) = 4140000 -800*p -----ANSWER c (second part)

d) profit = revenue - cost

Profit = 2500p-0.5p^2 -4140000+800p

P(p) = 3300*p-0.5*p^2 -4140000 ------ANSWER D (first part)

for maximizing , first find dP/dp =0

3300-p =0 ,so p = 3300

d^2P/dp^2 = -1 which is <0 , so it will be maximim ar p= 3300 -----Answer D (second part)

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