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 $2,600. With this pricing structure, the demand, measured by the number of contracts Montevideo signs per month, is 24 contracts. This is down 3contracts from the figure last year, when your company charged only $2,300.(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:$140,000 per monthVariable costs:    $70,000 per contractExpress 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

Question
Asked Nov 18, 2019
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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 $2,600. With this pricing structure, the demand, measured by the number of contracts Montevideo signs per month, is 24 contracts. This is down 3contracts from the figure last year, when your company charged only $2,300.

(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: $140,000 per month
Variable costs:     $70,000 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
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Expert Answer

Step 1

Assume that p is the price and q is the number of contracts.

Then, write the given information in the coordinate form such that (p, q).

a)given (p, q) = (2600, 24) and (2300, 27)

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y, 27-24 3 Slope, m 2300 2600 -300 m=-0.01 Then, equation of the line is y 0.01xx y240.01x2600) y =0.0150 That is q(p)= -0.01p+50

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Step 2

b)On average, Montevideo bills for 50 hours of production time on each contract. Then

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R(p)= q(p)x(50 hours of production)Sp/hour (-0.01p+50)x 50 p --0.5p2 +2500 p

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Step 3

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

Fixed costs = $140,000 per month

Variable costs = $70,000 per contract

Express Montevideo Productions' monthly cost as a function of the number q of contracts.

C(q) = Fixed cost...

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c(p) Fixed costs (number of contract) = $140,000+S70, 000 (-0.01p +50) 3640000-700p

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