Television Advertising 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 $2,800. With this pricing structure, the demand, measured by the number of contracts Montevideo signs per month, is 12 contracts. This is down 3 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 20 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: $50,000 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) =
Television Advertising 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 $2,800. With this pricing structure, the demand, measured by the number of contracts Montevideo signs per month, is 12 contracts. This is down 3 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 20 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: $50,000 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) =
Trigonometry (MindTap Course List)
10th Edition
ISBN:9781337278461
Author:Ron Larson
Publisher:Ron Larson
Chapter4: Complex Numbers
Section: Chapter Questions
Problem 40RE
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Question
Television Advertising 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 $2,800. With this pricing structure, the demand, measured by the number of contracts Montevideo signs per month, is 12 contracts. This is down 3 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 20 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: $50,000 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
Expert Solution
Step 1
Since the question has multiple subparts, we will answer only the first three subparts (a,b,c). If you want the remaining subpart to be answered, then please resubmit the question and mention the subpart you want us to answer in your message.
a)
From the given information, it is clear that if the pricing is $2,800 the demand is 12 per month. And if the company charged only $2,500, the demand is 15 per month.
Let the linear demand equation that gives the number of contracts q as a function of the hourly fee p Montevideo charges for development be .
Then the graph of passes through and .
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