elevision 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 $2,400. With this pricing structure, the demand, measured by the number of contracts Montevideo signs per month, is 26 contracts. This is down 4 contracts from the figure last year, when your company charged only $2,000. (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 eac
elevision 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 $2,400. With this pricing structure, the demand, measured by the number of contracts Montevideo signs per month, is 26 contracts. This is down 4 contracts from the figure last year, when your company charged only $2,000. (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 eac
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 $2,400. With this pricing structure, the demand, measured by the number of contracts Montevideo signs per month, is 26 contracts. This is down 4 contracts from the figure last year, when your company charged only $2,000.
(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: $100,000 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 (in dollars per hour).
p = $ per hour
Expert Solution
Step 1
Given that the number of contracts when the hourly price is $2400 is 26 and when the hourly price is $2000 is 30.
Let q be the number of contracts and p be the hourly price charged.
Then the linear function of q in terms of p passes through the points (2400,26),(2000,30)
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