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 $2,900. With this pricing structure, the demand, measured by the number of contracts Montevideo signs per month, is 21 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: $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

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
icon
Related questions
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 $2,900. With this pricing structure, the demand, measured by the number of contracts Montevideo signs per month, is 21 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: $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
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 5 steps

Blurred answer
Similar questions
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,