GreenLawns provides a lawn fertilizing and weed control service. The company is adding a special aeration treatment as a low-cost extra service option, which it hopes will help attract new customers. Management is planning to promote this new service in two media: radio and direct-mail advertising. A media budget of $2,500 Is available for this promotional campaign. Based on pas experience in promoting Its other services, GreenLawns obtained the following estimate of the relationship between sales and the amount spent on promotion in these two media. S = -2R²10M2 - 8RM+ 18R+ 34M where S = total sales in thousands of dollars R= thousands of dollars spent on radio advertising M= thousands of dollars spent on direct-mail advertising GreenLawns would like to develop a promotional strategy that will lead to maximum sales subject to the restriction provided by the media budget. (a) What is the value of sales (in dollars) if $1,500 is spent on radio advertising and $1,000 is spent on direct-mall advertising? S = $ X (b) Formulate an optimization problem that can be solved to maximize sales subject to the media budget of spending no more than $2,500 on total advertising. Max s.t. R, M20 X x ≤ 2.50 (c) Determine the optimal amount to spend (in dollars) on radio and direct-mail advertising. (Round your answers to the nearest dollar.)
GreenLawns provides a lawn fertilizing and weed control service. The company is adding a special aeration treatment as a low-cost extra service option, which it hopes will help attract new customers. Management is planning to promote this new service in two media: radio and direct-mail advertising. A media budget of $2,500 Is available for this promotional campaign. Based on pas experience in promoting Its other services, GreenLawns obtained the following estimate of the relationship between sales and the amount spent on promotion in these two media. S = -2R²10M2 - 8RM+ 18R+ 34M where S = total sales in thousands of dollars R= thousands of dollars spent on radio advertising M= thousands of dollars spent on direct-mail advertising GreenLawns would like to develop a promotional strategy that will lead to maximum sales subject to the restriction provided by the media budget. (a) What is the value of sales (in dollars) if $1,500 is spent on radio advertising and $1,000 is spent on direct-mall advertising? S = $ X (b) Formulate an optimization problem that can be solved to maximize sales subject to the media budget of spending no more than $2,500 on total advertising. Max s.t. R, M20 X x ≤ 2.50 (c) Determine the optimal amount to spend (in dollars) on radio and direct-mail advertising. (Round your answers to the nearest dollar.)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Transcribed Image Text:GreenLawns provides a lawn fertilizing and weed control service. The company is adding a special aeration treatment as a low-cost extra service option, which it hopes will help attract new
customers. Management is planning to promote this new service in two media: radio and direct-mail advertising. A media budget of $2,500 Is avallable for this promotional campaign. Based on past
experience in promoting its other services, GreenLawns obtained the following estimate of the relationship between sales and the amount spent on promotion in these two media.
S = -2R²10M2 - 8RM + 18R+ 34M
where
S = total sales in thousands of dollars
R = thousands of dollars spent on radio advertising
M = thousands of dollars spent on direct-mail advertising
GreenLawns would like to develop a promotional strategy that will lead to maximum sales subject to the restriction provided by the media budget.
(a) What is the value of sales (In dollars) if $1,500 is spent on radio advertising and $1,000 is spent on direct-mail advertising?
S = $
X
(b) Formulate an optimization problem that can be solved to maximize sales subject to the media budget of spending no more than $2,500 on total advertising.
Max
s.t.
R, M≥ 0
X
direct-mall
2.50
(c) Determine the optimal amount to spend (in dollars) on radio and direct-mail advertising. (Round your answers to the nearest dollar.)
radio
R = $
M = $
X
X
How much money (in dollars) will be generated in sales? (Round your answer to the nearest dollar.)
Total sales S = $
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 14 images
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
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…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
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…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
