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 $3,500 is available 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= -2R? - 10M? - BRM + 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 $2,000 is spent on radio advertising and $1,500 is spent on direct-mail advertising? S= $ (b) Formulate an optimization problem that can be solved to maximize sales subject to the media budget of spending no more than $3,500 on total advertising. Max –10M² – 8MR + 34M – 2R² + 18R s.t. M+ R S 3.50 R, M20
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 $3,500 is available 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= -2R? - 10M? - BRM + 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 $2,000 is spent on radio advertising and $1,500 is spent on direct-mail advertising? S= $ (b) Formulate an optimization problem that can be solved to maximize sales subject to the media budget of spending no more than $3,500 on total advertising. Max –10M² – 8MR + 34M – 2R² + 18R s.t. M+ R S 3.50 R, M20
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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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 $3,500 is available 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 = -2R? - 10M2 – 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 $2,000 is spent on radio advertising and $1,500 is spent on direct-mail advertising?
S = $
(b) Formulate an optimization problem that can be solved to maximize sales subject to the media budget of spending no more than $3,500 on total advertising.
Маx
-10M – 8MR + 34M – 2R² + 18R
s.t.
М+R
< 3.50
R, M 2 0
Transcribed Image Text:(c) Determine the optimal amount to spend (in dollars) on radio and direct-mail advertising. (Round your answers to the nearest dollar.)
radio
R = $ 1750
direct-mail
M = $ 750
How much money (in dollars) will be generated in sales? (Round your answer to the nearest dollar.)
Total sales
S = $ 34750
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