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 $4 (in thousands)is available for this promotional campaign. Based on past experience in promoting its other services, GreenLawns has obtained the following estimate of the relationship between sales and the amount spent on promotion in these two media: S-2R2-12M2-9RM+20R+37M, Where S = total sales R= amount spent on radio advertising M = amount 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. The problem is formulated as below: Max -2R2-12M²-9RM+20R+37M s.t. 1R+1M<=4 R,M>=0 Using Excel Solver, solve the above nonlinear optimization model. (a) What is the amount spent on radio advertising? (Just type the value without the dollar sign) (b) What is the amount spent on direct-mail advertising?(Just type the value without the dollar sign) (c) What is the total sales(Just type the value without the dollar sign)
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 $4 (in thousands)is available for this promotional campaign. Based on past experience in promoting its other services, GreenLawns has obtained the following estimate of the relationship between sales and the amount spent on promotion in these two media: S-2R2-12M2-9RM+20R+37M, Where S = total sales R= amount spent on radio advertising M = amount 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. The problem is formulated as below: Max -2R2-12M²-9RM+20R+37M s.t. 1R+1M<=4 R,M>=0 Using Excel Solver, solve the above nonlinear optimization model. (a) What is the amount spent on radio advertising? (Just type the value without the dollar sign) (b) What is the amount spent on direct-mail advertising?(Just type the value without the dollar sign) (c) What is the total sales(Just type the value without the dollar sign)
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter9: Decision Making Under Uncertainty
Section: Chapter Questions
Problem 46P
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 $4 (in thousands)is available for this promotional campaign. Based on-
past experience in promoting its other services, GreenLawns has obtained the following estimate of
the relationship between sales and the amount spent on promotion in these two media:
S-2R2-12M2-9RM
+ 20R +37M,
Where
S = total sales
R = amount spent on radio advertising
M = amount 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.
The problem is formulated as below:
Max
-2R2-12M²-9RM+20R+37M
s.t.
1R+1M<=4
R,M>=0
Using Excel Solver, solve the above nonlinear optimization model.
(a) What is the amount spent on radio advertising? (Just type the value without the dollar sign)
(b) What is the amount spent on direct-mail advertising?(Just type the value without the dollar sign)
(c) What is the total sales(Just type the value without the dollar sign)
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