GreenLawns provides a lawn fertilizing and weed control service. The company is adding a special aeration...

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GreenLawns provides a lawn fertilizing and weed control service.The company is adding a special aeration treatment as a low-costextra service option, which it hopes will help attract newcustomers. Management is planning to promote this new service intwo media: radio and direct-mail advertising. A media budget of$4,000 is available for this promotional campaign. Based on pastexperience in promoting its other services, GreenLawns has obtainedthe following estimate of the relationship between sales and theamount spent on promotion in these two media:
S = -2R²? 12M²?9RM + 18R + 33M,
Where
   S = total sales in thousands ofdollars
   R = thousands of dollars spent onradio advertising
   M = thousands of dollars spent ondirect-mail advertising
GreenLawns would like to develop a promotional strategy thatwill lead to maximum sales subject to the restriction provided bythe media budget.
(a) What isthe value of sales if $2,000 is spent on radio advertising and$2,000 is spent on direct-mail advertising? Enter amounts inthousands i. e. $1,012, should be written as $1,012.
$
(b) Formulatean optimization problem that can be solved to maximize salessubject to the media budget of spending no more than $4,000 ontotal advertising. If the constant is "1" it must be entered in thebox. For subtractive or negative numbers use a minus sign even ifthere is a + sign before the blank. (Example: -300). If your answeris zero enter “0”.
Max   R² +   M² +   RM +   R +   M
s.t
  R +   M - Select your answer-??<>=Item 9
R, M - Select your answer-??<>=Item 11
(c) Determinethe optimal amount to spend on radio and direct-mail advertising.How much in sales will be generated? Enter amounts in thousands i.e. $1,012, should be written as $1,012. If your answer is zeroenter “0”.
Amountspent on radio advertising = $
Amountspent on direct-mail advertising = $
TotalSales = $

Answer & Explanation Solved by verified expert

4.1 Ratings (742 Votes)

aThe given sales function is S 2R212M2 9RM 18R 33Mand where R is thousand of dollar spent on radio advertisingand M is thousand of dollar spent on mail advertisingIf 2000 is spent on radio advertisement and 2000 is spent onmail advertisement then the sales achieved isS See Answer

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GreenLawns provides a lawn fertilizing and weed control service.The company is adding a special aeration treatment as a low-costextra service option, which it hopes will help attract newcustomers. Management is planning to promote this new service intwo media: radio and direct-mail advertising. A media budget of$4,000 is available for this promotional campaign. Based on pastexperience in promoting its other services, GreenLawns has obtainedthe following estimate of the relationship between sales and theamount spent on promotion in these two media:S = -2R2? 12M2?9RM + 18R + 33M,Where S = total sales in thousands ofdollars R = thousands of dollars spent onradio advertising M = thousands of dollars spent ondirect-mail advertisingGreenLawns would like to develop a promotional strategy thatwill lead to maximum sales subject to the restriction provided bythe media budget.(a)What isthe value of sales if $2,000 is spent on radio advertising and$2,000 is spent on direct-mail advertising? Enter amounts inthousands i. e. $1,012, should be written as $1,012.$(b)Formulatean optimization problem that can be solved to maximize salessubject to the media budget of spending no more than $4,000 ontotal advertising. If the constant is "1" it must be entered in thebox. For subtractive or negative numbers use a minus sign even ifthere is a + sign before the blank. (Example: -300). If your answeris zero enter “0”.Max R2+ M2+ RM+ R+ Ms.t R+ M- Select your answer-??<>=Item 9R, M- Select your answer-??<>=Item 11(c)Determinethe optimal amount to spend on radio and direct-mail advertising.How much in sales will be generated? Enter amounts in thousands i.e. $1,012, should be written as $1,012. If your answer is zeroenter “0”.Amountspent on radio advertising = $Amountspent on direct-mail advertising = $TotalSales = $