GreenLawns provides a lawn fertilizing and weed control service. The company is
ID: 2949414 • Letter: G
Question
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 $4,000 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 + 39M,
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.
Determine the optimal amount to spend on radio and direct-mail advertising. How much in sales will be generated? Spent on Radio:_______ Spent on Direct Mail:______ Total Sales:_______Explanation / Answer
Sale (S) = -2R2_10M2-8RM+18R+34M
= -2( 4) - 10 (1) -8x2x1+18x2+34x1
= 36 Thousand
Maximizing S such that R+M = 3 Max.
Max. S = -2(3-M)2-10M2-8M(3-M)+18(3-M)+34M
Max S = -4M2+4M+36
For maximization of S, derivative of S ( dS/dM) should be zero
dS/dM = -8M+4 =0, which gives M=1/2 and R = 3-M = 3-0.5 = 2.5
S = -4x1/4+4x1/2+36 = 37
Thus maximum sales will happen with values of Radio Advt. spend -2500 and Direct mail adv.-500.
Amount spent on radio Ad. =2500
Amount spent of Direct Mail = 500
Total Sale = 37000
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