GreenLawns provides a lawn fertilizer and weed control service. The company is a
ID: 3133455 • Letter: G
Question
GreenLawns provides a lawn fertilizer 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 $6,000 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 + 16R + 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 if $5,000 is spent on radio advertising and $1,000 is spent on direct-mail advertising? $ (b) Formulate an optimization problem that can be solved to maximize sales subject to the media budget of spending no more than $6,000 on total advertising. Max R2 + M2 + RM + R + M s.t R + M - Select your answer -<>=Item 9 R, M - Select your answer -<>=Item 11Explanation / Answer
pro t is 32 thousand dollars. Sensitivity analysis in the Green Lawns example Consider sensitivity to a change in the total promotional budget. It is common practice to let represent the additional funds available (in thousands of dollars). Then the new constraint becomes x1 + x2 = 2 + : Note that at the current solution x1 = 1, = 0, and x2 =2+ x1 = 1. Step 1. Construct a function of by substituting x1 = 1 and x2 =2+ x1 =2+ 1=1+ into the total sales function: f () = S(1; 1 + ) = 2 10(1 + ) 2 8(1 + ) + 18 + 34(1 + ) = 32 + 6 102 : Step 2. Compute the rate of change of sales with respect to . That is, compute f 0(): f 0() = Step 3. Then dSALES/dRHS at the optimal solution is f 0(0): f 0(0) =
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.