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

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 $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 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? 7000 (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 12 RM + 16 34 R, M (c) Determine the optimal amount to spend on radio and direct-mail advertising. How much in sales will be generated? Amount spent on radio advertising- Amount spent on direct-mail advertising = Total Sales-S 32000 4000

Explanation / Answer

I believe you are concerened here with the last answer(c) since rest of the answers you have already answered correctly. So By solving the equation

S=-2*R^2-12*M^2-9*RM+16R+34M

Now we have optimum level of S and R calculates as 32 and 4 respectively (You need to take values in thousands and you have already determined 32000 anf 4000 for S and R respectively)

So., to solve this equation we get

32=-2*4^2 - 12*M^2 -9*4M+16*4+34M

12*M^2+2M+32+32-64=0

12*M^2+2M=0

so., 2M(6M+1)=0

M=0 or M=-1/6

since amt spent on Media can't be -ve the right answer is 0

So here there should not be any amt spent on Media

Hope the above explaination has helped you in understanding the problem Pls upvote the ans if it has really helped you. Good Luck!!

Related Questions

Navigate

• Browse (All)
• Browse G
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.