GreenLawns provides a lawn fertilizing and weed control service. The company is adding a special aeration treatment as a low-cost extra service option that 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 $3,000 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:
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 $2,000 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 $3,000 on total advertising.
- c. Determine the optimal amount to spend on radio and direct-mail advertising. How much in sales will be generated?
a.
To find the amount of sales generated when $2,000 and $1,000 is spend on radio and direct-mail advertising.
Explanation of Solution
To find the amount of sales generated, substitute $2,000 and $1,000 is spend on radio and direct-mail advertising in the below relationship equation.
Therefore, sales of $36,000 will be generated with the budget allocated for promotion.
b.
To formulate optimization problem to maximize sales when total advertising cost is not more than $3,000.
Explanation of Solution
The formulation is for the problem is shown below,
c.
To solve and find the optimal amount to be spend on advertising to determine the amount of sales generated.
Explanation of Solution
Formula:
Solver:
Output:
The solution is R = $2,500 and M = $500 with Sales of $37,000
Want to see more full solutions like this?
Chapter 10 Solutions
Essentials Of Business Analytics
- 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 $3,500 is available for this promotional campaign. Based on past experience in promoting its other services, GreenLawns obtained the following estimate of the relationship between sales and the amount spent on promotion in these two media. S = −2R2 − 10M2 − 8RM + 18R + 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 (in dollars) if $2,500 is spent on radio advertising and $1,000 is…arrow_forwardUnited Dairies, Inc., supplies milk to several independent grocers throughout Dade County, Florida. Managers at United Dairies want to develop a forecast of the number of half-gallons of milk sold per week. Sales data for the past 12 weeks follow and have been transferred in the data file UDFMilk.xlsx download(also posted under week 11 module). Week Sales Week Sales 1 2750 7 3300 2 3100 8 3100 3 3250 9 2950 4 2800 10 3000 5 2900 11 3200 6 3050 12 3150 By Thursday, April 15 (11:55pm PST), answer the following 2 questions and attach a word doc or excel file to show your work. Use the data in the file UDFMilk.xlsx downloadto construct a time series plot. What type of pattern exists in the data? Use exponential smoothing with to develop a forecast of demand for week 13.arrow_forwardGreenLawns 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 $3,500 is available for this promotional campaign. Based on past experience in promoting its other services, GreenLawns obtained the following estimate of the relationship between sales and the amount spent on promotion in these two media. S-2R²10M²8RM +18R+ 34M where 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 (in dollars) if $2,000 is spent on radio advertising and $1,500 is spent on direct-mail advertising? S = $ |x S = total sales in thousands of dollars R thousands of dollars spent on radio advertising M = thousands of dollars spent on…arrow_forward
- Compare the primary types of forecasting methods used to determine demand.arrow_forwardA mail-order catalog business that sells personal computer supplies, software, and hardware maintains a centralized warehouse for the distribution of products ordered. Management is currently examining the process of distribution from the warehouse and has the business objective of determining the factors that affect warehouse distribution costs. Currently, a handling fee is added to the order, regardless of the amount of the order. Data that indicate the warehouse distribution costs and the number of orders received have been collected over the past 24 months and can be seen below: Months Distribution Cost ($thousands) Number of Orders 1 52.95 4015 2 71.66 3806 3 85.58 5309 4 63.69 4262 5 72.81 4296 6 68.44 4097 7 52.46 3213 8 70.77 4809 9 82.03 5237 10 74.39 4732 11 70.84 4413 12 54.08 2921 13 62.98 3977 14 72.30 4428 15 58.99 3964 16 79.38 4582…arrow_forwardThe Excel file (Forecasting Assignment Data) contains quarterly motorcycle shipments for Harley-Davidson from 2000 through 2006. Forecast Harley-Davidson quarterly motorcycle shipments for 2007 using winter's methodarrow_forward
- You are on the board of directors for Sew and Tell, an up and coming apparel brand focusing on producing t-shirts with a positive message. The company is looking to ramp up production and has hired an independent consulting group to evaluate the profitability of either a medium or large scale expansion. Your boss, the company president Jack Pott, has sent you the following email: Board of Directors Member, The consulting group has completed the analysis. The following table breaks down the results with us pursuing either a medium or large scale expansion. It gives low, medium, and high projections, the associated amount of profits (in thousands of $), and the probability of each outcome happening. Medium-Scale Expansion Profit 50 Large-Scale Expansion Profit Probability Probability Low .2 .2 Medium 150 .5 100 .5 High 200 .3 300 .3 Personally, I would love to hit the jackpot and reach a profit of $300,000, but our goal as a company is to maximum profit in the least risky way. Taking…arrow_forwardGreenLawns 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. (a) What is the value of sales if $3,000 is spent on radio advertising and $1,000 is…arrow_forwardJensen Tire & Auto is deciding whether to purchase a maintenance contract for its newcomputer wheel alignment and balancing machine. Managers feel that maintenance expenseshould be related to usage, and they collected the following information on weeklyusage (hours) and annual maintenance expense (in hundreds of dollars). a. Develop a scatter chart with weekly usage hours as the independent variable. Whatdoes the scatter chart indicate about the relationship between weekly usage and annualmaintenance expense?b. Use the data to develop an estimated regression equation that could be used to predictthe annual maintenance expense for a given number of hours of weekly usage. Whatis the estimated regression model? c. Test whether each of the regression parameters b0 and b1 is equal to zero at a 0.05level of significance. What are the correct interpretations of the estimated regressionparameters? Are these interpretations reasonable?d. How much of the variation in the sample values of…arrow_forward
- Cost of Direct Materials Used in Production for a Manufacturing Company Walker Manufacturing Company reported the following materials data for the month ending June 30: Materials purchased $215,500 Materials inventory, June 1 68,000 Materials inventory, June 30 56,700 Determine the cost of direct materials used in production by Walker during the month ended June 30.arrow_forwardDetermine if the following scenarios involve an observational study or an experiment. Make sure your answers are legible and spelled correctly. A team of ecologists determines the different species of frogs that live in the local swamplands. A medical researcher divides patients into a treatment group and a control group to determine the effect of a new drug on overall cholesterol levels in patients. A medical insurance company determines the average cost to cover a tooth extraction procedure over the past 3 years. As part of a medical study to determine the effectiveness of a new technique for abdominal surgery, patients undergo the surgery with the new technique or with a traditional technique. The recovery time from surgery is then compared for the two different techniques. The general manager of a baseball team determines the on-base percentage (OBP) for his players over the past two seasons. A dietitian examined the effectiveness of a weight-loss program by randomly…arrow_forward
- Glencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw HillBig Ideas Math A Bridge To Success Algebra 1: Stu...AlgebraISBN:9781680331141Author:HOUGHTON MIFFLIN HARCOURTPublisher:Houghton Mifflin Harcourt