Question 5 Please Linear Programming Applications in Marketing, Finance, and Ope
ID: 329624 • Letter: Q
Question
Question 5 Please
Linear Programming Applications in Marketing, Finance, and Operations Management: Case Problem 1: Planning an Advertising Campaign
The Flamingo Grill is an upscale restaurant located in St. Petersburg, Florida. To help plan an advertising campaign for the coming season, Flamingo's management team hired the advertising firm of Haskell and Johnson (HJ). The management team requested HJ's recommendation concerning how the advertising budget should be distributed across television, radio, and newspaper advertisements. The budget has been set at $279,000.
In a meeting with Flamingo's management team, HJ consultants provided the following information about the industry exposure effectiveness rating per ad, their estimate of the number of potential new customers reached per ad, and the cost for each ad:
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The exposure rating is viewed as a measure of the value of the ad to both existing customers and potential new customers. It is a function of such things as image, message recall, visual and audio appeal, and so on. As expected, the more expensive television advertisement has the highest exposure effectiveness rating along with the greatest potential for reaching new customers.
At this point, the HJ consultants pointed out that the data concerning exposure and reach were only applicable to the first few ads in each medium. For television, HJ stated that the exposure rating of 90 and the 4000 new customers reached per ad were reliable for the first 10 television ads. After 10 ads, the benefit is expected to decline. For planning purposes, HJ recommended reducing the exposure rating to 55 and the estimate of the potential new customers reached to 1500 for any television ads beyond 10. For radio ads, the preceding data are reliable up to a maximum of 15 ads. Beyond 15 ads, the exposure rating declines to 20 and the number of new customers reached declines to 1200 per ad. Similarly, for newspaper ads, the preceding data are reliable up to a maximum of 20; the exposure rating declines to 5 and the potential number of new customers reached declines to 800 for additional ads.
Flamingo's management team accepted maximizing the total exposure rating across all media as the objective of the advertising campaign. Because of management's concern with attracting new customers, management stated that the advertising campaign must reach at least 100,000 new customers. To balance the advertising campaign and
make use of all advertising media, Flamingo's management team also adopted the following guidelines:
Use at least twice as many radio advertisements as television advertisements.
Use no more than 20 television advertisements.
The television budget should be at least $140,000.
The radio advertising budget is restricted to a maximum of $99,000.
The newspaper budget is to be at least $30,000.
HJ agreed to work with these guidelines and provide a recommendation as to how the $279,000 advertising budget should be allocated among television, radio, and newspaper advertising.
Managerial Report
Develop a model that can be used to determine the advertising budget allocation for the Flamingo Grill. Include a discussion of the following items in your report:
1. A schedule showing the recommended number of television, radio, and newspaper advertisements and the budget allocation for each medium. Show the total exposure and indicate the total number of potential new customers reached.
2. A discussion of how the total exposure would change if an additional $10,000 were added to the advertising budget.
3. A discussion of the ranges for the objective function coefficients. What do the ranges indicate about how sensitive the recommended solution is to HJ's exposure rating coefficients?
4. The resulting media schedule if the objective of the advertising campaign was to maximize the number of potential new customers reached instead of maximizing the total exposure rating.
5. A comparison of the two media schedules resulting from items 1 and 4, respectively. What is your recommendation for the Flamingo Grill's advertising campaign?
Advertising Media Exposure Rating per Ad New Customers per Ad Cost per Ad Television 90 4000 $10,000 Radio 25 2000 $ 3000 Newspaper 10 1000 $ 1000Explanation / Answer
Executive Report
Background
The Flamingo Grill is an upscale restaurant located in St. Petersburg, Florida. Flamingo’s management team hired advertising firm Haskell & Johnson to recommend how their advertising budget of $279,000 should be allocated across television, radio, and newspaper advertisements.
Objective
Maximize the total exposure rating across all media, while reaching at least 100,000 new customers.
Methodology
A Linear Mathematical Program was created. The program was then entered into Excel, and solved using Excel solver.
Results
Advertising Media
Television
Radio
Newspaper
T1
T2
R1
R2
N1
N2
Recommended Number of Ads
10
5
15
18
20
10
Max Total Exposure Rating
2160
Recommendation
I recommend that The Flamingo Grill uses 15 television ads, 33 radio ads, and 30 newspaper ads.
Rationale
Following this recommendation will maximize the Total Exposure Rating.
Managerial Report
1. Advertising Schedule:
Media
Number of Ads
Budget
Television
15
$150,000
Radio
33
$99,000
Newspaper
30
$30,000
Total
78
$279,000
Total Exposure: 2160
Total New Customers Reached: 127,100
2. The shadow price for the budget constraint is 0.0055. So, if an additional $10,000 were added to the advertising budget, total exposure will increase by 55 points.
3. The recommended solution is not very sensitive to the exposure rating coefficients. For example, there is a huge difference in the new customers reached and number of ads suggested in the part 1 and 4 schedules, but the total exposure does not change as drastically.
4. Advertising Schedule:
Media
Number of Ads
Budget
Television
14
$140,000
Radio
28
$84,000
Newspaper
55
$55,000
Total
97
$279,000
Total Exposure: 2130
Total New Customers Reached: 139,600
5. I would recommend using the advertising schedule from part 4 instead of the original schedule because more new customers would be reached and the exposure would only decrease by 30 points.
Appendix
Please see the attached Excel documents.
Initial Exposure
After Initial Exposure
Advertising
Media
Exposure
Rating per Ad
New Customers
per Ad
Cost
per Ad
Advertising
Media
Exposure
Rating per Ad
New Customers
per Ad
Cost
per Ad
Television
90
4000
$10,000
Television
55
1500
$10,000
Radio
25
2000
$3,000
Radio
20
1200
$3,000
Newspaper
10
1000
$1,000
Newspaper
5
800
$1,000
Exposure rating and new customers reached decreases after 10 TV ads, 15 radio ads, and 20 newspaper ads.
New Customers Reached > 100,000
Advertising Budget = $279,000; (Television ads > $140,000; Radio ads < $99,000; Newspaper ads > $30,000)
Decision Variables:
T1= number of television ads with a rating of 90 and 4000 new customers
T2= number of television ads with a rating of 55 and 1500 new customers
R1= number of radio ads with a rating of 25 and 2000 new customers
R2= number of radio ads with a rating of 20 and 1200 new customers
N1= number of newspaper ads with a rating of 10 and 1000 new customers
N2= number of newspaper ads with a rating of 5 and 800 new customers
Objective Function and Constraints
Max
90T1 + 55T2 + 25R1 + 20R2 + 10N1 + 5N2
s.t.
T1 < 10
R1 < 15
N1 < 20
10,000T1 + 10,000T2 + 3,000R1 + 3,000R2 + 1,000N1 + 1,000N2 < 279,000
4,000T1 + 1,500T2 + 2,000R1 + 1,200R2 + 1,000N1 + 800N2 > 100,000
-2T1 + -2T2 + R1 + R2 > 0
T1 + T2 < 20
10,000T1 + 10,000T2 > 140,000
3,000R1 + 3,000R2 < 99,000
1,000N1 + 1,000N2 > 30,000
T1, T2, R1, R2, N1, N2 > 0
Optimal Solution: Budget Allocation:
T1 = 10, T2 = 5; 10 + 5 = 15 Television ads 15 * 10,000 = $150,000
R1 = 15, R2 = 18; 15 + 18 = 33 Radio ads 33 * 3,000 = $99,000
N1 = 20, N2 = 10; 20 + 10 = 30 Newspaper ads 30 * 1,000 = $30,000
If $10,000 is added to budget: 10,000 * 0.0055(shadow price) = 55 points
Part 4 Exposure: 90(10) + 55(4) + 25(15) + 20(13) + 10(20) + 5(35) = 2130
Advertising Media
Television
Radio
Newspaper
T1
T2
R1
R2
N1
N2
Recommended Number of Ads
10
5
15
18
20
10
Max Total Exposure Rating
2160
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