Question

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 & 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.

Advertising Media	Exposure Rating per Ad	New Customers per Ad	Cost per Ad
Television	90	4000	$10,000
Radio	25	2000	$ 3,000
Newspaper	10	1000	$ 1,000

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 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. (Please provide both SOLVER and LINGO output)
2. Please write a report to describe the sensitivity report regarding the optimal solution, objective function values, slack/surplus variables, binding/nonbinding, shadow price, range of feasibility, and range of optimality.

Answer 1

The model is shown below

The formulas are shown below

The solver parameters are shown below

The result is shown below

The sensitivity report is shown below

Managerial report

The optimized approach to this advertisement campaign is to deploy 15 TV ads, 33 Radio ads and 30 Newspaper ads. The combined cost will be 279000. This is the exact budget for the campaign.

The result of this solution will be total exposure of 2160 people, expected total new customer acquisition is 127100. Thus we meet our primary requirements.

We also see that we have met other constraints such as TV ads are below 20 in number, the budget for TV ad is 150000. The budget for Radio Ad is 99000. And the budget for newspaper ads is 30000. Thus we have used the budget constraints efficiently.

In terms of slack/surplus we see that we have a surplus of new customer acquisition of 27100, we have slack of 5 TV ads and a surplus expenditure on budget on our requirement for TV ads by 10000.

The last three constraints, i.e. Radio budget, Newspaper budget, and Total budget, have 0 surplus or slack. This indicates that they are binding constraints and have shadow price present. These shadow prices indicate their sensitivity. For example, if we increase the total budget by $1, the overall exposure can be increased by 0.0055. The same way if we decrease the budget to 278999 then the exposure will reduce by 0.0055. These values of shadow price is applicable within their ranges shown in allowable increase and decrease. For example, the impact of 0.0055 exposure is applicable as long as the total budget remains between 279000-10000 and 279000+50000.