The Peak Grill is an upscale restaurant located in St. Petersburg, Florida. To help plan an advertising campaign for the coming season, Peak'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 $325,000. In a meeting with Peak'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:
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 re- call, 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. Peak'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 the advertising media, Peak's management team also adopted the following guidelines:
• 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.
HJ agreed to work with these guidelines and provide a recommendation as to how the $325,000 advertising budget should be allocated among television, radio, and newspaper advertising.
-What are the constraints?
- What is the objective function?
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. (Whole Numbers)
2. A discussion of how the total exposure would change if the budget was decreased by $10,000 from the advertising budget. (Whole numbers)
3. A discussion of the ranges for the objective function coefficients (original). 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 Peak Grill's advertising campaign?