Midtown Motors Inc., has hired a marketing services firm to develop an advertising strategy for promoting Midtown's used-car sales. The marketing firm has recommended that Midtown use spot announcements on both television and radio as the advertising media for the proposed promotional campaign. Advertising startegy guidelines are expressed as follows:

1. Use at least 30 announcements for combined television and radio coverage

2. Do not use more than 25 radio announcements

3. The number of radio announcements cannot be less than the number of television announcements

The television station has quoted a cost of $1200 per spot announcement, and the radio station has quoted a cost of $300 per spot announcement. Midtown's advertising budget has been set at $25,500. The marketing services firm has rated the various advertising media in terms of audience coverage and recall power of the advertisement. For Midtown's media alternatives, the television announcement is rated at 600, and the radio announcement is rated at 200. Midtown's president would like to know how many television and how many radio spot announcements should be used to maximize the overall rating of the advertising campaign.

Midtown's president believes the television station will consider running the Midtown spot announcement on its highly rated evening news program (at the same cost) if Midtown will consider using additional television announcements.

Managerial Report

Perform an analysis of advertising strategy for Midtown Motors, and prepare a report to Midtown's president presenting your findings and recommendations. Include (but do not limit your discussion to) a consideration of the following:

1. The recommended number of television and radio spot announcements

2. The relative merits of each advertising medium

3. The news program rating that would be necessary before it would make sense to increase the number of television spots

4. The number of television spots that should be purchased if the news program is rated highly enough to make increasing the number of television spots advisable

5. The restrictions placed on the advertising strategy that Midtown might want to consider relaxing or altering

6. The best use of any possible increase in the advertising budget

7. Any other information that may help Midtown's president make the advertising strategy decision

Include a copy of your linear programming model and graphical solution