Special Assignment: Linear Programming, statistics homework help

Special Assignment: Linear Programming

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 strategy guidelines are expressed as follows:

• Use at least 30 announcements for combined television and radio coverage.
• Do not use more than 25 radio announcements.
• The number of radio announcements cannot be less than the number of television

announcements.

The television station has quoted a cost of $1,200 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 in order to maximize the overall rating of the advertising campaign.

Midtown’s president believes that 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.

Building up a Managerial Strategy

Perform an analysis of advertising 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 items.

a. The recommended number of television and radio spot announcements.
b. The relative merits of each advertising medium.
c. The rating that would be necessary for the news program before it would make

sense to increase the number of television spots.
d. 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.

Summarize your results in a Microsoft WORD file and send your report to the Blackboard e-mail tool. Your report must show your graphical solutions including your LP model and a graph showing the feasible region. In addition, you must explain all your steps in detail.