Question
A fishing competition is scheduled for an upcoming week. Over the course of the week, the sponsor would like to promote the event through radio,
A fishing competition is scheduled for an upcoming week. Over the course of the week, the sponsor would like to promote the event through radio, television, newspaper, and internet advertising. The newspaper and internet ads have already been scheduled; however, the sponsor would like to determine the number of ads to run on a local sports radio station and a cable television network. The cost for each radio ad is $850, whereas the cost for each TV ad is $2475. Radio and television ads have diminishing returns with respect to new audience reached and exposure rating. This is shown in the table below:
| New audience reached per ad |
| Exposure rating per ad | ||||
| ads 1-4 | ads 5-8 | ads 9+ |
| ads 1-4 | ads 5-8 | ads 9+ |
Radio | 19,000 | 12,000 | 7,000 |
| 46 | 24 | 8 |
Television | 50,000 | 27,000 | 15,000 |
| 80 | 38 | 20 |
For example, if a decision was made to run 6 television ads, then each of the first four ads would be assumed to reach 50,000 new customers with an exposure rating of 80. However, each of the last two ads (5 and 6) would only reach 27,000 new audience members with an exposure rating of 38. The sponsor would like you to prepare a linear programming formulation that will determine the number of radio and television ads to make with the goal of maximizing total exposure rating. The sponsor has a promotional budget of $25,000 and wants to reach a new audience of at least 400,000 via the advertising plan. Write the LP formulation.
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