01 Jul Math, Statistics And Probability
The Chamber of Commerce periodically sponsors public service seminars and programs. Currently, promotional plans are under way for this year’s program. Advertising alternatives include television, radio, and newspaper. Audience estimates, costs, and maximum media usage limitations are as shown:
| Constraint | Television | Radio | Newspaper |
| Audience per advertisement | 110,000 | 17,000 | 30,000 |
| Cost per advertisement | $2,500 | $300 | $500 |
| Maximum media usage | 10 | 23 | 10 |
To ensure a balanced use of advertising media, radio advertisements must not exceed 40% of the total number of advertisements authorized. In addition, television should account for at least 10% of the total number of advertisements authorized.
| (a) | If the promotional budget is limited to $20,500, how many commercial messages should be run on each medium to maximize total audience contact? | |||||||
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| What is the allocation of the budget among the three media? | ||||||||
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| What is the total audience reached? | ||||||||
| 1020000 | ||||||||
| (b) | By how much would audience contact increase if an extra $100 were allocated to the promotional budget? | |||||||
| Increase in audience coverage of approximately |
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