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Math, Statistics and Probability : Course Help Online

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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?

Advertisement Alternatives
No of commercial
messages
Television  5
Radio  10
Newspaper  10
What is the allocation of the budget among the three media?
Advertisement Alternatives Budget ($)
Television $ 12500
Radio $ 3000
Newspaper $ 5000
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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