The Westchester 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:

To ensure a balanced use of advertising media, radio advertisements must not exceed 50% 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 $18,200, how many commercial messages should be run on each medium to maximize total audience contact? What is the allocation of the budget among the three media, and what is the total audience reached?
b. By how much would audience contact increase if an extra $100 were allocated to the promotionalbudget?

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Constraint Audience per advertisement Cost per advertisement Maximum media usage Television Radio 18,000 $300 20 Newspaper 100,000 $2000 10 40,000 S600 10