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 includes television, radio, and newspaper.

Audience estimates, costs, and maximum media usage limitations are as shown:

Constraint Television Radio Newspaper Audience per advertisement 100,000 18,000 40,000 Cost per advertisement $2000 $300 $600

Maximum media usage 10 20 10 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 promotionsl 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? Suppose the problem is changed as follows:

Instead of maximizing the total audience contact, we now want to achieve total audience contact of at least 900,000.

Write down this new constraint for the total audience contact using the variable names: T = number of television advertisements R = number of radio advertisements N = number of newspaper advertisements.