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

Constraint Television Radio Online

Audience per

Advertisement $100,00018,00040,000$

Cost per ad $2,000300600$

Maximum media

usage $102010$

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.

If the promotiomal 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 budget among the three media, and what is the total audience reached?

By how much would audience contact increase if an extra $$100$ were allocated to the promotional budget?