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 $100,00016,00035,000$

Cost per advertisement $$1,500$ $$250$ $$650$

Maximum media usage $102414$

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 $$18,400,$ how many commercial messages should be run on each medium to maximize total audience contact? If your answer is zero enter $0.$

Advertisement Alternatives No of commercial

messages

Television

$10$

Radio

$11$

Online

$1$

What is the allocation of the budget among the three media?

Advertisement Alternatives Budget Allocation

Television $

$15000$

Radio $

$2750$

Online $

$650$

What is the total audience reached?

$1211000$

$($b$)$ By how much would audience contact increase if an extra $$100$ were allocated to the promotional budget? Round your answer to the nearest whole number.

Increase in audience coverage of approximately

$18400$