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:

Constraint Television Radio Newspaper

Audience per advertisement $1000001800040000$

Cost per advertisement $$2000$ $$300$ $$600$

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 promotional budget is limited to $$18200,$ 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? If required, round your answer to nearest integer.

Let T $=$ number of television spot advertisements

R $=$ number of radio advertisements

N $=$ number of newspaper advertisements

Budget $

T $=$ fill in the blank $1$ fill in the blank $2$

R $=$ fill in the blank $3$ fill in the blank $4$

N $=$ fill in the blank $5$ fill in the blank $6$

fill in the blank $7$

What is the total audience reached?

fill in the blank $8$

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

fill in the blank $9$