Advertising alternatives include television, radio, and online. Audience estimates, costs, and maximum media usage limitations are as shown.

account for at least $10\%$ of the total number of advertisements authorized.

$($a$)$ If the promotional budget is limited to $$25,100,$ how many commercial messages should be run on each medium to maximize total audience contact?

Television

Radio

Online

What is the allocation of the budget among the three media, and what is the total audience reached?

Television Budget $($in dollars$)$ $

Radio Budget $($in dollars$)$ $

Online Budget $($in dollars$)$ $

Total Audience