A linear programming computer package is needed.

maximum media usage limitations are as shown.

$($a$)$ If the promotional budget is limited to $$20,500,$ 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

Radio Budget

Online Budget

$($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.$)$