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 $$18,200,$ how many commercial messages should be run on each medium to maximize total audience contact? If

your answer is zero enter $"0".$

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

What is the total audience reached?

$($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