Answer
(a) $-3000x^2+57000x$
(b) $9.5$ dollars
(c) $19$ dollars
Work Step by Step
(a) We can model the number of attendance (y) as linearly related to the ticket price (x).
When $x=10, y=27000$, and $x=9, y=27000+3000=30000$
The line equation is $\frac{y-27000}{x-10}=\frac{30000-27000}{9-10}$
$y=-3000x+57000$
The revenue is given by $R=xy=-3000x^2+57000x$
(b) The maximum of $R$ happens when $x=57000/6000=9.5$ dollars
(c) Let $y=0$, we get $x=57000/3000=19$ dollars