Difficult# Maximum of a Function 2

ACTMAT-E1FIEL

When a movie theater charges \$6 per ticket, an average of 300 paying customers attend. For every \$0.50 increase in price, 12 fewer paying customers on average attend.

If:

$$R(x) = (6 + 0.5x)(300-12x)$$

...where $x$ is the number of \$0.50 increases and $R(x)$ is the total revenue, at what price should the theater charge in order to maximize revenue?