A professional basketball team plays in an arena that holds 20 000 spectators. Average attendance at each game has been 14 000. The average ticket price is $75. Market research shows that for each $5 reduction in the ticket price, attendance increases by 800. Find the price that will maximize revenue.

Question

dan815 · Answer

sparkly did u see the anwer to your other qusetion?

anonymous · Answer

yes thank you

anonymous · Answer

$$
\text{population}(x) = \max(14000-75x,\; 20000) \
\text{revenue}(x) = \text{population}(x)\cdot x =\max(14000-75x,\; 20000)x \
$$

anonymous · Answer

i don't understand how you got those

anonymous · Answer

Hmmm I might have made a mistake.

anonymous · Answer

When $x=75$, the population is $14000$

anonymous · Answer

When $x = 70$, the population is $14800$

anonymous · Answer

You can use this to find the population function, since it is a line...

anonymous · Answer

This is from point-slope formula: $$
(y -14000) = -\frac{800}{5}(x-75)
$$