SOLUTION: The revenue at the Assembly Center depends on the number of seats sold for the Willie Williams and the Wranglers concert. At $10 per ticket, they will fill all 8000 seats. The mana

Question 1147418: The revenue at the Assembly Center depends on the number of seats sold for the Willie Williams and the Wranglers concert. At $10 per ticket, they will fill all 8000 seats. The manager knows that for every $1 increase in the price, 500 tickets will go unsold. If the revenue in dollars, 𝑅(𝑝), is given by
𝑅(𝑝) = −500𝑝^2 + 13000𝑝, where 𝑝 is the price per ticket sold.
What ticket price will produce a maximum revenue? What is the maximum
revenue? You must show this algebraically.
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
Let = the number of $1 increases in price/ticket

This shows the equation works
--------------------------------------

The maximum is at when the equation has the form

is at

The maximum revenue is at a ticket price of $13/ticket
which is after three $1 increases in price/ticket
Here's the plot:

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