Tickets for a theatre performance currently sell for 17 dollars. At this price, 500 tickets sell. It is estimated that for every 2 dollars increase in price, 10 fewer tickets will be sold. Determine the price that will result in the maximum revenue and determine the maximum revenue.
Answer: The ticket price of 37.75 dollars will result in the maximum revenue of 17111 dollars
I thought that I was supposed to find the roots of the parabola, but they aren't even close to the right answer, so now I'm lost. Any help is greatly appreciated.
You are supposed to find the vertex of the parabola. Write an equation for the revenue as a function of ticket price. Differentiate it with respect to ticket price, set the derivative to zero....