Question

1. A collage arena is the 13,000 seats. Suppose that when tickets are $16, the average attendance is around 7,700 per game. The management suspects that for every dollar that the ticket price is lowered, attendance will increase by 640. What should the ticket prices be to maximize revenue from ticket sales?

Answer 1

Let x be the amount(in dollars) of decrease in the ticket price.

The price of each ticket will be = (16 - x) dollars

The attendance will be = 7700 + 640x

The revenue from ticket sales is the product of price of each ticket and the attendance.

To maximize the revenue, first we have to find the critical point(s) by setting R'(x) to 0 and then we have to do the second derivative test.

Now,

As R''(1.984375) = -1280 < 0, the revenue is maximized at x = 1.984375.

Hence, to maximize the revenue the ticket price should be