A soccer stadium holds 62,000 people. With a ticket price of $17. The average attendance has been 26,000. When the price dropped to $13, the average attendance rose to 31,000. Assuming that attendance is linearly related to ticket price, what ticket price would maximize revenue?
the attendance change per $1 price decrease is 5000/4 = 1250
let x be the number of $1 price decreases. Then we have revenue
r = (17-x)(26000+1250x)
revenue decreases as x increases, so the max revenue occurs at a price of $13