The tickets to a charity concert will sell out if the price is $15 per ticket. it is estimated that for each $1 increase in ticket's price, 20 tickets will remain unsold. what ticket price will maximize the charity's profit, if there are total 500 seats in the concert hall?

Let's define variables: x: number of times the ticket price increases ($ 1). The income is given by: I(x) = (15 + x)(500-20x) We can rewrite this function in the following way: I (x) = - 20x ^ 2 + 200x + 7500 We use the following equation to find the maximum: max = (-b)/(2a) where: a=-20 b=200 c=7500 then, we have: max = (-200)/(2(-20)) max = (200)/(40) max=5 Thus, the ticket price that maximizes the benefit is: 15 + x = 15 + 5 = 20 $ Answer: A ticket price that will maximize the charity's profit, if there are total 500 seats in the concert hall is: $ 20