The promotions manager of a new band is deciding how much to charge for concert tickets. She has calculated that if the tickets are $25 each, then 310 people will come to the concert. The band
wants to improve their profit. So after analyzing some data, the manager expresses the relation
between the profit, P and the number of $1 price increases, x, is P = 10(25 + x)(31 - x)
a. Determine the price of the tickets that maximizes the profit.
b. Determine the maximum profit.
c. How many tickets sold, if they set the price so that it maximizes profit?