A football stadium has 25 000 seats. The football club know from past experience that they will sell only 10 000 tickets if each ticket costs £30. They also expect to sell 1000 more tickets every time the price goes down by £1.

a. The number of tickets sold t can be modelled by the linear equation t = M − 1000p, where £p is the price of each ticket and M is a constant. Find the value of M. The total revenue, £r, can be calculated by multiplying the number of tickets sold by the price of each ticket. This can be written as r = p(M − 1000p).

b. Rearrange r into the form A − B(p − C)², where A, B and C are constants to be found.

c. Using your answer to part b or otherwise, work out how much the football club should charge for each ticket if they want to make the maximum amount of money.