Lynn is selling cushions as part of an enterprise project. On her first attempt, she sold 80 cushions at the cost of £15 each. She hopes to sell more cushions next time. Her adviser suggests that she can expect to sell 10 more cushions for every £1 that she lowers the price.

a. The number of cushions sold c can be modelled by the equation c = 230 − Hp, where £p is the price of each cushion and H is a constant. Determine the value of H. To model her total revenue, £r, Lynn multiplies the number of cushions sold by the price of each cushion. She writes this as r = p(230 − Hp).

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, show that Lynn can increase her revenue by £122.50 through lowering her prices, and state the optimum selling price of a cushion.