A city centre tour guide currently charges $27 for a full day's tour. The average number of customers is 32. Market research suggests that for every $1 increase in tour price, the guide can expect to lose 3 customers per tour.

(a) If the price increase is $x calculate the expected revenue.

(b) The guide needs to ensure that the expected revenue is at least $750. By solving a quadratic inequality, find the range of prices that need to be charged.

(c) What price should be charged to maximise expected revenue?