The profit function for the Recklus Hang gliding Service is P(x) = -0.4x^2 + fx - m, where f represents the set up fee for a customer's daily excursion and m represents the monthly hanger rental. Also, P represents the monthly profit in dollars of the small business where x is the number of flight excursions facilitated in that month.

a) If $40 is charged for a set up fee, and the monthly hanger rental is $800; write an equation for the profit, P, in terms of x.

b) How much is the profit when 30 flight excursions are sold in a month?

c) How many flight excursions must be sold in order to maximize the profit? Show your work algebraically. Trial and error is not an appropriate method of solution use methods taught in class.

d) What is the maximum profit?