An airline sells all tickets for a certain route at the same price. If he charges $200 per ticket, he sells 10,000 tickets. For every $50 the ticket price is reduced, a thousand more tickets are sold. Therefore, if tickets sell for $150 each, then 11,000 tickets are sold. It costs the airline $100 to carry one person.
(a) Express the total profit P in terms of the number n of tickets sold.
(b) Express the total profit P in terms of the price p of a ticket.