Question: (a) A cruise line offers a trip for $2000 per passenger. If at least 100 passengers sign up, the price is reduced for all the passengers by $10 for every additional passenger (beyond 100) who goes on the trip. The boat can accommodate 250 passengers. What number of passengers maximizes the cruise line's total revenue? What price does each passenger pay then?
(b) The cost to the cruise line for n passengers is 80,000+ 400n. What is the maximum profit that the cruise line can make on one trip? How many passengers must sign up for the maximum to be reached and what price will each pay?