Question: A sports club plans to charter a plane, and charge its members 10% commission on the price they pay to buy seats. That price is arranged by the charter company. The standard fare for each passenger is $800. For each additional person above 60, all travellers (including the first 60) get a discount of $10. The plane can take at most 80 passengers.
(a) How much commission is earned when there are 61, 70, 80, and 60 + x passengers?
(b) Find the number of passengers that maximizes the total commission earned by the sports club.