(Solved): An airline sells all the tickets for a certain route at the same price. If it charges 200 dollars ...

An airline sells all the tickets for a certain route at the same price. If it charges 200 dollars per ticket, it sells 10,000 tickets. For every 35 dollars the ticket price is reduced, an extra thousand tickets are sold. Thus if the tickets are sold for 165 dollars each, then 11,000 tickets sell. It costs the airline 100 dollars to fly a person. a. Express the total profit \( P \) in terms of the number \( n \) of tickets sold. \[ P(n)=\$ \] b. Express the total profit \( P \) in terms of the price \( p \) of one ticket. \[ P(p)=\$ \] You will see this type problem a lot when we do \( \mathrm{max} / \mathrm{min} \) problems in calculus. Hint: \( ( \) total profit \( )=( \) profit on one ticket \( ) \times( \) number of tickets sold \( ) \). Both terms depend on \( p \), and \( ( \) profit on one ticket \( )=( \) price of ticket \( )-( \) cost to fly passenger \( ) \)