A regional airline has a regular flight between two cities. They sell two types of tickets for this flight, business and economy. If they price business class tickets at $P , they can expect to sell 21 P 40 business class tickets; if they price economy class tickets at $P , they can expect to sell 170 P 2 economy class tickets. If the flight has n passengers, the cost to operate the flight is 1000 40n dollars. (a) Write a function giving the profit the airline makes on the flight if they sell business class tickets for $P1 and economy class tickets for $P2. (b) Find and classify all critical points of the profit function. (c) Naturally, the airline wants to maximize its profit. The graph of the profit function is a paraboloid.(2) Based on that, do you have enough information to determine how the airline should price its busi- ness and economy class tickets to maximize profit? Explain