I operate 81 flights a day on 30 seat planes, and for each flight I can sell up to 32 seats at $200 each. If more people show up than I have seats for, I have to pay them $500 each. If I sell 32 tickets, the probability that all 32 show up is 5%, 31 people show up is 10%, and thus the probability that 30 or fewer people show up is 85%. If I sell 31 tickets, the probability that exactly 31 people show up is 10%. If I sell the profit maximizing number of tickets on each flight, how much money would I expect to earn each day? Assume all of the tickets I offer for sale will be bought.