Donald Blowshisown Trumpet is an extremely wealthy and successful businessman. Trumpet Airlines is one of his many companies. Trumpet Airlines flies a 100-seat aircraft every day from New York to Washington DC. They sell two types of tickets: discount tickets for $350 and full-fare tickets for $1000. Discount tickets must be purchased at least 21 days before the plane departs. Based on their past experience, more than 100 customers are willing to purchase discount tickets. In addition, all of the customers who arrive 21 days before the plane departs are only willing to purchase discount tickets. The number of full-fare customers who arrive within the 21 days of the plane’s departure is approximately normally distributed with mean 50 and standard deviation 15. For this question, assume that Trumpet Airlines does not practice overbooking, and that the variable cost of carrying an additional passenger is zero (assuming that there is at least one empty seat on the plane).

(a) What is the underage cost? That is, what is the cost per seat of under-estimating demand, i.e., selling a seat to a discount customer, and not reserving that seat for a full-fare customer who later appears and wants to buy the seat?

(b) What is the overage cost? That is, what is the cost per seat of over-estimating demand, i.e., not selling a seat to a discount customer, and reserving that seat for a full-fare customer, but no full-fare customer appears to buy the seat?