There are several risks and costs associated with the airline's decision to overbook flights. If too many passengers show up, the airline may need to offer incentives for customers to give up their seats, which can be costly. If too few passengers show up, the airline may be forced to fly with empty seats, resulting in lost revenue. Furthermore, overbooking can lead to negative publicity and damage to the airline's reputation if too many customers are bumped from their flights. In terms of strategy, the airline must weigh the potential benefits of overbooking (maximizing revenue by filling as many seats as possible) against the potential risks and costs. The airline may also consider adjusting its overbooking policy based on factors such as the route, time of day, and historical data on no-show rates for specific flights. Overall, effective demand forecasting and capacity planning are crucial for the airline to optimize its operations and profitability while minimizing negative customer experiences. This example presents a simplified version of calculations used by airlines when they overbook flights. They realize that a certain percentage of ticketed passengers will cancel at the last minute. Therefore, to avoid empty seats, they sell more tickets than there are seats, hoping that just about the right number of passengers show up. We assume that the no-show rate is 10%. In binomial terms, we assume that each ticketed passenger, independently of the others, shows up with probability 0.90 and cancels with probability 0.10. For a flight with 200 seats, the airline wants to see how sensitive various probabilities are to the number of tickets it issues. In particular, it wants to calculate (a) the probability that more than 205 passengers show up, (b) the probability that more than 200 passengers show up, (c) the probability that at least 195 seats are filled, and (d) the probability that at least 190 seats are filled. The first two of these are “bad” events from the airline’s perspective; they mean that some customers will be bumped from the flight. The last two events are “good” in the sense that the airline wants most of the seats to be occupied. a) What is the probability of the airline having to bump customers from the flight if they sell 215 tickets for a 200-seat flight? b) How does the probability of the airline having to bump customers change if the no-show rate increases from 10% to 15%? c) If the airline wants to ensure that there is only a 5% chance of having to bump customers from the flight, how many tickets should they sell? d) How might an airline's demand planning process be affected by the calculations used for overbooking flights and the sensitivity analysis of ticket issuance?