Question: America West Airlines

The management of America West Airlines has decided to base its overbooking policy on a stochastic single period model to maximize expected profit. This policy now needs to be implemented on a new flight from Las Vegas to Atlanta. The aircraft has 125 seats available for a one-way fare of $250. However, since there are commonly a few no-shows, the airline accepts more than 125 reservations. On those occasions when more than 125 people arrive to take the flight, the airline finds volunteers to be put on a later flight in return for a certificate worth $150 toward any future travel on Alaska Airlines.
Based on previous experience with similar flights, it is estimated that the relative frequency of no-shows will be as indicated below:

Determine the number of overbooking reservations America West Airlines should accept for this flight. Provide a narrative of the solution technique used.