Problem 12-21 (Algorithmic)
South Central Airlines operates a commuter flight between Atlanta and Charlotte. The plane holds 32 passengers, and the airline makes a $130 profit on each passenger on the flight. When South Central takes 30 reservations for the flight, experience has shown that, on average, two passengers do not show up. As a result, with 32 reservations, South Central is averaging 30 passengers with a profit of 30(130) = $3,900 per flight. The airline operations office has asked for an evaluation of an overbooking strategy in which the airline would accept 34 reservations even though the airplane holds only 32 passengers. The probability distribution for the number of passengers showing up when 34 reservations are accepted is as follows:
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