In the time interval between t and t - 1 seconds before the departure of Braneast Airlines Flight 313, there is a probability pt that the airline will receive a reservation for the flight and a...

In the time interval between t and t - 1 seconds before the departure of Braneast Airlines Flight 313, there is a probability pt that the airline will receive a reservation for the flight and a probability 1 - pt that the airline will receive no reservation. The flight can seat up to 100 passengers. At departure time, if r reservations have been accepted by the airline, there is a probability q(y|r) that y passengers will show up for the flight. Each passenger who boards the flight adds $500 to Braneast’s revenues, but each passenger who shows up for the flight and cannot be seated receives $200 in compensation. Formulate a dynamic programming recursion to enable the airline to maximize its expected revenue from Flight 313. Assume that no reservations are received more than 100,000 seconds before flight time.