This overbooking model determines the number of
 reservations, M, to allow on a flight if the
 no-show distribution is binomial;

! Some available data ;
   N = 16;   ! Total seats available;
   V = 225;  ! Revenue from a sold seat;
   P = 100;  ! Penalty for a turned down customer;
   Q = .04;  ! Probability a customer is a no-show;

! The probability to turn down customers is 
  @PBN( Q, M, M - N), therefore the corresponding
  expected loss due to imperfect information is:
  ( V + P) * @PBN( Q, M, M - N), and we want the 
  loss to equal the revenue V on the margin.  So,
  the break-even equation is:;

   ( V + P) * @PBN( Q, M, M - N) = V;

! Note, you should round up if M is fractional;