Abroadway theater has 700700 seats, divided into orchestra, main, and balcony seating. orchestra seats sell for $ 40 comma$40, main seats for $ 30 comma$30, and balcony seats for $ 20.$20.  if all the seats are sold, the gross revenue to the theater is $ 20 comma 100.$20,100.  if all the main and balcony seats are sold, but only half the orchestra seats are sold, the gross revenue is $ 17 comma 300.$17,300. how many are there of each kind of seat?

When booking personal travel by air, one is always interested in actually arriving at one’s final destination even if that arrival is a bit late. the key variables we can typically try to control are the number of flight connections we have to make in route, and the amount of layover time we allow in those airports whenever we must make a connection. the key variables we have less control over are whether any particular flight will arrive at its destination late and, if late, how many minutes late it will be. for this assignment, the following necessarily-simplified assumptions describe our system of interest: the number of connections in route is a random variable with a poisson distribution, with an expected value of 1. the number of minutes of layover time allowed for each connection is based on a random variable with a poisson distribution (expected value 2) such that the allowed layover time is 15*(x+1). the probability that any particular flight segment will arrive late is a binomial distribution, with the probability of being late of 50%. if a flight arrives late, the number of minutes it is late is based on a random variable with an exponential distribution (lamda = .45) such that the minutes late (always rounded up to 10-minute values) is 10*(x+1). what is the probability of arriving at one’s final destination without having missed a connection? use excel.