3. A typical subway in Manhattan has six turnstiles, each of which can be controlled by the station manager to be used for either entrance or exit, but not both. The manager must decide at different times of day how many turnstiles to use for entering passengers and how many to use for exiting passengers. At the NYU station stop, passengers enter the station at a rate of about 84 per minute between the hours of 7:00 a. m. – 9:00 a. m. Passengers exiting the station in this time window, leave at a rate of around 48 per minute. Each turnstile can allow an average of 30 passengers per minute to enter or exit. Arrival and service times have been thought to follow a Poisson and negative exponential distribution, respectively. Assume riders form a common queue at both entry and exit turnstiles and proceed to the first empty turnstile. The NYU station foreman, Dudley Doright, does not want the average passenger at his station to wait in a turnstile line for more than 6 seconds, nor does he want more than 8 people in any queue during this 7:00 a. m. – 9:00 a. m. time. (15 points) a). How many turnstiles should be open in each direction every morning between 7:00 a. m. – 9:00 a. m.? b). What assumptions are necessary to insure that Dudley has accurately assessed this waiting-line system?