Flight 77 has just opened for check-in. There is a dedicated check-in area for this flight, consisting of several check-in counters pulling passengers from a single queue operating on a first-in-first-out basis. The check-in counters have a total processing capacity of 80 passengers per hour. Although the airline recommends that passengers arrive between 2h and 1h30min before departure, in practice passengers begin arriving 3 hours before departure, and the last passenger arrives at the queue about 1 hour before the plane departs. During the 30-minute recommended arrival period, passengers arrive at a rate of 140 passengers per hour. During the rest of the arrival period between 3h and 1h before the flight departs (that is excluding the 30 minute recommended arrival period), passengers arrive at a rate of 50 passengers per hour. For simplicity assume that there is a single class in this flight, and that all passengers need to go through the same check-in process. Ignoring any unpredictable variability in both arrivals and processing times and assuming a continuous/fluid and deterministic flow of passengers, construct a build-up diagram to answer the following questions:

3.1 - What is the largest number of passengers waiting in the queue at any point during the check-in process?

3.2 How many passengers are still in the queue 1 hour before the flight departs?

3.3 - How much time before the planes departure will the very last passenger check-in?