San Francisco International Airport (SFO) is initiating4 new early morning flights, all departing at 6 AM. There are no other departures before 6 AM and until 12 PM. Each plane has exactly 150 passengers. No no-shows/cancellations. Passengers begin arriving 2 hours and 15 minutes before the scheduled departure and continue to arrive until 45 minutes before departure; they arrive steadily. SFO is determining the number of security stations to handle this new set of flights.

• Each station can process 90 passengers /hour.
• Each passenger must begin security processing 20 minutes before the scheduled departure to make her flight. It is required that all passengers must make their flights.
• Total cost of one station is $500 / operating day (from 0 AM to 11:59 PM).
• The passenger waiting cost is incurred at a rate of $3 / passenger / hour.

The first proposal is to have 3 stations.

Q1. What is the rate at which the line grows, starting from 3:45AM?(in passengers per hour)

Q2. How many passengers are waiting in line when the line is the longest?

Q3. What time does the last passenger in line start going through security? (HH:MM AM/PM) The second proposal is to have 5 stations.

Q4. How many passengers are waiting in line when the line is the longest?

Q5. Between the two proposals(3 vs 5 stations), which one should be adopted by SFO? Justify your recommendation