7. 35 points: Every student who wishes to enter the public library at Hotel de Ville (HdV) in the center of Paris, needs to go through the following steps:

1. Show your ID to one of the two guards at the entrance of the HdV building—20 seconds
2. Have your bag go through the metal detector—30 seconds
3. Give your ID card to the ground floor desk clerk, who will give you in exchange a magnetic badge—1 minute
4. Take the stairs up to the fourth floor of the building, where the library is located—2 minutes (Note: the stairs are very wide, 30 people can be on the stairs at the same time)
5. Show your badge to one of the two desk clerks at the library entrance to have your badge number archived—30 seconds
6. Enter the library and get assigned to a numbered seat by one of the two librarians—40 seconds

a) Which step is the bottleneck step?

b) What is the process capacity?

c)  When the library opens at 9 a.m., there is usually a very long queue of people waiting to get in. How long does it take for the 25 seats in the library to be occupied (assuming there are at least 25 people in the queue)?

d) Throughout the day, 3 students typically enter the library per minute. How many students, on average, are on the ground floor?