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: a$)$ show your id card to the ground floor desk clerk. this takes $1$ minute. b$)$ take an elevator up to the fourth floor. the elevator can only hold three people at a time. it takes each person two minutes to get on the elevator and then two seconds to get off. the elevator takes two minutes to go from the ground floor to the fourth and then another two minutes to return to the ground floor. c$)$enter the library and get assigned to a numbered seat by one of the two librarians based on the magnetic badge. this takes $40$ seconds. QUESTIONS: a$)$ DETERMINE THE CAPACITY AT EACH OF THE THREE STEPS B$)$WHICH STEP IS THE BOTTEL NECK STEP C$)$WHAT IS THE PROCCESS CAPACITY? D$)$ SUPPOSE THE LIBRARY WANTS TO INCREASE THE CAPACITY OF THIS PROCESS. TO DO SO SHOULD THEY INCREASE THE SIZE OF THE ELAVATOR? IF SO HOW BIG SHOULD IT BE$?$