Problem:

Customers arrive at the lobby of the exclusive and expensive Ritz Hotel at the rate of 40 per hour (Poisson distributed) to check in. The hotel normally has three clerks available at the desk to check guests in. The average time for a clerk to check in a guest is four minutes (exponentially distributed). Clerks at the Regency are paid $12 per hour and the hotel assigns a goodwill cost of $2 per minute for the time a guest must wait in line.

Required:

Question 1) How many clerks should the hotel employ for the check-in system to be cost effective? Solve the problem and show all work.