Problem:
Customers arrive at a fast food restaurant with one server according to a Poisson process at a mean rate of 30 per hour. The server has just resigned, and the two candidates for the replacement are X (fast but expensive) and Y (slow but inexpensive). Both candidates would have an exponential distribution for service times with X having a mean of 1.2 minutes and Y having a mean of 1.5 minutes. Restaurant revenue per month is given by $(6,000/W) where W is the expected waiting time (in minutes) of a customer in the system.
Determine the expected difference in the monthly revenues if X rather than Y is hired.