Customers arrive at a fast food restaurant with one server 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 upper bound on the difference in their monthly compensations that would justify hiring X rather than Y.3