The registration area has just opened at a large convention of building contractors in Las Vegas. There are 200 people arriving per hour (Poisson distributed), and the cost of their waiting time in the queue is valued at $100 per person per hour. The Las Vegas Convention Bureau provides servers to register guests at a fee of $15 per person per hour. It takes about one minute to register an attendee (exponentially distributed), A single waiting line, with multiple servers, is set up.
(a) What is the minimum number of servers for this system?
(b) What is the optimal number of servers for this system?
(c) What is the cost for the system, per hour at the optimum number of servers?
(d) What is the server utilization rate with the minimum number of servers?