Refer to Problem. A new registration manager, Dwayne Cole, is hired who initiates a program to entertain the people in line with a juggler whom he pays $15/hour. This reduces the waiting costs to $50 per hour.
a) What is the optimal number of servers?

b) What is the cost for the system, per hour, at the optimal service level?

Problem

The registration area has just opened at a large convention of dentists in Tallahassee, Florida. 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 Tallahassee Convention Center provides servers to register guests at a fee of $15 per person per hour. It takes about one minute to register an attendee (negative 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?