You have been asked to analyze the queue for registrations for a popular MSOM seminar at a major national conference. Conference attendees arrive to register at the rate of 4 people every 12 minutes (Poisson distributed). It takes each host, any number of which can be hired directly through the conference at the cost of $15 per hour. It takes 8 minutes to register a guest, following a (negative exponential distribution). The conference recognizes a waiting cost of $45 per hour per guest in line.

A single waiting line is set up, but can accommodate multiple servers.

a. What is the minimum number of hosts that could be hired for this system?

b. Based on total system cost, what is the optimal number of servers needed to minimize total costs?

c. Rounded to the nearest dollar, what is the total cost at the optimal number of servers if the registration desk is open for an 8 hour day?

d. At the optimal number of servers, what is the average time a guest would spend waiting to register?