You have been asked to analyze the queue for registrations at a large Las Vegas hotel. Guests arrive to register at the rate of 3 people every 12 minutes (Poisson distributed). It takes each host an average of 6 minutes to register a guest (following a negative exponential distribution), any number of which can be hired by the hotel at the cost of $15 per hour. The hotel recognizes a waiting cost of $55 per hour per guest in line. The hotel has decided that guests' average wait in line is not more than 6.5 minutes.

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

a. Based on the goal (average wait in line is less than 6.5 minutes) stated above, what is the minimum number of hosts that could be hired for this system? [ Select ] ["1", "3", "4", "5", "2"] hosts

b. Based on wait cost, what is the optimal number of servers needed to minimize total costs? [ Select ] ["2", "5", "3", "4", "1"] hosts

c. What is total (providing service plus time in queue costs) daily cost at the optimal number of servers if the registration desk is open for 3 hours? [ Select ] ["$174.08", "$58.02", "$62.46", "$203.31", "$342.89"]

d. At the optimal number of servers, what is the average time to check in an attendee? [ Select ] ["8.12 minutes", ".94 of a minute", ".55 of a minute", "1.11 minutes", "6.94 minutes"]