You manage a hotel with one reception desk. On a typical day, you receive on average 8 customers per hour. It takes on average 6 minutes to check-in the customer. For the sake of this problem, we assume that checking-in ONLY happens daily between 2:00-5:00pm.

Assume that the inter-arrival times between customers are exponentially distributed, and that the time to check-in is also exponentially distributed.

a) What are the demand rate and service rate at the reception? What is the utilization of the reception desk during checking times?

b) What is the average time that a customer has to wait before actually being served? You often drop by at 3:00pm to monitor the reception, how many customers do you expect to see at the reception (checking-in or waiting to check in) at this time?

c) Suppose the cost of waiting in the queue is estimated to be $2/min/customer. The hotel is considering buying an automated checking-in system that will cost $100,000/year. The automated system is expecting to reduce checking-in time from 6 minutes to 4 minutes. Is it worth it? Assume 1 year = 300days

PS: the current person working at the desk will still be there helping the customers using the automated system.