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...

You manage a hotel with one reception desk. On a typical day, you receive on average 8 customersper hour. It takes on average 6 minutes to check-in the customer. For the sake of this problem, weassume that checking-in ONLY happens daily between 2:00-5:00pm.Assume that the inter-arrival times between customers are exponentially distributed, and that thetime to check-in is also exponentially distributed.a) What are the demand rate and service rate at the reception? What is the utilization of thereception desk during checking times?b) What is the average time that a customer has to wait before actually being served? You oftendrop by at 3:00pm to monitor the reception, how many customers do you expect to see at thereception (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 isconsidering buying an automated checking-in system that will cost $100,000/year. Theautomated system is expecting to reduce checking-in time from 6 minutes to 4 minutes. Is itworth it? Assume 1 year = 300days