1. An automated car wash facility consists of a single service bay that is capable of serving 12 cars per hour on a first come, first served basis. Historical data indicates that cars arrive at an average rate of 6 cars per hour. a. What is the utilization factor for the facility? b. What percentage of the time is the facility idle? c. What is the average number of cars waiting in line to be served? d. What is the average amount of time that a car spends waiting in line to be served? e. What is the probability that two or more cars are waiting in line to be served? 2. A fast food restaurant has a single drive thru service window that is capable of serving 15 customers per hour on a first come, first served basis. Historical data indicates that customers arrive at an average rate of 10 per hour. The drive thru window is open 24 hours each day. The estimated cost of operating the drive thru window is $17.50 per hour. The estimated cost of waiting is $30 per hour. a. What is the total daily service cost? b. What is the total daily waiting cost? c. What is the total daily system cost? 3. The service counter in a local bank has two teller windows. Customers wait in a single line before being served by the first available teller. Historical records indicate that customers arrive at an average rate of 30 per hour and are served at an average rate of 24 per hour. The teller windows are open for 8 hours each day. The estimated cost of operating each teller windows is $30 per hour. The estimated cost of waiting is $20 per hour. a. What is the utilization factor for the customer service counter? b. What is the average number of customers waiting in line to be served? c. What is the average amount of time that a customer spends waiting in line to be served? d. What is the probability that there are no customers waiting in line to be served? e. What is the total daily system cost? 4. A small local retailer has two check-out counters available; however, only one check-out counter is currently being used on a particular 8-hour shift. Customers arrive at an average rate of 8 per hour. The person currently working at the check-out counter is capable of serving an average of 10 customers per hour at a cost of $25 per hour. The manager has received numerous complaints from customers threatening to take their business to a local competitor who offers faster customer service. The manager has estimated that the cost of waiting is $50 per hour. a. What is the average number of people waiting in line to be served? b. What is the average amount of time that a customer currently spends waiting in line to be served? c. What is the currently total daily system cost? The manager is considering two options for reducing the amount of time that a customer spends waiting in line to be served in order to improve customer satisfaction. Option 1: Continue using use only a single check-out counter, but hire a different person to work the counter who is capable of serving an average of 12 customers per hour, which would increase the cost of operating the check-out counter to $40 per hour. All other parameters would remain the same. d. What is the average number of people that would be waiting in line to be served? e. What is the average amount of time that a customer would spend waiting in line to be served? f. What would be the new total daily system cost? Option 2: Use both check-out counters, which would require hiring an additional person capable of serving an average of 10 customers per hour. The estimated cost for operating each check-out counter would be $25 per hour. All other parameters would remain the same. g. What is the average number of people that would be waiting in line to be served? h. What is the average amount of time that a customer would spend waiting in line to be served? i. What would be the total daily system cost?