Question 4 A bank is considering opening a drive-through window for customer service. Customers are estimated to arrive at the average rate of 15 per hour. The teller who works at the window can service customers at the average rate of one every three minutes. Assume Poisson arrivals and exponential service time. 1) Find the average number of customers in the waiting line (waiting but not being serviced). 2) Find the average waiting time in the system (including waiting in line and in service). 3) Suppose that now the service times are deterministic at the same rate; that is, the teller can service exactly one customer every three minutes. Do you think your answer in (b) will become larger, or smaller, or remain the same? No calculation needed. 4) Currently, the teller's hourly wage is $20. The bank estimates that for a customer to wait in the line for one hour, it costs the bank a goodwill loss of $30. Once the customer goes into service, there is no goodwill loss for the bank. Find out the current average total cost to the bank for an hour. 5) The manager of the bank is considering equipping the teller with a machine that helps speed up the service. The hourly rent for the machine is $10. With the machine, the teller's average service time decreases from the original three minutes to two minutes. The hourly wage of the teller, as well as the goodwill loss due to customer waiting in the line, stay the same as described in (d). Help the manager figure out whether adding this additional machine is worthwhile