Question 1 (5 points) Consider an airline that has a reservations clerk taking calls. If the clerk is busy, the caller is put on hold. The calls are taken in the order received. Assume that calls arrive following a Poisson process at the rate of one every 3 minutes. The time for service is assumed to be exponentially distributed. The clerk takes on average 2.5 minutes to complete a reservation. The clerk is paid $30 per hour. All customers wait patiently till their calls are answered. It has been estimated that each minute that a customer spends on hold costs the airline $3 due to customer dissatisfaction and loss of future business. Under the same assumptions as Question 1, suppose the airline hires another clerk who is as- signed a new telephone number. The new clerk has the same level of productivity as the original clerk, and is paid at the same rate. Customers are now free to call either of the two numbers. Once they are put on hold, customers tend to stay on the line since the other number may be worse. Assume that customers randomly choose either number with equal probability. Consider the same situation as in Question 2, except that now both clerks have the same tele- phone number and customers on hold are in a single queue. a) (1 point) In queueing terminology, how do you best describe this reservation system? In other words, what type of queuing system is this? b) (0.5 point) What is the average time a customer spends on hold in this reservation sys- tem? Give your answer in minutes. c) (0.5 point) What is the average number of customers on hold in this reservation system? d) (1 point) What is the average number of customers speaking to a reservation clerk in this reservation system? e) (1 point) What is the probability that a customer speaks to the reservation clerk without being on hold? f) (1 point) What is the hourly total cost of operating this reservation system? g) (1 point) In this reservation system, what is the probability of having exactly one cus- tomer waiting in line? h) (1 point) Compare your answers 2(c) and 3). Explain the difference, if any, with intui- tion. 1) (1 point) Compare your answers 2(d) and 3(d). Explain the difference, if any, with intui- tion