1. (60 pts.) A bank that pays great attention to customer satisfaction, has decided to make invoice collections in Maslak branch between 10:00 and 11:30 on the basis of requests from its customers who are over the middle age. According to the characteristics of the demanding customer population, it is requested that the customers who come to pay their invoices wait in the queue as little time as possible. In addition to this, the bank focuses on two options in order not to interfere with other banking transactions carried out. The first option is to use a single experienced teller officer whose average processing time (one invoice processing time) has an exponential distribution with a mean of 4 min. The other option uses two inexperienced teller officers, each of which is of equal quality and has an exponential distribution a mean of 7 minutes. The operation of both systems is schematized as follows. Option-1 Option -2 As it can be seen in the figure, the incoming customers in both systems enter a single queue and also the systems serves with the logic of who comes first is served first (FIFO). The analysis results of the previous period data show that the number of customers to pay the invoice in the specified time interval corresponds to the Poisson distribution, which has a mean of 30 people. Consider this information, and at the beginning, that there are no customers in the system. Answer the following questions. a) (30 pts.) By building a simulation model for each option / system, calculate the average waiting times in the system by running both models for the first 8 customers. b) (15 pts.) Find the confidence interval for the average waiting time per customer by doing 3 replications for each model. c) (15 pts.) Show which of these two options / systems is better 1. (60 pts.) A bank that pays great attention to customer satisfaction, has decided to make invoice collections in Maslak branch between 10:00 and 11:30 on the basis of requests from its customers who are over the middle age. According to the characteristics of the demanding customer population, it is requested that the customers who come to pay their invoices wait in the queue as little time as possible. In addition to this, the bank focuses on two options in order not to interfere with other banking transactions carried out. The first option is to use a single experienced teller officer whose average processing time (one invoice processing time) has an exponential distribution with a mean of 4 min. The other option uses two inexperienced teller officers, each of which is of equal quality and has an exponential distribution a mean of 7 minutes. The operation of both systems is schematized as follows. Option-1 Option -2 As it can be seen in the figure, the incoming customers in both systems enter a single queue and also the systems serves with the logic of who comes first is served first (FIFO). The analysis results of the previous period data show that the number of customers to pay the invoice in the specified time interval corresponds to the Poisson distribution, which has a mean of 30 people. Consider this information, and at the beginning, that there are no customers in the system. Answer the following questions. a) (30 pts.) By building a simulation model for each option / system, calculate the average waiting times in the system by running both models for the first 8 customers. b) (15 pts.) Find the confidence interval for the average waiting time per customer by doing 3 replications for each model. c) (15 pts.) Show which of these two options / systems is better