(Part 1) Your friend Alan manages a coffee shop and has gathered the following information. During the opening hours (8:00 am to 5:00 pm, Monday to Sunday), customers arrive at a rate of eleven per hour according to a Poisson distribution. On average, Alan can serve twelve customers per hour. His service times can be described by an exponential distribution. Alan is concerned about the number of customers waiting in line. He has asked your help in guring out the following system characteristics: (a) Average system utilization (i.e. percentage of time that Alan is busy). (b) Average number of customers waiting in line. (c) The average time a customer spends waiting in line. ((1) The average time a customer spends in the system. (Part 2) Alan decides to hire his niece Catherine to work part-time this summer. Catherine will greet each customer, help the customer place an order and make payments, and relay the order information to Alan. Alan will focus solely on lllling the coffee order. Alan estimates that because of this streamlined operation, he can now serve fifteen customers per hour, while Catherine can serve eighteen customers per hour. Their service times are independent and each follows an exponential distribution. Once again, he has asked your help in guring out the following system characteristics: (a) Average utilization of Catherine. (b) Average utilization of Alan. (0) Average number of customers waiting in line (Hint: customers may need to wait at Catherine's station and/or at Alan's station). ((1) The average time a customer spends waiting in line