$1.$ A call center has analyzed the calls received in the last month and found that, on average, $64$ calls were received per hour. Assume that call arrivals follow Poisson distribution and come from an infinite population. Service times follow an exponential distribution with an average of $45$ seconds per call served. Assume the queue length can be infinite with FCFS discipline. a$)$What is the average number of people in line? b$)$What is the average number of people in the system? c$)$What is the average amount of time that a person can expect to spend in line? d$)$On average, how much time will a person spend in the system? e$)$During the weekends, the call arrival rate can be expected to increase to over $80$ per hour. What effect will this have on the average number of people waiting in line?