i want solution for all parts

Problem 6) An average of 50 customers per hour arrive at a post office. Interarrival times are exponentially distributed. Each postal worker can serve an average of 15 customers per hour. Service times are exponentially distributed. a) What is the minimum number of postal workers needed to ensure that there will be no customer congestion in the post office? Justify your answer. b) Suppose the post office is currently staffed with 6 postal workers to serve the customers. What is the average wait time in queue? Justify your answer. c) Given the staffing condition speficied in part (b), what fraction of customers experience a wait time longer than 10 minutes in queue? Justify your answer. d) Suppose it costs $25 per hour to hire a postal worker and the post office values the time a customer spends waiting in line at $15 per customer-hour. To minimize the expected total hourly cost, how many postal workers should be hired? Justify your