At the post office, patrons wait in a single line for the first open window. An average of100patrons per hour enter the post office, and each window can serve an average of45patrons per hour. The post office estimates a cost of 0.1for each minute a patron waits in line and believes that it costs 20per hour to keep a window. Inter-arrival times and service times are independent and exponentially distributed.

(a) How many windows should be kept in order to minimize the total expected hourly cost? What is the minimal total expected hourly cost (round to three decimal places)?

(b) What is the minimal number of windows that should be kept in order to ensure that at most5%of all patrons will spend more than5minutes in line?