At the Franklin Post Office, patrons wait in a single line for the first open window. On average, 100 patrons enter the post office per hour, and each window can serve an average of 45 patrons per hour. The post office estimates a cost of $0.10 for each minute a patron waits in line and believes that it costs $20 per hour to keep a window open. Interarrival times and service times are exponential.
a. To minimize the total expected hourly cost, how many windows should be open?
b. If the post office's goal is to ensure that at most 5% of all patrons will spend more than five minutes in line, how many windows should be open?