Q$4)-($A Busy Post Office$)$: At the Smalltown Post Office, patrons wait in a single line for the first open window. An average of $100$ patrons per hour enter the post office, and each window can serve an average of $45$ patrons per hour. The post office estimates a cost of $10$ for each minute a patron waits in line and believes that it costs $$20$ per hour to keep a window open. Inter$-$arrival times and service times are exponential.$($a$)-$ To minimize the total expected hourly cost, how many windows should be open?$($b$)-$ Under this optimized situation you have recommended in part$($a$)$ above, how much would be the average time spent by a single average customer in the post office?$($c$)-$ What percent of the time all the customer service staff at the windows will be sitting idle?$($d$)-$ Suppose the Post Office decides to keep three windows open: one for men, the other for women, and the third for corporate customers with more than $5$ Kg of postal requests. The ratio of men to women arriving at the Post Office would be $70$ men to $30$ women.And of all customers coming to the Post Office, $40$ percent have a consignment weighing more than $5$ Kg and $60$ percent with normal consignment requests. What would be total time spent by customers in the post office in each of the three categories? What would be the total time spent by a customer at the Post Office if they decide to keep three windows open but either window can take any type of customer?