The Wizard Tax Service is analyzing its operations during the month prior to the April 15 tax filing date. There is currently only one tax preparer at Wizard. On the basis of past data, it has been estimated that customers arrive according to a Poisson process with an average time between arrivals of 12 minutes. When the tax return is being completed, the customer is at the tax preparers desk working with the preparer and this is considered the service time. The time to complete a return for a customer is exponentially distributed with a mean time of 10 minutes. Customers are processed in the order of arrival. Based on this information, answer the following questions. a) On average and measured from when a customer arrives at Wizard, how much time does the customer spend at the tax service having his tax return completed? b) What is the average number of customers at the tax service, whether waiting for the tax preparer or having the return prepared? c) An arriving customer will not wait if there are at least three others waiting for the tax preparer. What is the probability that the arriving customer will not wait? The following information is for parts d) and e). Wizard is considering adding a second tax preparer. This tax preparer will also complete returns following an exponential distribution with a mean time of 10 minutes. As a result of the adding the second tax preparer, the arrival rate increases to a customer arriving every 8 minutes following a Poisson arrival process. d) Suppose the cost of the first preparer is $50 per hour and the cost of the second preparer is only $40 per hour. Also, the cost of a customer while waiting for a tax preparer to start preparing the return is $125 per hour. What is the cost of each option (the single tax preparer and the two tax preparer options)? e) Suppose the servers in the two server model are complaining about their hourly pay ($50 per hour and $40 per hour respectively for the first and second servers). How much could Wizard afford to pay the two servers in total (combined) to be indifferent between the one server and two server options? For the single server scenario, assume that the server will continue to receive the $50 hourly pay. The pay only changes for the two server model