ONLY E AND F PLEASE

Sharp Discounts Wholesale Club has two service desks (call them A and B) with one server at each desk. There is one desk at each entrance of the store. Customers arrive at each service desk at an average of one every six minutes following a Poisson distribution. The average service time at each service desk is 4 minutes per customer following the exponential service distribution. a) How many customers, on average, are at service desk A waiting in line for service? b) How much time does a customer spend at service desk B either waiting for help or being helped by the clerk? c) Looking at service desk A, on average, what is the probability that there are at least two customers in line already waiting for service when the next individual arrives at this service desk? d) Sharp is now considering consolidating its two service desks into one location, staffed by two clerks. The clerks will continue to work at the same individual speed of 4 minutes per customer. How many customers, on average, are waiting in line? How much total time does a customer spend at the service desk? e) Do you think the Sharp Discounts Wholesale Club should consolidate the service desks? Explain and your discussion must consider both the economics and the customer service aspects of this waiting line operation. There would be no extra cost for moving the two operations to one operation. The clerks would continue to be paid the same as they were paid at the single desk operation. Note: this may simply be an explanation and calculations would not need to be provided. f) Suppose that it is no longer required that the clerks be paid the same under either operation. For the consolidated operation and based on past work experience one clerk is paid $45 per hour and the second clerk is paid $35 per hour. The estimated cost to Sharp for time a customer is at the consolidated service desk either waiting or being helped is $0.50 per minute. For the two-service desk operation, the store is going to change its pay scale and pay each clerk $36 per hour. Because of the convenience of having two desks, one at each entrance, Sharp estimates that the estimated cost to Sharp for a customer either waiting or being helped is $0.40 per minute. Compare the cost of the consolidated operation to the two desk operation using the total cost of operation analysis. Assume that there is no cost for consolidating the service.