At the start of football season, the York student ticket office gets busy the day before the first game. Customers arrive at the rate of four every ten minutes. A ticket seller can service a customer in four minutes. Traditionally, there are two ticket sellers working. The university is considering an automated ticket machine similar to the airlines' e-ticket system. The automated ticket machine can service a customer in 2 minutes. (a) What is the average length of the queue for the in-person model? (b) What is the average length of the queue for the automated system model? (c) What is the average time in the system for the in-person model? (d) What is the average time in the system for the automated system model? (e) Assume the ticket sellers earn $8 per hour and the machine costs $20 per hour (amortized over 5 years). The wait time is only $4 per hour because students are patient. What is the total cost of each model? (f) A ticket agency offers to take over the ticket distribution at a cost of $15/hour. The university will only accept an outside agency if (i) the cost is lower than providing the services internally (either in-person or using an automated ticket machine) and (ii) if the average queue length is lower than providing the services internally. The ticket agency promises an average service rate of 36 per hour. What standard deviation on SERVICE TIME does the agency have to achieve in order for the university to be willing to hire them?