At the start of football season, the ticket office gets busy the day before the first game. Customers arrive randomly at the rate of 3 every 10 minutes. Currently there are two ticket sellers working at the office. Based on queuing analysis, the average time in the system for the in-person model is 3 minutes. The university is considering an automated ticket machine similar to the airlines' e-ticket system. The automated ticket machine can service a customer in 1.25 minutes. (a) What is the average time in the system for the automated system model? (round to 4 decimal places) The ticket sellers earn $11 per hour and the machine costs $30 per hour (amortized over 5 years). The customer wait time is assumed to be $10 per hour. (b) What is the total hourly cost of the automated system model? (c) Should the university switch to the automated system model? Justify your answer. Note: Show your steps for full credits