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The check-in line at Alpha Airlines has two agents who serve all passengers during peak hours. Arrivals to the check-in counter are Poisson with a mean of 50 passengers per hour. Approximately, thirty percent of the arrivals are Priority Class (e.g., First Class, Gold members, etc) while the remainder holds coach tickets. The time that a passenger spends at the ticket check-in counter with an agent is exponentially distributed with a mean of 44 minutes. Alpha promises that if a passenger waits in line for more than 5 minutes, a coach passenger will be awarded 500 frequent flyer miles while a Priority Class passenger will be awarded 1000 miles. Currently, all passengers go through the same queue for check-in.
How many total miles are awarded per hour on average currently?
Management is considering the creation of two separate lines, one for each of the two classes of passengers. In this situation, each check-in line will have one agent who will serve their respective passengers; line switching will not be allowed. Find the average total miles awarded hourly under this configuration.
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