Each airline passenger and his or her luggage must be checked to determine whether he or she is carrying weapons onto the airplane. Suppose that at Gotham City Airport, an average of 10 passengers per minute arrive (inter-arrival times are exponential). To check passengers for weapons, the airport must have a checkpoint consisting of a metal detector and baggage X-ray machine. Whenever a checkpoint is in operation, two employees are required. A checkpoint can check an average of 12 passengers per minute (the time to check a passenger is exponential). Assume that the airport has only one checkpoint,

Referring to the statement above, suppose the airline wants to determine how many checkpoints to operate to minimize operating costs and delays costs over a ten-year period. Assume that the cost of delaying a passenger for 1 hour is $10 and that the airport is open everyday for 16 hours per day. It costs $1 million to purchase, staff and maintain a metal detector and baggage X-ray machine for a ten-year period. Finally, assume that each passenger is equally likely to enter a given checkpoint.

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