Each airline passenger and his or her luggage must be checked to determine whether he or she is carrying weapons on to the airplane. suppose that at gotham city airport an average of 10 passengers per minute arrive (inter-arrival times are exponential). to check passengersfor weapons, the airport must have a checkpoint consisting of ametal detector and baggage x-ray machine. whenever a checkpoint isin operation, two employees are required. a checkpoint can check an average of 12 passengers per minute (the time to check a passenger is exponential) under the assumption that the airport has only one checkpoint.
referring to problem above, suppose the airline wants to determine how many check points to operate to minimize operating cost and delay cost over a ten-year period. assume that the cost fordelaying a passenger for one hour is $10 and that the airport is open every day 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.