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The Northeast Airlines gate agent Gray distributes seat assignments to ticket holders. She has a performance rating of 110% and averages 50 seconds per passenger. how long should an average agent be given to allocate seats?
The usual fare for a Lofty Airlines flight is $200, while the per-passenger variable cost is $50. In an effort to fill the final 30 available seats on Northeast Airlines, Lofty provides standby passengers with a 50% discount on tickets.
Each possible configuration of the passenger seats can be represented by a permutation of the numbers between 1 and N. We can claim that the "proper" approach is A = 12345N. (each passenger in their designated seat). Consequently, the first person on the seat 1; occupant of seat 2; etc. Northeast Airlines must determine which of the N! total permutations places each number in a different position than in A. When N=4 passengers, one permutation in which no individual is seated in his or her assigned seat is 2413.
As we can put any integer in the first seat but not 1, there are (N-1) alternatives. We can therefore put (N-2) potential numbers in the second seat since neither 2 nor the number can be seated in the first one. This line of thinking will result in (N-1)! permutations where none of the passengers are sitting in their assigned seats.
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