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Air Traffic at a large airport is limited by the number of aircraft that can depart during the day. One of the limiting factors is the amount of Wake Turbulence caused by departing aircraft. Wake turbulence is a disturbance in the air that is caused by a large object moving at a high-speeds and is dangerous to fly through it is often in proportion to the size of the aircraft. Because of these safety concerns, no aircraft can depart for 3 minutes following a large aircraft, 1 minute after the departure of a medium sized aircraft, and 30 seconds for a small aircraft. Airlines are free to use any mix of aircraft at the airport, as long as they do not exceed their amount of departure times.

An airline recently purchased the rights for 30 additional minutes of departure time per day, and is considering which mix of flights is optimal for this additional 30 minutes:

Size of Aircraft	Small	Medium	Large
Time before next plane can depart (in minutes)	0.5	1.0	3.0
Average ticket price per passenger (in $)	400	500	600
Average variable cost per passenger (in $)	8	8	15
Average fixed cost per passenger (in $)	100	200	300
Average profit per passenger (in $)	292	292	285
Average number of passengers per flight	20	50	100
Average profit per flight (in $)	?	?	?
Potential demand (in flights per day)	18	13	6

Required:

1. Which is the most profitable mix in flights?
2. How much would they pay for an extra minute of departure time?
3. What qualitative factors should be considered?

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