At what price level must air carriers set their fares to maximize revenues?

The student’s question clearly specifies “revenues” and not “profits.” The distinction is important, as “revenue” refers to the total amount of money generated as income; “profit” is how much “revenue” is left over after expenses are paid, such as labor and material costs.
Large commercial aircraft consume a great deal of fuel, as much as one gallon per second. For transcontinental flights, that is a lot of jet fuel. Even short commercial flights are expensive, as a disproportionate amount of fuel is burned during routine take-offs. Additionally, there are substantial labor costs associated with operating a commercial airline, including salaries for pilots, flight attendants, ground crew, administrative personnel, and so on. Insurance costs alone can represent a major strain on airline companies’ budgets, especially when commercial airliners are intentionally or accidentally shot down by militants or governments. Revenues must cover, at a minimum, these basic expenses. Airline companies, then, maximize profits through careful determinations of how much they can charge passengers relative to their competitors. With air travel increasingly characterized by significant additional charges (beyond the use of a seat), for carry-on as well as checked baggage, and for food (which used to be included as part of the initial charge for a seat), the cost of a flight for a family going on vacation has become more burdensome than in the past.
Operating an airline is like many businesses, with material costs in particular fluctuating due to perturbations in fuel and lubricant costs. Airline executives must routinely sit down and calculate anticipated revenue measured against anticipated expenses. They maximize revenues by performing the best calculations they can of the amount then can charge customers relative to their competitors and relative to the cost of operating the airline.
https://therocketscienceblog.wordpress.com/2016/08/01/how-much-fuel-does-an-airplane-use/

https://www.ft.com/content/d57bc542-0e62-11e4-a1ae-00144feabdc0