Optimal Chapter-Flight Fare  If exactly 196 people sign up for a charter flight, Leisure World Travel Agency charges $314/person. However, if more than 196 people sign up for the flight (assume this is the case), then each fare is reduced by $1 for each additional person. Determine how many passengers will result in a maximum revenue for the travel agency. Hint: Let x denote the number of passengers above 196. Show that

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Author:Jerome E. Kaufmann, Karen L. Schwitters
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Optimal Chapter-Flight Fare

 If exactly 196 people sign up for a charter flight, Leisure World Travel Agency charges $314/person. However, if more than 196 people sign up for the flight (assume this is the case), then each fare is reduced by $1 for each additional person. Determine how many passengers will result in a maximum revenue for the travel agency. Hint: Let x denote the number of passengers above 196. Show that the revenue function R is given by 
R(x) = (196 + x)(314 − x).
  passengers
What is the maximum revenue?
$  
What would be the fare per passenger in this case?
  dollars per passenger
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