If exactly 194 people sign up for a charter flight, Leisure World Travel Agency charges

Question

 If exactly 194 people sign up for a charter flight, Leisure World Travel Agency charges $306/person. However, if more than 194 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 194. Show that the revenue function R is given by R(x) = (194 + x)(306 − x).

1) ______passengers?

2)What is the maximum revenue?$ 

3)What would be the fare per passenger in this case?

 

4) ______dollars per passenger

Answer 1

Revenue = quantity×price = QP

Let x = the extra passengers over 194

Quantity, Q = 194+x

The price, P, is reduced by $1 for extra passenger or 306-x

R(x) = QP = (194+x)(306-x)

To find the maximum, take the derivative of the revenue, set that to zero and solve for x.

R'(x)=112-2x

112-2x=0

x=56

1) 56 passengers

2) R(56) = (250)(250)= $62500

3) R(56)/(194+56) = 62500/(194+56) = $250 per passenger