If exactly 200 people sign up for a charter flight, Leisure World Travel Agency

Question

If exactly 200 people sign up for a charter flight, Leisure World Travel Agency charges $320/person. However, if more than 200 people sign up for the flight (assume this is the case), then every fare is reduced by $1 times the number of passengers above 200. Determine how many passengers will result in a maximum revenue for the travel agency. Hint: Let x denote the number of passengers above 200. Show that the revenue function R is given by

R(x) = (200 + x)(320 x).

passengers

a. What is the maximum revenue?
$  

b. What would be the fare per passenger in this case?
dollars per passenger

Explanation / Answer

From the given question,

Let x denote the number of passengers above 200.

Total pasengers= 200+x

Initial fare per person=$ 320/person

New fare if passengers are x more than 200= $(320-x)

Revenue= Number of passengers x fare per passenger

R(x)=(200+x)(320-x)

a) dR/dx= (200+x) d/dx (320-x) + (320-x) d/dx (200+x)

= (200+x) (-1) + (320-x) (1)

=-200-x+320-x

=120-2x

To calculate maximum revenue, dR/dx=0

120-2x=0

x= 60

Maximum revenue=(200+x)(320-x)

=(200+60)(320-60)

=$ 67600

Maximum revenue is $ 67600

Fare per passenger= $ (320-x)

=$ 260.

Fare per passenger will be $ 260

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