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If exactly 180 people sign up for a charter flight, Leisure World Travel Agency charges $298/person. However, if more than 180 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. What is the maximum revenue? Whatwould be the fare per passenger in this case?
Hint: Let x denote the number of passengers above 200. Show that the revenue function R is given by R(x)=(200+x)(300-x)

Respuesta :

Answer:

The max. revenue is $57,121.

This happens with 239 passengers.

The price of the ticket is $239 per person.

Step-by-step explanation:

Let the variable "P" denote the number of passengers.

If P=180, then the ticket cost is $298/person. Then the price is reduced by $1 for each additional person.

In general, if P=(180+x), then the ticket cost becomes (298-x) per person.

The revenue can be defined as the ticket cost multplied by the number of passengers:

[tex]R=P*T=(180+x)(298-x)=53,640-180x+298x-x^2\\\\R(x)=-x^2+118x+53,640[/tex]

We can derive R and equal to zero to maximize the function.

[tex]dR/dx=-2x+118=0\\\\x=118/2=59[/tex]

The amount of passengers is:

[tex]P=180+x=180+59=239[/tex]

The price of the tickets is

[tex]T=298-59=239[/tex]

The revenue is:

[tex]R(59)=(180+59)(298-59)=239*239\\\\R(59)=57,121[/tex]

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