If exactly 214 people sign up for a charter flight, Leisure World Travel Agency

Question

If exactly 214 people sign up for a charter flight, Leisure World Travel Agency charges $282/person. However, if more than 214people sign up for the flight (assume this is the case), then every fare is reduced by $1 times the number of passengers above 214. Determine how many passengers will result in a maximum revenue for the travel agency. Hint: Let x denote the number of passengers above 214. Show that the revenue function R is given by R(x) = (214 + x)(282 x).

[ANSWER] passengers

What is the maximum revenue?
$ [ANSWER]

What would be the fare per passenger in this case?
[ANSWER] dollars per passenger

Explanation / Answer

R(x) = k*p(x) where k= total number of passengers and p(x) = price/ passengers

In our case Total number of passengers = 214+x

and p(x) = 282-x*1 = 282-x

Therefore R(x) = (214 + x)(282 x)

To maximize R(x) we need to set R'(x)=0

(1 )R'(x)=(282 x)-(214 + x) = 0

282-214 = 2x

x = 34

R(34) = (282 34).(214 + 34) = 61504 (maximum revenue)

2)Fare per passenger = 282-34 = 248

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