hvney
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A ferry operator takes tourists to an island.
The operator carries an average of 500
people per day for a round-trip fare of $20.
The operator estimates that for each $1
increase in fare, 20 fewer people will take
the trip. What fare will maximize the
number of people taking the ferry?

Respuesta :

ashishdwivedilVT

The fare of $(20 - 2.5) = $17.5 will maximize the total fare.

What is Differentiation?

Differentiation means the rate of change of one quantity with respect to another. The speed is calculated as the rate of change of distance with respect to time.

Here, The operator for a round-trip fare of $20, carries an average of 500 people per day.

It is estimated that 20 fewer people will take the trip, for each $1 increase in fare.

for $x  increase in fare, 20x less people will take the trip and at that time the total fare F is given by  

f(x) =(20 + x)(500 - 20x)

f (x) = 10000 + 100x - 20x²

For f(x) to be maximum, the condition is dy/dx = 0

 100 - 40x = 0

⇒ x = 2.5  

Thus, the fare of $(20 - 2.5) = $17.5 will maximize the total fare.

Learn more about Differentiation from:

https://brainly.com/question/24062595

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