Question

Metre

1. 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?

Answer 1

$17.5

Explanation:

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.

Therefore, for $x dollars 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) = 10000 + 100x - 20x²

For F(x) to be maximum, the condition is
`(dF(x))/(dx) = 0`

Hence, 100 - 40x = 0

⇒ x = 2.5

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