metre1. A ferry operator takes tourists to an island,The operator carries an average of 500people per day for a round-trip fare of $20,The operator estimates that for each $1increase in fare, 20 fewer people will takethe trip. What fare will maximize thenumber of people taking the ferry?

Accepted Solution

Answer:$17.5Step-by-step 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 [tex]\frac{dF(x)}{dx} = 0[/tex] Hence, 100 - 40x = 0 ⇒ x = 2.5  Therefore, the fare of $(20 - 2.5) = $17.5 will maximize the total fare. (Answer)