Question

A ferry service is transporting passengers to an island charges a fare of $10 and carries 300 persons per day. The manager estimates that the company will lose 15 passengers for each increase of $1 in the fare. Find the fare that yields the greatest income.

Answer 1

From the proble data this equation is assumed:
Cash = ticket * passengers
Cash: F(x) = (10+x)*(300-15x)
=> F(x) = -15x^2 +150x - 3000.

Max money is where df(x)/dx = 0 => F'(x) = 0

F'(x) = -30x +150

We want F'(x) = 0 => -30x + 150 = 0 => x=5

So ticket was 10+x, so in that case, best ticket is 15$