Calculus problem

Question

If exactly 50 people sign up for a charter flight, Rob's Travel Agency will charge $240 per person. But if more than 50 people sign up, then the price per person is reduced by $3 for each additional person. Assuming that at least 50 people sign up, how many total passengers will result in the maximum revenue for the travel agency? Make sure you justify that your answer gives the maximum.

Answer 1

p represents each additional passengers

f(p) = (50 + p)(240 - 3p)

f(p) = 12000 + 90p - 3p²

f(p) = -3p² + 90p + 12000

Maximum at -90 / 2(-3), or p = 15