Question

Last year, 200 people came to see the fall play at Jones High School. The ticket price was $2.00. This year, the drama teacher wants to increase the ticket price. He estimates that for every $0.25 increase, 10 fewer people will come to the play. What ticket price will maximize the income?

Answer 1

income = ticket price * people = (2 + .25 n)(200 - 10 n)

i = 400 + 50 n - 20 n - 2.5 n^2 = -2.5 n^2 + 30 n + 400

the max is on the axis of symmetry ... -b / 2a = -30 / -5 = 6

2 + (.25 * 6) = 3.50