Question 1030225
Let x = # of tickets sold.
==> Total revenues  = x(30 - 0.25x) and Total costs = 200

==> Total profits = {{{x(30 - 0.25x) - 200 = -0.25x^2 + 30x -200}}}

Taking the derivative and equating to 0 to get the extreme value, 

-0.5x + 30 = 0
==> x = 30/0.5 = 60

(The 2nd derivative p" = -0.5 < 0, hence we are assured an absolute maximum.)

Therefore, he has to sell 60 tickets to maximize profits.