The given equation is

The greatest income refers to the vertex of the function V(h,k), where

a = -40 and b = 400.

Then, we find k evaluating the function

Hence, the greatest income is $1000. The number of tickets is 5.
The ticket price with no income refers to the x-intercept

When the tickets have a price of $10, there's no income. We obtained the answer by solving the function where l(t) = 0.