Solution:
Let the number of $5 increases be m. We get the following two equations:
new charge = 180 + 5n
membership = 1000 - 10n
thus, the revenue would be:
revenue = (180 + 5n)( 1000 - 10n)
Applying the distributive property, this is equivalent to:

If we factor this equation, we obtain:

notice that this is a parabola and the vertex will yield our answer. The n of the vertex is:

Applying this data into the first two equations, we get:
new charge = 180 + 5n = 180 + 5(32)= 340
membership = 1000 - 10n = 1000 - 10(32) = 680
So that, we can conclude that the correct answer is:
The new fee is $340.