Continuing from the setup in the question linked above (and using the same symbols/variables), we have




The next part of the question asks to maximize this result - our target function which we'll call

- subject to

.
We can see that

is quadratic in

, so let's complete the square.

Since

are non-negative, it stands to reason that the total product will be maximized if

vanishes because

is a parabola with its vertex (a maximum) at (5, 25). Setting

, it's clear that the maximum of

will then be attained when

are largest, so the largest flux will be attained at

, which gives a flux of 10,800.