let's say the numbers are "a" and "b"
thus [tex]\bf y=ab\qquad
\begin{cases}
a+b=80\\
b=80-a
\end{cases}\implies y=a(80-a)\implies y=80a-a^2\\\\
-----------------------------\\\\
\cfrac{dy}{da}=80-2a[/tex]
set the derivative to 0, and check the critical points, there's only one anyway
and do a first-derivative test, to see if it's a maximum
