we know that
We want to minimize A
subbing the first into the second we get...
Since we want the minimum value we need to find the vertex of the parabola.
There are a few different ways. Since it is symmetric about its vertex the vertex is half way between its intercepts -24 and 0 so at -12
or we could use the vertex fromula
Now that we know y we can solve for x
so the minimum product is