# How do you find two numbers whose difference is 100 and whose product is a maximum?

Unfortunately, there is no solution for this question since the product can be made as big as you wish. For any $x$ and $y$ that satisfy the condition, $\left(x + 1\right)$ and $\left(y + 1\right)$ will yield a larger product assuming that $x$ and $y$ are nonnegative.
$\left(x + 1\right) \left(y + 1\right) = x y + x + y + 1 > x y$