What is the best way to represent a NP-Hardness result for a decision problem with two decision parameters? Suppose we have a problem $P$ which asks to minimize two parameters $x$ and $y$ and we show that given a constant $x$ deciding whether $y \leq k$ is NP-Hard and given a constant $y$, deciding whether $x \leq k$ is NP-Hard.
What is the best way of stating this result? $P$ is NP-Hard to solve? Or should the statement be more specific? Furthermore, for such two parameter decision problems, what should be proven if we want to obtain an NP-Hardness result? A result of the type I proved or a result that proves it is NP-Hard to decide if $x + y \leq k$ etc.