Find $f$ that solves the following optimization problem: $\min_{f} \frac{f(x, y)}{f(y, x) \times x}$, where $x$, $y$ are constant real numbers.

Question

I'm trying to find an $f$ that solves the following optimization problem:

$\min_{f} \frac{f(x, y)}{f(y, x) \times x}$, where $x$, $y$ are constant positive real numbers.

subject to $f$: $\mathbb{{R}^+}^2 \rightarrow \mathbb{R^+}$

There are no other restrictions on $f$. I've gotten to this problem by modelling an engineering problem, so I may be able to place additional restrictions on $f$ if it will help lead to a solution. I'd really like to know if a general solution exists, though. I'd appreciate it if anyone could point me in a possible direction to solve this problem.

Thanks!