Question 46
Let $x$, $y$, $z \gt 0$ be real numbers such that $x + y + z = 1399$. Determine the maximum value of
$$
y\lfloor x \rfloor + z\lfloor y \rfloor + x\lfloor z \rfloor,
$$
where $\lfloor x \rfloor$ is the largest integer less than or equal to $x$.
$$
y\lfloor x \rfloor + z\lfloor y \rfloor + x\lfloor z \rfloor,
$$
where $\lfloor x \rfloor$ is the largest integer less than or equal to $x$.