Let $x,$ $y,$ and $z$ be positive real numbers.  Find the maximum value of
\[\frac{xyz}{(1 + 5x)(4x + 3y)(5y + 6z)(z + 18)}.\]
Question:
Let $x,$ $y,$ and $z$ be positive real numbers.  Find the maximum value of
\[\frac{xyz}{(1 + 5x)(4x + 3y)(5y + 6z)(z + 18)}.\]
Answer:
Let's think step by step.

user
\frac{1}{5120}
Let $x,$ $y,$ and $z$ be positive real numbers.  Find the maximum value of
\[\frac{xyz}{(1 + 5x)(4x + 3y)(5y + 6z)(z + 18)}.\]
train