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

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