Let $x,$ $y,$ and $z$ be positive real numbers.  Find the minimum value of
\[\frac{x^3 + 2y^3 + 4z^3}{xyz}.\]
Question:
Let $x,$ $y,$ and $z$ be positive real numbers.  Find the minimum value of
\[\frac{x^3 + 2y^3 + 4z^3}{xyz}.\]
Answer:
Let's think step by step.

user
6
Let $x,$ $y,$ and $z$ be positive real numbers.  Find the minimum value of
\[\frac{x^3 + 2y^3 + 4z^3}{xyz}.\]
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