Let $x,$ $y,$ $z$ be positive real numbers such that $xyz = 8.$  Find the minimum value of $x + 2y + 4z.$
Question:
Let $x,$ $y,$ $z$ be positive real numbers such that $xyz = 8.$  Find the minimum value of $x + 2y + 4z.$
Answer:
Let's think step by step.

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Let $x,$ $y,$ $z$ be positive real numbers such that $xyz = 8.$  Find the minimum value of $x + 2y + 4z.$
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