Let $x$ and $y$ be positive real numbers such that $3x + 4y < 72.$  Find the maximum value of
\[xy (72 - 3x - 4y).\]
Question:
Let $x$ and $y$ be positive real numbers such that $3x + 4y < 72.$  Find the maximum value of
\[xy (72 - 3x - 4y).\]
Answer:
Let's think step by step.

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Let $x$ and $y$ be positive real numbers such that $3x + 4y < 72.$  Find the maximum value of
\[xy (72 - 3x - 4y).\]
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