$\"\"$

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The function is $\"\"$ , $\"\"$ .

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Consider $\"\"$ .

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Apply derivative on each side with respect to $\"\"$ .

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$\"\"$

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$\"\"$ .

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Find the critical points by equating $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$ and $\"\"$

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$\"\"$ and $\"\"$ .

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$\"\"$

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$\"\"$ .

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Apply derivative on each side with respect to $\"\"$ .

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$\"\"$

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$\"\"$

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Substitute $\"\"$ in $\"\"$ .

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$\"\"$ .

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$\"\"$

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Substitute $\"\"$ in $\"\"$ .

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$\"\"$ .

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The maximum profit is obtained when $\"\"$ .

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At $\"\"$ the value is $\"\"$ .

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Therefore, the correct choice is $\"\"$ .

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$\"\"$

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The correct choice is option $\"\"$ .