$\"\"$

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A wooden beam has a rectungular cross section of height $\"\"$ and width $\"\"$ .

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Let $\"\"$ be the strength and $\"\"$ is the constant proponality.

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The Strength of the beam is $\"\"$ .

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$\"\"$

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Substitute $\"\"$ in the strength of the beam.

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$\"\"$

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

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$\"\"$

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Evaluate $\"\"$ .

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$\"\"$

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$\"\"$ .

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Susbstitute $\"\"$ in $\"\"$ .

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$\"\"$

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$\"\"$ inches.

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$\"\"$ which yeilds a maximum value.

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$\"\"$

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Width : $\"\"$ inches and Height : $\"\"$ inches.