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The poster design should be top margin is $\"\"$ -inch bottom and sides margins are each $\"\"$ -inch.

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$\"\"$

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Consider $\"\"$ and $\"\"$ are the length and width of the poster.

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Therefore $\"\"$ and $\"\"$ are the length and width of the printed poster.

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The area of the poster is $\"\"$ .

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But area of the poster is $\"\"$ in².

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$\"\"$

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The area of the printed on the poster is $\"\"$ .

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$\"\"$

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

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$\"\"$

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The area of the printed poster is maximum when its first derivative becomes zero.

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Equate $\"\"$ to zero.

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$\"\"$

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Therefore the length of the printed poster is $\"\"$ in.

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

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$\"\"$

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Therefore the width of the printed poster is $\"\"$ in.

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The length of the printed poster is $\"\"$ in.

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The width of the printed poster is $\"\"$ in.