$\"\"$

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Draw the related figure.

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$\"\"$

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$\"\"$ is the offshore well, $\"\"$ is oil refinery.

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$\"\"$ is a right angle triangle.

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

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$\"\"$ is the point between $\"\"$ and $\"\"$ such that $\"\"$ and $\"\"$ .

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Let $\"\"$ be the cost per km on land.

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Cost of $\"\"$ .

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Cost of $\"\"$ .

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Total cost $\"\"$ .

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$\"\"$

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$\"\"$

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Since $\"\"$ is cost per km on land, $\"\"$ is constant.

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$\"\"$

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Differentiate on each side with respect to $\"\"$ .

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$\"\"$ .

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$\"\"$

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Find the critical numbers by equating first derivative to zero.

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$ is minimum when $\"\"$ .

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$\"\"$

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$\"\"$ .