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Minimize the Surface Area of a Box

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A closed rectangular box with volume 576 in^3 is to be made so its top (and bottom) is a rectangle whose length is twice its width. Find the dimensions of the box that will minimize its surface area.

Could you please show all work so I can better grasp the concept? Thank you.

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The surface area of a box is minimized.

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Suppose this rectangular box has length x, width y and height z.
From the condition, the length is twice of its width, so x=2y. The volume of the box is ...

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