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Packaging an open rectangular box having a surface area of

Question: PACKAGING An open rectangular box having a surface area of 300 in.2 is to be constructed from a tin sheet. Find the dimensions of the box if the volume of the box is to be as large as possible. What is the maximum volume?

Hint: Let the dimensions of the box be x × y × z (see the figure that follows). Then the surface area is xy + 2xz + 2yz, and its volume is xyz.

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