Denote the length, width, and height of the box by , , and , respectively (). It is given that . We have to make the surface area as small as possible.

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Denote the length, width, and height of the box by , , and , respectively (). It is given that . We have to make the surface area as small as possible.

Mathematics
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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Denote the length, width, and height of the box by x, y, and z, respectively (x,y,z > 0). It is given that xyz=110. We have to make the surface area [S]=2xy+2xz+2yz as small as possible.
Write z by x and y, insert it in the function you are trying to minimize and then find local minima through the derivatives.

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