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Suppose you want to build a hollow rectangular box with volume 2000 cm^3. If the material...

Suppose you want to build a hollow rectangular box with volume 2000 cm^3. If the material for the top costs $3/cm^2 and the material for the side and bottom faces cost $1/cm^2, what are the dimensions of the cheapest box? (Here, we ignore the thickness of the faces of the box.)

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