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Use the method of Lagrange Multipliers to solve it.
A rectangular tank with a bottom and sides but no top is to have volume 500 cubic feet. Determine the dimensions (length, width, height) with the smallest possible surface area.
Use Lagrange multipliers to find the dimensions of a rectangular box with largest volume if the total surface area is given as 676 cm2. (Enter the dimensions (in centimeters) as a comma separated list.)