Squares with sides of length x are cut out of each corner of a rectangular piece of cardboard measuring 37ft by 20 ft. The resulting piece of cardboard is then folded into a box without a lid. Find the volume of the largest box that can be formed in this way.
b) Suppose that in part a the original piece of cardboard is a square with side lengths k. Find the volume of the largest box that can be formed in this way.
c)Suppose that in part (a) the original piece of cardboard is a rectangle with sides of length k and L. Holding k fixed, find the size of the corner squares x that maximizes the volume of the box as W→∞.
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