In: Math
a. Squares with sides of length x are cut out of each corner of a rectangular piece of cardboard measuring 7 ft by 5 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 sides of length s. Find the volume of the largest box that can be formed in this way.