A manufacturer cuts squares from the corners of a rectangular piece of sheet metal that measures 2 inches by 8 inches. (See Figure 1.) The manufacturer then
folds the metal upward to make an open-topped box. (See Figure 2.) Letting x represent the side-lengths (in inches) of the squares, find the value of x that maximizes the volume enclosed by this box. Then give the maximum volume. Round your responses to two decimal places.