An open-top box is to be constructed from a 8 in by 16 in rectangular sheet of tin by cutting out squares of equal size at each corner, then folding up the resulting flaps. Let x denote the length, in inches, of the side of each cut-out square. Assume negligible thickness. (a) Find a formula for the volume, V, of the box as a function of x. V(x) = (16 - 2x ) (8-2x) (x) (b) For what values of a does the formula from part (a) make sense in the context of the problem? (0,4) (enter an interval) (c) On a separate piece of paper, sketch a graph of the volume function. (d) What is the maximum volume of the box? Round your answer to 2 decimal places. 66.67 cubic inches (include units)