(a) A box with an open top and a square base is to be constructed to contain 4000 cubic inches. Find the dimensions that will require the minimum amount of material to construct the box.

(b) A box with an open top and a square base is to be constructed to contain k cubic inches. Show that the minimum amount of material is used to construct the box when each side of the base is x=(2k)1/3 and the height is y= (k /4)1/3