An open box with square base is to be made of a given quantity of card board of area c^{2}. Show that the maximum volume of the box is c^{3}/6√3 cubic units.
Let the length of side of the square base of open box be x unit and its height be y units.∴ Area of the card board used = x^{2} + 4xy∴ x^{2} + 4xy = c^{2} (given).