A company produces juice containers which have the shape of a box with squares on the base and the top, and a capacity of 2 litres.

[list=1][br][*] Find a formula for the surface area, [math]A[/math], of the container in terms of the apothem [math]a[/math] of the container. [br]The apothem is the segment from the centre of the square to the midpoint of one of its sides.[br][*] Find the apothem of the container which will minimize the cost of the material required to make the box.[br][*] Find the corresponding height and side of the square.[br][/list]