1995 6. A rectangular box without a lid is to be made from 12 m² of sheet metal.
i) If the length, width and height of the box are given by \(x\), \(y\) and \(z\) metres respectively,
show that the constraint function for this problem is given by:
\(g(x, y, z) = 2xz + 2yz + xy - 12 = 0\).
ii) Use the method of Lagrange multipliers and the constraint function given in part (i)
to determine the maximum possible volume of the box.