The diagram shows an open container in the shape of a cuboid of width \(x\) cm, length \(4x\) cm and height \(h\) cm. The volume of the container is \(800\text{ cm}^3\).

(i) Show that the external surface area, \(S\text{ cm}^2\), of the open container is such that \(S=4x^2+\frac{2000}{x}\).

(ii) Given that \(x\) can vary, find the stationary value of \(S\) and determine its nature.