A rectangular package with a square cross-section (see Figure1) is to be sent via Australia Post.

1. Figure 1: Illustration of the package to be sent via Australia Post.

The allowable size(L)(L)is determined by adding the length and perimeter of the cross-section to get:

1. L=4x+y;L=4x+y;while the volumeVVis:V=x2y.V=x2y.

IfL=280cmL=280cm, show that the volume(V)(V)of the package can be expressed as:

1. V=280x24x3.V=280x24x3.

FinddV / dx.

Hence, or otherwise, find the dimensions so that the volume(V)(V)of the package is maximised.