Farmer Fred wants to construct a rectangular chook pen, using his barn for one of the sides. The other three sides will be constructed using only 80 metres of chicken wire.

Fred had decided to build a pen that was 10 metres wide and 60 metres long, an enclosure of 600 m2, until his wife Francis pointed out that dimensions of 15 metres and 50 metres would enclose a larger area of 800 m2.

How long and how wide should the pen be if Fred wants to enclose as much land as possible? ( Write an algebraic function that will determine the area of the pen in terms of its width and use it to find the answer)