A farmer has 600 m of fencing with which to enclose a rectan

A farmer has 600 m of fencing with which to enclose a rectangular pen adjacent to a long existing wall. She will use the wall for one side of the pen and the available fencing for the remaining three sides. Write the area of the pen as a function of a single variable.

Solution

Pen has one side as wall and three sides fence

let length of pen be l and width be w

So, let wall be along length

So, l +2*w = 600

l = 600-2w

Now Area = length*width = (600-2w)w

= -2w^2 +600w