A farmer wishes to build a pen for his (non-swimming) animals next to a lake
as shown in the figure below.
The lakeshore has the shape of the parabola *y* = −*x*^{2}.
Two sides of the pen are parallel to the axis of the parabola and the third side
is perpendicular to it.
If the farmer has *d* units of fencing, what dimensions of the pen will
maximize the area of the land bounded by the fence and the lake?