Farmer Ed has 2000 meters of fencing and wants to enclose a

Farmer Ed has 2,000 meters of fencing, and wants to enclose a rectangular plot that borders on a river. If Farmer Ed does not fence the side along the river, what is the largest area that can be enclosed? The largest area that can be enclosed is _____ square meters.

Solution

Area ,A(x)= length *width = x(2000-2x)

A(x)= 2000x -2x²

Area is maximum at maximum value of x which is x =-2000/2(-2) =500 m

Therefore maximum area is A(500) = 2000(500)=2(500²) = 500,000square meters