Answer:
781250 Square Meters
Step-by-step explanation:
Let the dimensions of the rectangular plot be x and y
Farmer Ed wants to enclose three sides of a rectangular plot with a fencing of 2500 meters.
Therefore: Perimeter, P=x+2y=2500
We want to find the largest area that can be enclosed.
Area of the plot, A(x,y)=xy
Substitute x=2500-2y
A(y)=(2500-2y)y
[tex]A(y)=2500y-2y^2[/tex]
To maximize A, we first find its derivative
[tex]A'(y)=2500-4y\\$Setting A'=0\\2500-4y=0\\2500=4y\\y=625 meters\\Recall: x=2500-2y\\x=2500-2(625)=1250meters[/tex]
The largest area that can be enclosed(at x=1250m,y=625m) is:
1250 X 625
=781250 Square Meters
