Question

Farmer Ed has 550 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, find the length and width of the plot that will maximize the area. What is the largest area that can be enclosed?

Answer 1

Because it is a rectangle, the area is expressed as A = xy, or length times width. Because it is next to the river, he only needs to fence three sides, so F = x + 2y. Knowing the amount of fencing available is 7500m, we get: 7500 = x + 2y solve for x x = 7500 - 2y substitute into the area equation A = (7500 - 2y)y distribute A = -2y2 +7500y You can see that this is a parabola which opens down, meaning that the point of maximum area will be at the vertex, y = -b/2a = -7500/[2(-2)] = 1875 x = 7500 - 2(1875) = 3750 A = 3750(1875) = 7,031,250 m2