Farmer Ed has 3,500 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?
Accepted Solution
A:
Answer:Because it is a rectangle, the area is expressed as A = xy, or length times width.Step-by-step explanation: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 xx = 7500 - 2y substitute into the area equationA = (7500 - 2y)y distributeA = -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