Due to an influx of wild animals, you need to enclose your garden. You have 500 feet of fencing and will enclose the garden on three sides, with your barn providing protection for the fourth size. Determine the length of the fence opposite the barn which maximizes the area enclosed.

so length of the fence is 250 feet

Explanation:

Given data

fencing (L) = 500 feet

enclose the garden = 3 sides

to find out

length of the fence

solution

we consider barn length x and width y

so we say x + 2y = 500 ... 1

we want to maximize length i. e xy = f

so we say

df/dx = ƛ * dL/dx

y = ƛ * 1

and

df/dy = ƛ * df/dy

x = ƛ * 2

from equation 1 we can say

2 ƛ + 2 ƛ = 500

so ƛ = 500/4 = 125

so that x = 2 * 125, y = 125

so x = 250, y = 125

so length of the fence is 250 feet