Question

A wildlife organization wants to fence off an area of a beach. the organization can only fence 1000 yd2. what length (x) and width (y) should the organization use to use the least amount of fencing as possible?

Answer 1

We assume in this number that the fence is in a rectangular shape such that its perimeter is equal to,
                                   P = 2x + 2y
From the equation of the area,
                       A = xy = 1000   ; x = 1000/y
Substituting this to the equation,
                                   P = 2(1000/y) + 2
                                  P = 2000/y + 2y
Getting the differential and equating it to zero.
                                 dP = -2000/y²+ 2 = 0
The value of y from the equation is 31.62 yd
The value of x:
                                x = 1000/31.62 = 31.62 yd
Therefore, the dimension of the area to be fenced is 31.62 yd by 31.62 yd.