Carol has 2000 ft of fencing to fence in a rectangular horse

Carol has 2000 ft of fencing to fence in a rectangular horse corral. Find a function that models the area A of the corral in terms of the width x of the corral. Find the dimensions of the rectangle that maximize the area of the corral.

Solution

a) Area of rectnagle = length*width

A(x) = x(1000 -x) = -x^2 + 1000x

b) Function of area is a quadratice function

y = ax^2 +bx +c maximises at x = -b/2a

So, x = -(1000/(2*-1)) = 500 ft

width = 500 ft

length = 1000 -x = 500 ft for maximum area