Word problem

Question

the back of tons property is a creek. Time would like to enclose a rectangular area, usuing the creek as one side and fencing for the other three sides, to create a corral. If there is 860 feet of fencing available what is the maximum possible area of the corral? 

Answer 1

Let x = length of side parallel to the creek

      y = length of each side perpendicular to the creek

 

Given:  x + 2y = 860

Maximize:  A = xy

 

Since x + 2y = 860, x = 860 - 2y

 

So, A = (860-2y)y 

 

      A = -2y² + 860y

 

        A has a maximum when y = -860/[2(-2)] = 860/4 = 215

                                                  x = 860 - 2y = 860 - 2(215) = 430

 

maximum area = xy = (430(215) = 92450 ft²