Question

1.You have 150 yards of fencing to enclose a rectangular region. One side of the rectangle does not need fencing. Find the dimensions of the rectangle that maximize the enclosed area. What is the maximum area?

Answer 1

Let the dimensions be x and y. 2 of the sides measuring x and only one of the sides measuring y should be fence. 
                                  150 = 2x + y
The area of the rectangular figure,
                                      A = xy
Substituting the y in the first equation to the second,
                                      A = x(150 - 2x)
                                   A = 150x - 2x²
Differentiate the equation and equate to zero,
                                  dA/dx = 0 = 150 - 4x
The value of x is 37.5 yard and y is equal to 75 yard. The maximum area is 2812.5 yd².