Question 189349
A farmer has 500 feet of fencing to use to make a rectangular garden.
 One side of the garden will be a barn, which requires no fencing.
 How should the pen be built in order to enclose the largest amount of area possible?
:
Let L = the length
Let x = the width
:
We only need 3 sides so the perimeter equation would be:
L + 2x = 500
L = (500-2x)
:
Area = x * L
Substitute (500-2x) for L
A = x(500-2x)
A = -2x^2 + 500x
:
A quadratic equation, we can use the axis of symmetry and vertex to find the maximum area; 
x = -500/(2*-2)
x = -500/-4
x = 125 ft is the width which will give max area
:
The length:
L = 500 - 2(125)
L = 250 ft is the length for max area
:
Find the max area
:
A = 250 * 125
A = 31,250 sq/ft
:
I'll let you fill in the blanks
"The farmer should build the pen ______ feet away from the barn, and ________ 
feet wide, for an area of _______ square feet