Question 1142708
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<pre>
Let x be the dimension of the pen (in feet) perpendicular to the wall. 


Then the side parallel to the wall is  (500-2x)  feet long,


and the area of the pen is


    A(x) = x*(500-2x)  = -2x^2 + 500x  square feet.


They want you find the maximum of the function A(x) using Calculus.


For it, differentiate A(x) over x and equate the derivative to zero:


    A'(x) = -4x + 500 = 0,


which gives you  x = {{{500/4}}} = 125 feet.


Thus you obtain the


<U>ANSWER</U>.  Under given conditions, the maximum area is achieved for the rectangle 

         with the short side of 125 ft perpendicular to the wall and long side of 500 - 2*125 = 250 ft parallel to the wall.
</pre>

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I re-wrote/corrected my post after getting a notice from @greenestamps.


@greenestamps, thanks for your notice !