document.write( "Question 1142708: Calculus Optimization Question\r
\n" ); document.write( "\n" ); document.write( "A rectangular pen is being constructed with 500 feet of fencing. One side of the pen is the wall of a barn and does not require fencing. The other three sides are fenced. What are the dimensions of the pen that will maximize the area of the pen? \n" ); document.write( "

Algebra.Com's Answer #763430 by ikleyn(52781) $\"\"$ $\"About$

You can put this solution on YOUR website!
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document.write( "Let x be the dimension of the pen (in feet) perpendicular to the wall. \r\n" );
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document.write( "Then the side parallel to the wall is  (500-2x)  feet long,\r\n" );
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document.write( "and the area of the pen is\r\n" );
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document.write( "    A(x) = x*(500-2x)  = -2x^2 + 500x  square feet.\r\n" );
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document.write( "They want you find the maximum of the function A(x) using Calculus.\r\n" );
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document.write( "For it, differentiate A(x) over x and equate the derivative to zero:\r\n" );
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document.write( "    A'(x) = -4x + 500 = 0,\r\n" );
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document.write( "which gives you  x =  = 125 feet.\r\n" );
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document.write( "Thus you obtain the\r\n" );
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document.write( "ANSWER.  Under given conditions, the maximum area is achieved for the rectangle \r\n" );
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document.write( "         with the short side of 125 ft perpendicular to the wall and long side of 500 - 2*125 = 250 ft parallel to the wall.\r\n" );
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\n" ); document.write( "\n" ); document.write( "I re-wrote/corrected my post after getting a notice from @greenestamps.\r
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\n" ); document.write( "\n" ); document.write( "@greenestamps, thanks for your notice !\r
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