document.write( "Question 1146865: What is the maximum amount of fencing needed to construct a rectangle enclosure containing 1800 ft^2 using a river as a natural boundary on one side? \n" ); document.write( "

Algebra.Com's Answer #768171 by ikleyn(52781) $\"\"$ $\"About$

You can put this solution on YOUR website!
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\n" ); document.write( "\n" ); document.write( "            Regarding this post, I have two notices.\r
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\n" ); document.write( "\n" ); document.write( "1.   Your formulation is INCORRECT.\r
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\n" ); document.write( "\n" ); document.write( "       The question should ask about the MINIMUM length of the fencing ---- NOT about the maximum length. \r
\n" ); document.write( "\n" ); document.write( "       The maximum length DOES NOT EXIST.   You can make your enclosure longer and narrower, by keeping the same area.\r
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\n" ); document.write( "\n" ); document.write( "       The correct formulation is THIS :\r
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document.write( "           What is the  fencing length needed to construct a rectangle enclosure \r\n" );
document.write( "           containing 1800 ft^2 using a river as a natural boundary on one side? \r\n" );
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\n" ); document.write( "\n" ); document.write( "2.   The \"solution\" by @josgarithmetic is   TOTALLY   WRONG, starting from its third line to the end.\r
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\n" ); document.write( "\n" ); document.write( "       So you better simply IGNORE it.\r
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\n" ); document.write( "\n" ); document.write( "      Below find my correct solution.\r
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document.write( "xy = 1800              (1)\r\n" );
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document.write( "x + 2y -----> minimize        (x is the length along the river)\r\n" );
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document.write( "So your task is to minimize (x+2y) under the given condition/restriction  (1).\r\n" );
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document.write( "From (1),  x = ,  so we need to minimize the function  f(y) = .\r\n" );
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document.write( "The derivative  f'(y) = - + 2.\r\n" );
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document.write( "To find the minimum of f(y), equate its derivative to zero\r\n" );
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document.write( "    - + 2 = 0\r\n" );
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document.write( "     = 2\r\n" );
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document.write( "     =  = 900\r\n" );
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document.write( "    y =  = 30.\r\n" );
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document.write( "ANSWER.  The minimum fencing is at y = 30 ft perpendicular to the river and x =  =  = 60 ft along the river.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved.\r
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