document.write( "Question 1114168: A fence must be built to enclose a rectangular area of 45,000 ft squared. Fencing material costs $3 per foot for the two sides facing north and south and $6 per foot for the other two sides. Find the cost of the least expensive fence. \n" ); document.write( "

Algebra.Com's Answer #729178 by ikleyn(52778) $\"\"$ $\"About$

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document.write( "The problem asks to minimize the sum  2*(3x + 6y)  under the condition  xy = 45000.\r\n" );
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document.write( "It is the same as to minimize  the form  x+2y  under the condition  xy = 45000.\r\n" );
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document.write( "Then  x + 2y =  = .\r\n" );
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document.write( "To find the minimum of this function of x, take the derivative and equate it to zero:\r\n" );
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document.write( " -  =  = 0,\r\n" );
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document.write( "and the root (the solution) is   x = 300.\r\n" );
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document.write( "Answer.  The dimensions  x= 300 ft (north and south sides)  and   = 150 ft  (other two sides)  give the required minimum.\r\n" );
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document.write( "         The minimum cost of the fence is  2*(3*300 + 6*150) = 3600 dollars.\r\n" );
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