document.write( "Question 1140031: A landscape architect wished to enclose a rectangular garden on one side by a brick wall costing $20/ft and on the other three sides by a metal fence costing $10/ft. If the area of the garden is 122 square feet, find the dimensions of the garden that minimize the cost. \n" ); document.write( "

Algebra.Com's Answer #760487 by math_helper(2461) $\"\"$ $\"About$

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document.write( "L*W = 122                   (1)\r
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document.write( "Cost equation:
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document.write( "C = 20L + 10L + 10W + 10W   
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document.write( "C = 30L + 20W               (2)  \r
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document.write( "Eq (1) -->   L = 122/W\r
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document.write( "Substitute for L in (2):\r
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document.write( "C = 30*(122/W) + 20W
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document.write( "C = 3660/W + 20W\r
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document.write( "Differentiate WRT to W:
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document.write( "dC/dW = -(3660/W^2) + 20\r
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document.write( "Set the derivative to 0:
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document.write( "  -(3660/W^2) + 20 = 0
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document.write( "   20W^2 = 3660
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document.write( "     W^2 = 183
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document.write( "     W  =  ft\r
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document.write( "L = 122/13.52775 =  ft\r
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document.write( "[ min(C) = $541.11   for these dimensions ]\r
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