document.write( "Question 1143014: If x+y+z=16 then find the maximum value of (x-3)(y-5)(z-2). Given that (x-3)>0, (y-5)>0, (z-2)>0 \n" ); document.write( "

Algebra.Com's Answer #763788 by Edwin McCravy(20055) $\"\"$ $\"About$

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If x+y+z=16 then find the maximum value of (x-3)(y-5)(z-2). Given that
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document.write( "We wish to maximize \r\n" );
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document.write( "So we solve x+y+z=16 for z and substitute:\r\n" );
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document.write( "Next we find both partial derivatives and set them equal to zero:\r\n" );
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document.write( "Setting that equal to zero gives:\r\n" );
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document.write( "y-5=0;  -2x-y+17=0\r\n" );
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document.write( "Since y-5 > 0 we ignore the first\r\n" );
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document.write( "-2x-y+17=0\r\n" );
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document.write( "x-3=0;  -2y-x+19=0\r\n" );
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document.write( "Since x-3 > 0 we ignore the first.\r\n" );
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document.write( "-2y-x+19=0\r\n" );
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document.write( "So we solve this system:\r\n" );
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document.write( "That has solution (x,y)=(5,7)\r\n" );
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document.write( "Substituting in\r\n" );
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document.write( "So the maximum value of (x-3)(y-5)(z-2) is 8.\r\n" );
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document.write( "Edwin

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