document.write( "Question 293406: from a thin piece of cardboard 40in. by 40in., square corners are cut out so that the sides can be foled to make a box. what dimensions will yield a bos of maximum volume? what is the maximum volume? \n" ); document.write( "
Algebra.Com's Answer #211819 by stanbon(75887)\"\" \"About 
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from a thin piece of cardboard 40in. by 40in., square corners are cut out so that the sides can be folded to make a box.
\n" ); document.write( "what dimensions will yield a box of maximum volume?
\n" ); document.write( "what is the maximum volume?
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\n" ); document.write( "Volume = height*length*width
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\n" ); document.write( "V = x(40-2x)(40-2x)
\n" ); document.write( "V = 4x(20-x)(20-x)
\n" ); document.write( "V = 4x[400-40x+x^2)
\n" ); document.write( "V = 4x^3 - 160x^2 + 1600x
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\n" ); document.write( "Take the derivative:
\n" ); document.write( "V' = 12x^2 - 320x + 1600
\n" ); document.write( "---
\n" ); document.write( "Solve 4(3x^2-80x+400) = 0
\n" ); document.write( "4(3x-20)(x-20) = 0
\n" ); document.write( "Realistic value for \"x\":
\n" ); document.write( "3x = 20
\n" ); document.write( "x = 20/3 = 6 2/3
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\n" ); document.write( "Volume when x = 20/3 inches
\n" ); document.write( "V(20/3) = 4740.7 cu. inches
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\n" ); document.write( "Cheers,
\n" ); document.write( "Stan H.
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