document.write( "Question 173211: A rectangular piece of metal 32cm by 22cm, has a square of side X cm removed from each corner in order to form a rectangular box. If the volume of the box is to be a maximum what is the value of X? \n" ); document.write( "
Algebra.Com's Answer #128222 by ankor@dixie-net.com(22740)\"\" \"About 
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A rectangular piece of metal 32cm by 22cm, has a square of side X cm removed
\n" ); document.write( " from each corner in order to form a rectangular box.
\n" ); document.write( "If the volume of the box is to be a maximum what is the value of X?
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\n" ); document.write( "From the given information we know the dimensions (L,W,H) of the box is:
\n" ); document.write( "(32-2x) by (22-2x) by x
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\n" ); document.write( "Area = length * width * height
\n" ); document.write( "A = (32-2x) * (22 - 2x) * x
\n" ); document.write( "FOIL
\n" ); document.write( "A = x(704 - 64x - 44x + 4x^2)
\n" ); document.write( "A = x(704 - 108x + 4x^2)
\n" ); document.write( "A = 704x - 108x^2 + 4x^3
\n" ); document.write( "or the standard arrangement is:
\n" ); document.write( "y = 4x^3 - 108x^2 + 704x
\n" ); document.write( ":
\n" ); document.write( "Plot this equation, we only are interested in the positive values x,y values
\n" ); document.write( "\"+graph%28+300%2C+200%2C+-6%2C+15%2C+-500%2C+1600%2C+4x%5E3-108x%5E2%2B704x%29+\"
\n" ); document.write( ":
\n" ); document.write( "Using my trusty Ti83, max volume occurs when x = 4.274 cm about 1348 cu/cm\r
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