document.write( "Question 1135447: Please answer this optimization problem again hehehe
\n" ); document.write( "1:An open box is to be made from a 16 cm by 30 cm piece of cardboard by cutting out squares of equal size from the four corners and bending up the sides. How long should the sides of the squares be to obtain a box with the largest volume? \n" ); document.write( "
Algebra.Com's Answer #753057 by ankor@dixie-net.com(22740)\"\" \"About 
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An open box is to be made from a 16 cm by 30 cm piece of cardboard by cutting out squares of equal size from the four corners and bending up the sides.
\n" ); document.write( " How long should the sides of the squares be to obtain a box with the largest volume?
\n" ); document.write( ":
\n" ); document.write( "let x = the length of the side of the squares
\n" ); document.write( "then
\n" ); document.write( "(16-2x) = the width of the box
\n" ); document.write( "(30-2x) = the length
\n" ); document.write( "and
\n" ); document.write( "x = height of the box
\n" ); document.write( ":
\n" ); document.write( "Volume the height * width * length
\n" ); document.write( "V(x) = x(16-2x)(30-2x)
\n" ); document.write( "FOIL
\n" ); document.write( "V(x) = x(480 - 32x - 60x + 4x^2,)
\n" ); document.write( "V(x) = 4x^3 - 92x^2 + 480x
\n" ); document.write( ":
\n" ); document.write( "graphing this equation
\n" ); document.write( "\"+graph%28+300%2C+200%2C+-6%2C+10%2C+-200%2C+800%2C+4x%5E3+-+92x%5E2+%2B+480x%2C+726%29+\"
\n" ); document.write( ":
\n" ); document.write( "x = 3.333 cm, to give a max volume of 726 cu/cm (green line) \n" ); document.write( "
\n" );