document.write( "Question 1035166: You have been asked to design a rectangular box with a square base and lid. The volume of the box must be 12 m3. The cost per square meter of material for the base is $0.50, for the sides $0.20, and for the lid $0.10. If the total cost of materials is a minimum, then the dimensions (in meters) of the box are \n" ); document.write( "

Algebra.Com's Answer #649988 by ankor@dixie-net.com(22740) $\"\"$ $\"About$

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The volume of the box must be 12 m3.
\n" ); document.write( "The cost per square meter of material for the base is $0.50, for the sides $0.20, and for the lid $0.10.
\n" ); document.write( " If the total cost of materials is a minimum, then the dimensions (in meters) of the box are
\n" ); document.write( ":
\n" ); document.write( "let x = the side of the square base
\n" ); document.write( "then
\n" ); document.write( "x^2 = the area of the base and the lid
\n" ); document.write( "and the volume is to be 12 cu/m. therefore:
\n" ); document.write( "12/x^2 = height of the box
\n" ); document.write( ":
\n" ); document.write( "Cost = base area + side areas + lid area
\n" ); document.write( "C = .5x^2 + .2(4*x* $\"12%2Fx%5E2\"$ ) + .1x^2
\n" ); document.write( "cancel x
\n" ); document.write( "C = .6x^2 + .2(4* $\"12%2Fx\"$ )
\n" ); document.write( "C = .6x^2 + $\"9.6%2Fx\"$
\n" ); document.write( "Graphically, we can see minimum cost occurs when x = 2
\n" ); document.write( " $\"+graph%28+300%2C+200%2C+-3%2C+5%2C+-5%2C+20%2C+.6x%5E2%2B%289.6%2Fx%29%29+\"$
\n" ); document.write( "The dimensions
\n" ); document.write( "L=2;
\n" ); document.write( "W=2
\n" ); document.write( "H = 12/2^2 = 3 m
\n" ); document.write( " \n" ); document.write( "

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