document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=146018>Question 146018</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A rectangular box with volume 468 cubic feet is built with a square base and top. The cost is $1.50 per square foot for the top and the bottom and $2.00 per square foot for the sides. Let x represent the length of a side of the base in feet. Express the cost of the box as a function of x and then graph this function. From the graph find the value of x, to the nearest hundredth of a foot, which will minimize the cost of the box. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #106567 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=106567\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A rectangular box with volume 468 cubic feet is built with a square base and top. The cost is $1.50 per square foot for the top and the bottom and $2.00 per square foot for the sides. Let x represent the length of a side of the base in feet. Express the cost of the box as a function of x and then graph this function. From the graph find the value of x, to the nearest hundredth of a foot, which will minimize the cost of the box.<BR>\n" );
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document.write( "Let h = the height of the box<BR>\n" );
document.write( "the area of the bottom = x^2<BR>\n" );
document.write( "Therefore:<BR>\n" );
document.write( "x^2*h = volume<BR>\n" );
document.write( "x^2*h = 468<BR>\n" );
document.write( "Find h<BR>\n" );
document.write( "h = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=468%2Fx%5E2 ALIGN=MIDDLE  ALT=\"468%2Fx%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Area of the sides = x*h<BR>\n" );
document.write( "Substituting <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=468%2Fx%5E2 ALIGN=MIDDLE  ALT=\"468%2Fx%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > for h<BR>\n" );
document.write( "Area of the sides = x(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=468%2Fx%5E2 ALIGN=MIDDLE  ALT=\"468%2Fx%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=468%2Fx ALIGN=MIDDLE  ALT=\"468%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Cost of 4 sides = 2(4(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=468%2Fx ALIGN=MIDDLE  ALT=\"468%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" >)) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3744%2Fx ALIGN=MIDDLE  ALT=\"3744%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Cost of the bottom and the top = 1.50(2x^2) = 3x^2<BR>\n" );
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document.write( "Total cost = f(x)<BR>\n" );
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document.write( "f(x) = 3x^2 + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3744%2Fx ALIGN=MIDDLE  ALT=\"3744%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Use this equation to plot a graph y = f(x) = cost<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+200%2C+-10%2C+20%2C+-200%2C+1200%2C+3x%5E2%2B%283744%2Fx%29%29+ ALIGN=MIDDLE  ALT=\"+graph%28+300%2C+200%2C+-10%2C+20%2C+-200%2C+1200%2C+3x%5E2%2B%283744%2Fx%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "I graphed it on my TI83, and found the minimum:<BR>\n" );
document.write( "minimum cost at; x = 8.545 ft,<BR>\n" );
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document.write( " </SPAN>\n" );
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