document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=273573>Question 273573</A>: <I><SPAN STYLE=\"word-break: break-all;\"> We want to build a 600 square metre rectangular enclosure, three sides of which<BR>\n" );
document.write( "will be built of wooden fencing at a cost of $15 per metre. The remaining side<BR>\n" );
document.write( "will be made of cement blocks at $30 per metre. How will we set the dimensions<BR>\n" );
document.write( "of the enclosure in order to minimize the cost of materials? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #199994 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=199994\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> We want to build a 600 square metre rectangular enclosure,<BR>\n" );
document.write( " three sides of which<BR>\n" );
document.write( "will be built of wooden fencing at a cost of $15 per metre.<BR>\n" );
document.write( " The remaining side will be made of cement blocks at $30 per metre.<BR>\n" );
document.write( " How will we set the dimensions of the enclosure in order to minimize the cost of materials?<BR>\n" );
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document.write( "Interesting problem<BR>\n" );
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document.write( "Area:<BR>\n" );
document.write( "L * W = 600<BR>\n" );
document.write( "L = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=600%2FW ALIGN=MIDDLE  ALT=\"600%2FW\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "The wooden fencing cost<BR>\n" );
document.write( "15(2L + W)<BR>\n" );
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document.write( "The cement block cost<BR>\n" );
document.write( "30W<BR>\n" );
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document.write( "Total cost <BR>\n" );
document.write( "C = 15(2L + W) + 30W<BR>\n" );
document.write( "C = 30L + 15W + 30w<BR>\n" );
document.write( "C = 30L + 45W<BR>\n" );
document.write( "Replace L with 600/W<BR>\n" );
document.write( "C = 30(600/W) + 45W<BR>\n" );
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document.write( "C = 45W + 18000/W<BR>\n" );
document.write( "Graph this equation<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+200%2C+-10%2C+50%2C+-1000%2C+5000%2C+45x%2B18000%2Fx%29+ ALIGN=MIDDLE  ALT=\"+graph%28+300%2C+200%2C+-10%2C+50%2C+-1000%2C+5000%2C+45x%2B18000%2Fx%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Cost is the vertical y axis and width is the x <BR>\n" );
document.write( "Minimum cost occurs when x = 20<BR>\n" );
document.write( "So we can say, Make the width 20 meters and the Length 30 meters (30*20=600)<BR>\n" );
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document.write( "What is the min cost:<BR>\n" );
document.write( "15(2(30) + 20) + 30(20) = <BR>\n" );
document.write( "15(80) + 600 =  $18,000<BR>\n" );
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document.write( "You can prove this to yourself. Try other dimensions like L=25 W=24 (nearly a square)<BR>\n" );
document.write( "15(50 + 24) + 30(24) = $1830, slightly more <BR>\n" );
document.write( "  </SPAN>\n" );
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