document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=773758>Question 773758</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Randy is building a rectangular, fenced dog run beside his barn. He has a budget of $1050 for fencing and it costs him $8.75 per meter for the materials. He plans to use the side of the barn as one side of the fenced area. What are the dimensions of a dog run that maximizes the area Randy can enclose? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #471881 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=471881\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Randy is building a rectangular, fenced dog run beside his barn.<BR>\n" );
document.write( " He has a budget of $1050 for fencing and it costs him $8.75 per meter for the materials.<BR>\n" );
document.write( " He plans to use the side of the barn as one side of the fenced area.<BR>\n" );
document.write( " What are the dimensions of a dog run that maximizes the area Randy can enclose?<BR>\n" );
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document.write( "Find out how much fence he can get with $1050,<BR>\n" );
document.write( " this is the total distance of the three sides<BR>\n" );
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document.write( "1050/8.75 = 120 meters<BR>\n" );
document.write( "therefore <BR>\n" );
document.write( "L + 2W = 120<BR>\n" );
document.write( "L = (120-2W)<BR>\n" );
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document.write( "Area<BR>\n" );
document.write( "A = L*W<BR>\n" );
document.write( "Replace L with (120-2W)<BR>\n" );
document.write( "A = W(120-2W)<BR>\n" );
document.write( "A = -2W^2 + 120W; a quadratic equation<BR>\n" );
document.write( "We can find the max area by finding the axis of symmetry x = -b/(2a)<BR>\n" );
document.write( "In this equation we have<BR>\n" );
document.write( "W = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-120%29%2F%282%2A-2%29 ALIGN=MIDDLE  ALT=\"%28-120%29%2F%282%2A-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "W = 30 meters width for max area<BR>\n" );
document.write( "L = 120-2(30)<BR>\n" );
document.write( "L = 60 meters length for max area<BR>\n" );
document.write( "therefore the dimension: 60 by 30 meters, that would be 1800 sq/m<BR>\n" );
document.write( " </SPAN>\n" );
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