document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=864949>Question 864949</A>: <I><SPAN STYLE=\"word-break: break-all;\"> HI,<BR>\n" );
document.write( "A wire of length 40 inches is to be cut into two pieces, each of which will be used to form a circle. Suppose we will be charged $2 for each square inch of area enclosed by the first circle, and $1 for each inch in the second circle's circumference. Find the lengths of the two pieces of wire which will<BR>\n" );
document.write( "minimize the total cost. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #521410 by </B><A HREF=/tutors/aboutme.mpl?userid=Alan3354><B>Alan3354(69443)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Alan3354><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=Alan3354><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=521410\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A wire of length 40 inches is to be cut into two pieces, each of which will be used to form a circle. Suppose we will be charged $2 for each square inch of area enclosed by the first circle, and $1 for each inch in the second circle's circumference. Find the lengths of the two pieces of wire which will<BR>\n" );
document.write( "minimize the total cost.<BR>\n" );
document.write( "--------------<BR>\n" );
document.write( "C = length of wire in the 1st circle ($2 per sq inch)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C+=+2pi%2Ar ALIGN=MIDDLE  ALT=\"C+=+2pi%2Ar\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r+=+C%2F2pi ALIGN=MIDDLE  ALT=\"r+=+C%2F2pi\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Area+=+pi%2Ar%5E2+=+pi%2A%28C%5E2%2F4pi%5E2%29+=+C%5E2%2F4pi ALIGN=MIDDLE  ALT=\"Area+=+pi%2Ar%5E2+=+pi%2A%28C%5E2%2F4pi%5E2%29+=+C%5E2%2F4pi\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----<BR>\n" );
document.write( "--> $1/inch of 40 - C for the 2nd circle<BR>\n" );
document.write( "----<BR>\n" );
document.write( "Price = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2AC%5E2%2F4pi+%2B+40+-+C ALIGN=MIDDLE  ALT=\"2%2AC%5E2%2F4pi+%2B+40+-+C\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "P(C) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%5E2%2F2pi+-+C+%2B+40 ALIGN=MIDDLE  ALT=\"C%5E2%2F2pi+-+C+%2B+40\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "P'(C) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%2Fpi+-+1+=+0 ALIGN=MIDDLE  ALT=\"C%2Fpi+-+1+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "C = pi inches for the 1st circle<BR>\n" );
document.write( "40 - pi inches for the 2nd </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );