document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1118294>Question 1118294</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the dimensions (radius and height) that give the minimum cost for producing cylindrically shaped aluminum cans with lids and a volume of 16pi in^3. How much would it cost to produce 100,000 cans if aluminum price is 0.03 cents/in^2? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #733573 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39618)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=733573\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Look for minimum AREA for the minimum cost.\r<BR>\n" );
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document.write( "h, height<BR>\n" );
document.write( "r, radius<BR>\n" );
document.write( "A, area\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28h%2Api%2Ar%5E2=16pi%2CA=2%2Api%2Ar%5E2%2Bh%2A2pi%2Ar%29 ALIGN=MIDDLE  ALT=\"system%28h%2Api%2Ar%5E2=16pi%2CA=2%2Api%2Ar%5E2%2Bh%2A2pi%2Ar%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=hr%5E2=16 ALIGN=MIDDLE  ALT=\"hr%5E2=16\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=16%2Fr%5E2 ALIGN=MIDDLE  ALT=\"h=16%2Fr%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=2pi%2Ar%5E2%2B%2816%2Fr%5E2%29%282pi%2Ar%29 ALIGN=MIDDLE  ALT=\"A=2pi%2Ar%5E2%2B%2816%2Fr%5E2%29%282pi%2Ar%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=2pi%2Ar%5E2%2B32pi%2Fr ALIGN=MIDDLE  ALT=\"A=2pi%2Ar%5E2%2B32pi%2Fr\"   DISABLED_style= \"max-width:90%; height:auto;\" >------------------(technology is showing minimum at about r=2)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=dA%2Fdr=4pi%2Ar%2B%2832pi%29%28-1%29%28r%5E%28-2%29%29 ALIGN=MIDDLE  ALT=\"dA%2Fdr=4pi%2Ar%2B%2832pi%29%28-1%29%28r%5E%28-2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=dA%2Fdr=4pi%2Ar-32pi%2Fr%5E2 ALIGN=MIDDLE  ALT=\"dA%2Fdr=4pi%2Ar-32pi%2Fr%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=common_denominator_r%5E2 ALIGN=MIDDLE  ALT=\"common_denominator_r%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=dA%2Fdr=%284pir%5E3-32pi%29%2Fr%5E2 ALIGN=MIDDLE  ALT=\"dA%2Fdr=%284pir%5E3-32pi%29%2Fr%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Need the NUMERATOR to be 0.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4pi%2Ar%5E3-32pi=0 ALIGN=MIDDLE  ALT=\"4pi%2Ar%5E3-32pi=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4pi%2Ar%5E3=32pi ALIGN=MIDDLE  ALT=\"4pi%2Ar%5E3=32pi\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%5E3=8 ALIGN=MIDDLE  ALT=\"r%5E3=8\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28r=2%29 ALIGN=MIDDLE  ALT=\"highlight%28r=2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "With this r value found for minimum A, the value for h, minimum A, can be evaluated, and also the corresponding cost. </SPAN>\n" );
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