document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1155851>Question 1155851</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Suppose a cylindrical storage tank is to contain V=16,000π cubic feet (about 400,000 gallons) is to be built into the ground to catch runoff water so it needs no top. Suppose, further, that the cost of the base of the tank is $10 per square foot and sides $8.64 per square foot. What dimensions will lead to minimal  -  cost tank? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #778556 by </B><A HREF=/tutors/aboutme.mpl?userid=josmiceli><B>josmiceli(19441)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josmiceli><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=josmiceli><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=778556\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+d+ ALIGN=MIDDLE  ALT=\"+d+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = the diameter of the base<BR>\n" );
document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+h+ ALIGN=MIDDLE  ALT=\"+h+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = the height of the tank<BR>\n" );
document.write( "-----------------------------------------<BR>\n" );
document.write( "The circumference, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+C+ ALIGN=MIDDLE  ALT=\"+C+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, of the base is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+C+=+pi%2Ad+ ALIGN=MIDDLE  ALT=\"+C+=+pi%2Ad+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The area, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+A%5Bb%5D+ ALIGN=MIDDLE  ALT=\"+A%5Bb%5D+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, of the base is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+A%5Bb%5D+=+pi%2A%28d%2F2%29%5E2+ ALIGN=MIDDLE  ALT=\"+A%5Bb%5D+=+pi%2A%28d%2F2%29%5E2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "----------------------------------------<BR>\n" );
document.write( "The volume, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+V+ ALIGN=MIDDLE  ALT=\"+V+\"   DISABLED_style= \"max-width:90%; height:auto;\" > is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+V+=+pi%2A%28+d%2F2+%29%5E2+%2A+h+ ALIGN=MIDDLE  ALT=\"+V+=+pi%2A%28+d%2F2+%29%5E2+%2A+h+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+16000%2Api+=+pi%2A%28+d%5E2%2F4+%29%2Ah+ ALIGN=MIDDLE  ALT=\"+16000%2Api+=+pi%2A%28+d%5E2%2F4+%29%2Ah+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+64000+=+d%5E2%2Ah+ ALIGN=MIDDLE  ALT=\"+64000+=+d%5E2%2Ah+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+h+=+64000+%2F+d%5E2+ ALIGN=MIDDLE  ALT=\"+h+=+64000+%2F+d%5E2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "--------------------------------------<BR>\n" );
document.write( "The area of the sides, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+A%5Bs%5D+ ALIGN=MIDDLE  ALT=\"+A%5Bs%5D+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+A%5Bs%5D+=+pi%2Ad%2A%28+64000+%2F+d%5E2+%29+ ALIGN=MIDDLE  ALT=\"+A%5Bs%5D+=+pi%2Ad%2A%28+64000+%2F+d%5E2+%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%5Bs%5D+=+%28+64000%2Api+%29+%2F+d+ ALIGN=MIDDLE  ALT=\"+A%5Bs%5D+=+%28+64000%2Api+%29+%2F+d+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "--------------------------------------<BR>\n" );
document.write( "The cost, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+C%5Bt%5D+ ALIGN=MIDDLE  ALT=\"+C%5Bt%5D+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, of the tank is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+C%5Bt%5D+=+8.64%2A%28%28+64000%2Api+%29%2Fd+%29+%2B+10%2A%28+pi%2Ad%5E2+%29+%2F+4+ ALIGN=MIDDLE  ALT=\"+C%5Bt%5D+=+8.64%2A%28%28+64000%2Api+%29%2Fd+%29+%2B+10%2A%28+pi%2Ad%5E2+%29+%2F+4+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+C%5Bt%5D+=+1737175.07+%2F+d+%2B+7.85398%2Ad%5E2+ ALIGN=MIDDLE  ALT=\"+C%5Bt%5D+=+1737175.07+%2F+d+%2B+7.85398%2Ad%5E2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The slope of this curve is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+C%5Btt%5D+=+-1737175.07+%2F+d%5E2+%2B+15.70796d+ ALIGN=MIDDLE  ALT=\"+C%5Btt%5D+=+-1737175.07+%2F+d%5E2+%2B+15.70796d+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Set slope = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+0+=+-1737175.07+%2F+d%5E2+%2B+15.70796d+ ALIGN=MIDDLE  ALT=\"+0+=+-1737175.07+%2F+d%5E2+%2B+15.70796d+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+1737175.07+%2F+d%5E2+=++15.70796d+ ALIGN=MIDDLE  ALT=\"+1737175.07+%2F+d%5E2+=++15.70796d+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+d%5E3+=++1737175.07+%2F+15.70796+ ALIGN=MIDDLE  ALT=\"+d%5E3+=++1737175.07+%2F+15.70796+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+d+=+120.21201+%2F+2.5044167+ ALIGN=MIDDLE  ALT=\"+d+=+120.21201+%2F+2.5044167+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+d+=+48.0000003+ ALIGN=MIDDLE  ALT=\"+d+=+48.0000003+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+d+=+48+ ALIGN=MIDDLE  ALT=\"+d+=+48+\"   DISABLED_style= \"max-width:90%; height:auto;\" > ft<BR>\n" );
document.write( "and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+h+=+64000+%2F+d%5E2%0D%0A%7B%7B%7B+h+=+64000+%2F+2304+ ALIGN=MIDDLE  ALT=\"+h+=+64000+%2F+d%5E2%0D%0A%7B%7B%7B+h+=+64000+%2F+2304+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+h+=+27.778+ ALIGN=MIDDLE  ALT=\"+h+=+27.778+\"   DISABLED_style= \"max-width:90%; height:auto;\" > ft<BR>\n" );
document.write( "------------------------------------<BR>\n" );
document.write( "The diameter for min cost is 48 ft<BR>\n" );
document.write( "The height for min cost is 27.778 ft<BR>\n" );
document.write( "-----------------------------------------------<BR>\n" );
document.write( "Here's the plot:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+500%2C+500%2C+-250%2C+250%2C+-100000%2C+350000%2C+1737175.07%2Fx+%2B+7.85398x%5E2+%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----------------------------<BR>\n" );
document.write( "The min cost is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+C%5Bt%5D+=+1737175.07+%2F+d+%2B+7.85398%2Ad%5E2+ ALIGN=MIDDLE  ALT=\"+C%5Bt%5D+=+1737175.07+%2F+d+%2B+7.85398%2Ad%5E2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+C%5Bt%5D+=+1737175.07+%2F+48+%2B+7.85398%2A48%5E2+ ALIGN=MIDDLE  ALT=\"+C%5Bt%5D+=+1737175.07+%2F+48+%2B+7.85398%2A48%5E2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+C%5Bt%5D+=+36191.15+%2B+18095.57+ ALIGN=MIDDLE  ALT=\"+C%5Bt%5D+=+36191.15+%2B+18095.57+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+C%5Bt%5D+=+54286.72+ ALIGN=MIDDLE  ALT=\"+C%5Bt%5D+=+54286.72+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "$54,286.72 looks close to min in the plot<BR>\n" );
document.write( "Get a 2nd opinion if needed<BR>\n" );
document.write( "and check my math\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );