document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=194959>Question 194959</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The owner of a sidewalk expresso stand that the weekly profit for their business is a function of the price they charge per cup. If x equals the price(in dollars) of one cup, the weekly profit is given by P(x) = -2900x^2+7250x -2900.\r<BR>\n" );
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document.write( "Approximate the maximum profit and the price per cup that produces that profit </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #149295 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=149295\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28x%29+=+-2900x%5E2+%2B+7250x+-+2900 ALIGN=MIDDLE  ALT=\"P%28x%29+=+-2900x%5E2+%2B+7250x+-+2900\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "When an equation is of the form<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ax%5E2+%2B+bx+%2B+c ALIGN=MIDDLE  ALT=\"ax%5E2+%2B+bx+%2B+c\"   DISABLED_style= \"max-width:90%; height:auto;\" >, the max or min<BR>\n" );
document.write( "occurs where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-b%2F%282a%29 ALIGN=MIDDLE  ALT=\"x+=+-b%2F%282a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "In this case,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+=+-2900 ALIGN=MIDDLE  ALT=\"a+=+-2900\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b+=+7250 ALIGN=MIDDLE  ALT=\"b+=+7250\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The maximum (in this case) occurs at<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5Bmax%5D+=+%28-7250%29+%2F+%282%2A%28-2900%29%29 ALIGN=MIDDLE  ALT=\"x%5Bmax%5D+=+%28-7250%29+%2F+%282%2A%28-2900%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5Bmax%5D+=+%28-7250%29+%2F+-5800 ALIGN=MIDDLE  ALT=\"x%5Bmax%5D+=+%28-7250%29+%2F+-5800\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5Bmax%5D+=+5%2F4 ALIGN=MIDDLE  ALT=\"x%5Bmax%5D+=+5%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The price per cup for maximum profit is $1.25<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28max%29+=+-2900x%5E2+%2B+7250x+-+2900 ALIGN=MIDDLE  ALT=\"P%28max%29+=+-2900x%5E2+%2B+7250x+-+2900\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28max%29+=+-2900%2A%285%2F4%29%5E2+%2B+7250%2A%285%2F4%29+-+2900 ALIGN=MIDDLE  ALT=\"P%28max%29+=+-2900%2A%285%2F4%29%5E2+%2B+7250%2A%285%2F4%29+-+2900\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28max%29+=+-4531.25+%2B+9062.5+-+2900 ALIGN=MIDDLE  ALT=\"P%28max%29+=+-4531.25+%2B+9062.5+-+2900\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%5Bmax%5D+=+1631.25 ALIGN=MIDDLE  ALT=\"P%5Bmax%5D+=+1631.25\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The maximum profit is $1631.25<BR>\n" );
document.write( "To check this answer, both $1.24 per cup<BR>\n" );
document.write( "and $1.26 per cup should give a little<BR>\n" );
document.write( "less profit.<BR>\n" );
document.write( "For $1.26/cup, I get $1630.96 </SPAN>\n" );
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