document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1060581>Question 1060581</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Jack & Jill charge $20 for a custom painted water pail. They currently sell 80 water pails a month. They estimate that for each $1 decrease in the cost of the pails, they could sell 15 more pails a month. What price will maximize Jack & Jill's income? If they charges this price, how much income should they expect? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #675502 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=675502\">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=+n+ ALIGN=MIDDLE  ALT=\"+n+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = the number of $1 decreases in price<BR>\n" );
document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+I+ ALIGN=MIDDLE  ALT=\"+I+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = the total income from sales of water pails<BR>\n" );
document.write( "-------------------------------<BR>\n" );
document.write( "[ income ] = [ price per pail ] x [ number of pails sold ]<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+I+=+%28+20+-+1%2An+%29%2A%28+80+%2B+15n+%29+ ALIGN=MIDDLE  ALT=\"+I+=+%28+20+-+1%2An+%29%2A%28+80+%2B+15n+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+I+=+1600+-+80n+%2B+300n+-+15n%5E2+ ALIGN=MIDDLE  ALT=\"+I+=+1600+-+80n+%2B+300n+-+15n%5E2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+I+=+-15n%5E2+%2B+220n+%2B+1600+ ALIGN=MIDDLE  ALT=\"+I+=+-15n%5E2+%2B+220n+%2B+1600+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The n-value of the vertex ( max in this case ) is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+n%5Bv%5D+=+-b%2F%282a%29+ ALIGN=MIDDLE  ALT=\"+n%5Bv%5D+=+-b%2F%282a%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+=+-15+ ALIGN=MIDDLE  ALT=\"+a+=+-15+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+b+=+220+ ALIGN=MIDDLE  ALT=\"+b+=+220+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+n%5Bv%5D+=+-220%2F%28+2%2A%28-15%29+%29+ ALIGN=MIDDLE  ALT=\"+n%5Bv%5D+=+-220%2F%28+2%2A%28-15%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=+n%5Bv%5D+=+7.333+ ALIGN=MIDDLE  ALT=\"+n%5Bv%5D+=+7.333+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----------------------------<BR>\n" );
document.write( "Going back to original equation:<BR>\n" );
document.write( "[ price/pail ] = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+20+-+n+ ALIGN=MIDDLE  ALT=\"+20+-+n+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The price that maximizes income is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+20+-+7.333+=+12.333+ ALIGN=MIDDLE  ALT=\"+20+-+7.333+=+12.333+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "$12.33<BR>\n" );
document.write( "-----------------------------<BR>\n" );
document.write( "The max income at this price is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+I+=+-15n%5E2+%2B+220n+%2B+1600+ ALIGN=MIDDLE  ALT=\"+I+=+-15n%5E2+%2B+220n+%2B+1600+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+I%5Bmax%5D+=+-15%2A7.333%5E2+%2B+220%2A7.333+%2B+1600+ ALIGN=MIDDLE  ALT=\"+I%5Bmax%5D+=+-15%2A7.333%5E2+%2B+220%2A7.333+%2B+1600+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+I%5Bmax%5D+=+-806.593+%2B+1613.26+%2B+1600+ ALIGN=MIDDLE  ALT=\"+I%5Bmax%5D+=+-806.593+%2B+1613.26+%2B+1600+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+I%5Bmax%5D+=+2406.67+ ALIGN=MIDDLE  ALT=\"+I%5Bmax%5D+=+2406.67+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "$2,406.67 <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+600%2C+400%2C+-2%2C+25%2C+-300%2C+2600%2C+-15x%5E2+%2B+220x+%2B+1600+%29+ ALIGN=MIDDLE  ALT=\"+graph%28+600%2C+400%2C+-2%2C+25%2C+-300%2C+2600%2C+-15x%5E2+%2B+220x+%2B+1600+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );