document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=960240>Question 960240</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A shoe store sells a new model of athletic shoe for $90. On average, the store sells 45 pairs of these shoes each week. Jason, the sales manager, estimates that he will sell 4 additional pairs of shoes each week for every $5 reduction in the price.\r<BR>\n" );
document.write( "\n" );
document.write( "Find the following:<BR>\n" );
document.write( "1.) A quadratic function modeling the store's average weekly revenue from the sales of these shoes as related to reduction in price.<BR>\n" );
document.write( "2.) The range of prices which would allow the store to maintain or increase its current weekly revenue from these shoes.<BR>\n" );
document.write( "3.) The maximum amount by which the store can increase its revenue from these shoes each week. Round off to the nearest whole dollar. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #586832 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=586832\">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=+R+ ALIGN=MIDDLE  ALT=\"+R+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = average weekly revenue<BR>\n" );
document.write( "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;\" > = number of $5 reductions in the price of shoes<BR>\n" );
document.write( "--------------------------<BR>\n" );
document.write( "(1)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+R+=+%28+45+%2B+4n+%29%2A%28+90+-+5n+%29+ ALIGN=MIDDLE  ALT=\"+R+=+%28+45+%2B+4n+%29%2A%28+90+-+5n+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+R+=+4050+%2B+360n+-+225n+-+20n%5E2+ ALIGN=MIDDLE  ALT=\"+R+=+4050+%2B+360n+-+225n+-+20n%5E2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+R+=+-20n%5E2+%2B+135n+%2B+4050+ ALIGN=MIDDLE  ALT=\"+R+=+-20n%5E2+%2B+135n+%2B+4050+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-------------------------------<BR>\n" );
document.write( "(2)<BR>\n" );
document.write( "Current weekly revenue is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+45%2A90+=+4050+ ALIGN=MIDDLE  ALT=\"+45%2A90+=+4050+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "I need values for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+n+ ALIGN=MIDDLE  ALT=\"+n+\"   DISABLED_style= \"max-width:90%; height:auto;\" > for which <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+R+%3E=+4050+ ALIGN=MIDDLE  ALT=\"+R+%3E=+4050+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+4050+=+-20n%5E2+%2B+135n+%2B+4050+ ALIGN=MIDDLE  ALT=\"+4050+=+-20n%5E2+%2B+135n+%2B+4050+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+0+=+-20n%5E2+%2B+135n+ ALIGN=MIDDLE  ALT=\"+0+=+-20n%5E2+%2B+135n+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+0+=+5n%2A%28+-4n+%2B+27+%29+ ALIGN=MIDDLE  ALT=\"+0+=+5n%2A%28+-4n+%2B+27+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The solutions are:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+n+=+0+ ALIGN=MIDDLE  ALT=\"+n+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-4n+%2B+27+=+0+ ALIGN=MIDDLE  ALT=\"+-4n+%2B+27+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+4n+=+27+ ALIGN=MIDDLE  ALT=\"+4n+=+27+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+n+=+6.75+ ALIGN=MIDDLE  ALT=\"+n+=+6.75+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "------------------<BR>\n" );
document.write( "The price per shoe when <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+n+=+6.75+ ALIGN=MIDDLE  ALT=\"+n+=+6.75+\"   DISABLED_style= \"max-width:90%; height:auto;\" > is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+90+-+5n+=+90+-+5%2A6.75+ ALIGN=MIDDLE  ALT=\"+90+-+5n+=+90+-+5%2A6.75+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+90+-+5n+=+90+-+33.75+ ALIGN=MIDDLE  ALT=\"+90+-+5n+=+90+-+33.75+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+90+-+5n+=+56.25+ ALIGN=MIDDLE  ALT=\"+90+-+5n+=+56.25+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "----------------------<BR>\n" );
document.write( "The range of prices to maintain or increase is<BR>\n" );
document.write( "$56.25 to $90<BR>\n" );
document.write( "---------------<BR>\n" );
document.write( "check:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+R+=+%28+45+%2B+4%2A6.75+%29%2A%28+90+-+5%2A6.75+%29+ ALIGN=MIDDLE  ALT=\"+R+=+%28+45+%2B+4%2A6.75+%29%2A%28+90+-+5%2A6.75+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+R+=+%28+45+%2B+27+%29%2A56.25+ ALIGN=MIDDLE  ALT=\"+R+=+%28+45+%2B+27+%29%2A56.25+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+R+=+72%2A56.25+ ALIGN=MIDDLE  ALT=\"+R+=+72%2A56.25+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+R+=+4050+ ALIGN=MIDDLE  ALT=\"+R+=+4050+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "----------------------<BR>\n" );
document.write( "(3)<BR>\n" );
document.write( "I want the maximum possible <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+R+ ALIGN=MIDDLE  ALT=\"+R+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "This is where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+n%5Bmax%5D+=+-b%2F%282a%29+ ALIGN=MIDDLE  ALT=\"+n%5Bmax%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+=+-20+ ALIGN=MIDDLE  ALT=\"+a+=+-20+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+b+=+135+ ALIGN=MIDDLE  ALT=\"+b+=+135+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+n%5Bmax%5D+=+-135+%2F+%28+2%2A%28-20%29%29+ ALIGN=MIDDLE  ALT=\"+n%5Bmax%5D+=+-135+%2F+%28+2%2A%28-20%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%5Bmax%5D+=+3.375+ ALIGN=MIDDLE  ALT=\"+n%5Bmax%5D+=+3.375+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Plug this back in and find <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+R%5Bmax%5D+ ALIGN=MIDDLE  ALT=\"+R%5Bmax%5D+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "----------------------------------<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+R%5Bmax%5D+=+%28+45+%2B+4%2A3.375+%29%2A%28+90+-+5%2A3.375+%29+ ALIGN=MIDDLE  ALT=\"+R%5Bmax%5D+=+%28+45+%2B+4%2A3.375+%29%2A%28+90+-+5%2A3.375+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+R%5Bmax%5D+=+%28+45+%2B+13.5+%29%2A%28+90+-+16.875+%29+ ALIGN=MIDDLE  ALT=\"+R%5Bmax%5D+=+%28+45+%2B+13.5+%29%2A%28+90+-+16.875+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+R%5Bmax%5D+=+58.5%2A73.125+ ALIGN=MIDDLE  ALT=\"+R%5Bmax%5D+=+58.5%2A73.125+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+R%5Bmax%5D+=+4277.81+ ALIGN=MIDDLE  ALT=\"+R%5Bmax%5D+=+4277.81+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The maximum amount by which the store can <BR>\n" );
document.write( "increase its revenue from these shoes each week is<BR>\n" );
document.write( "$4,277.81<BR>\n" );
document.write( "---------------------<BR>\n" );
document.write( "Here's the plot of the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+R+ ALIGN=MIDDLE  ALT=\"+R+\"   DISABLED_style= \"max-width:90%; height:auto;\" > function:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+500%2C+500%2C+-4%2C+20%2C+-200%2C+4700%2C+-20x%5E2+%2B+135x+%2B+4050+%29+ ALIGN=MIDDLE  ALT=\"+graph%28+500%2C+500%2C+-4%2C+20%2C+-200%2C+4700%2C+-20x%5E2+%2B+135x+%2B+4050+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( " \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );