document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=906174>Question 906174</A>: <I><SPAN STYLE=\"word-break: break-all;\"> An orchard contains 40 apple trees, each of which yields about 500 apples over the growing season. The owner plans to add more trees, but each new tree will reduce the average yield per tree by about 10 apples over the season. How many trees should be added to maximize the total yield of apples? What would be the maximum yield for the apple orchard for the season?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #549659 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=549659\">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=+x+ ALIGN=MIDDLE  ALT=\"+x+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = number of apple trees added<BR>\n" );
document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+ ALIGN=MIDDLE  ALT=\"+y+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = the yield for the orchard<BR>\n" );
document.write( "----------------<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=++%28+40+%2B+x+%29%2A%28+500+-+10x+%29+ ALIGN=MIDDLE  ALT=\"+y+=++%28+40+%2B+x+%29%2A%28+500+-+10x+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+20000+%2B+500x+-+400x+-+10x%5E2+ ALIGN=MIDDLE  ALT=\"+y+=+20000+%2B+500x+-+400x+-+10x%5E2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+-10x%5E2+%2B+900x+%2B+20000+ ALIGN=MIDDLE  ALT=\"+y+=+-10x%5E2+%2B+900x+%2B+20000+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-------------------------------<BR>\n" );
document.write( "Find <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5Bmax%5D+ ALIGN=MIDDLE  ALT=\"+x%5Bmax%5D+\"   DISABLED_style= \"max-width:90%; height:auto;\" > and then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y%5Bmax%5D+ ALIGN=MIDDLE  ALT=\"+y%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=+x%5Bmax%5D+=+-b%2F%282a%29+ ALIGN=MIDDLE  ALT=\"+x%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+=+-10+ ALIGN=MIDDLE  ALT=\"+a+=+-10+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+b+=+900+ ALIGN=MIDDLE  ALT=\"+b+=+900+\"   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=+x%5Bmax%5D+=+-900%2F%282%2A%28-10%29%29+ ALIGN=MIDDLE  ALT=\"+x%5Bmax%5D+=+-900%2F%282%2A%28-10%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+=+45+ ALIGN=MIDDLE  ALT=\"+x%5Bmax%5D+=+45+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y%5Bmax%5D+=+-10%2A45%5E2+%2B+900%2A45+%2B+20000+ ALIGN=MIDDLE  ALT=\"+y%5Bmax%5D+=+-10%2A45%5E2+%2B+900%2A45+%2B+20000+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y%5Bmax%5D+=+-20250+%2B+40500+%2B+20000+ ALIGN=MIDDLE  ALT=\"+y%5Bmax%5D+=+-20250+%2B+40500+%2B+20000+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y%5Bmax%5D+=+40250+ ALIGN=MIDDLE  ALT=\"+y%5Bmax%5D+=+40250+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-------------------<BR>\n" );
document.write( "45 more trees will maximize yield<BR>\n" );
document.write( "40,250 will be the maximum yield<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+-30%2C+150%2C+-4000%2C+45000%2C+-10x%5E2+%2B+900x+%2B+20000+%29+ ALIGN=MIDDLE  ALT=\"+graph%28+500%2C+500%2C+-30%2C+150%2C+-4000%2C+45000%2C+-10x%5E2+%2B+900x+%2B+20000+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "( note that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x=0+ ALIGN=MIDDLE  ALT=\"+x=0+\"   DISABLED_style= \"max-width:90%; height:auto;\" > doesn't mean no apples- it means no ADDITIONAL apples )\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " <BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );