document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=417894>Question 417894</A>: <I><SPAN STYLE=\"word-break: break-all;\"> An orchard contains 30 apple trees, each of which yields approximately 400 apples over the growing season. <BR>\n" );
document.write( "The owner plans to add more trees, but the guys at Texas A&M advise that because of crowding, each new tree will reduce the average yield per tree by about 10 apples over the growing season. <BR>\n" );
document.write( "How many trees should be added to maximize the total yield of apples, and what is the maximum yield? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #292519 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=292519\">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 trees to be 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;\" > = yield from orchard<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Y+=+400%2A%2830+%2B+x%29+-+10x%2A%28+30+%2B+x%29+ ALIGN=MIDDLE  ALT=\"Y+=+400%2A%2830+%2B+x%29+-+10x%2A%28+30+%2B+x%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+=+%28400+-+10x%29%2A%2830+%2B+x%29+ ALIGN=MIDDLE  ALT=\"Y+=+%28400+-+10x%29%2A%2830+%2B+x%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+=+12000+-+300x+%2B+400x+-+10x%5E2+ ALIGN=MIDDLE  ALT=\"+Y+=+12000+-+300x+%2B+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+100x+%2B+12000 ALIGN=MIDDLE  ALT=\"Y+=+-10x%5E2+%2B+100x+%2B+12000\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The maximum of a quadratic is at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-b%2F%282a%29+ ALIGN=MIDDLE  ALT=\"+-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=-b%2F%282a%29+=+-100%2F%28-20%29+ ALIGN=MIDDLE  ALT=\"-b%2F%282a%29+=+-100%2F%28-20%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-100%2F%28-20%29+=+5 ALIGN=MIDDLE  ALT=\"-100%2F%28-20%29+=+5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "5 trees should be added to maximize yield<BR>\n" );
document.write( "The yield, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Y ALIGN=MIDDLE  ALT=\"Y\"   DISABLED_style= \"max-width:90%; height:auto;\" >, is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Y+=+-10%2A5%5E2+%2B+100%2A5+%2B+12000 ALIGN=MIDDLE  ALT=\"Y+=+-10%2A5%5E2+%2B+100%2A5+%2B+12000\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Y+=+-250+%2B+500+%2B+12000 ALIGN=MIDDLE  ALT=\"Y+=+-250+%2B+500+%2B+12000\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Y+=+12250 ALIGN=MIDDLE  ALT=\"Y+=+12250\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Here's a plot:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+400%2C+400%2C+-20%2C+60%2C+-1000%2C+15000%2C+-10x%5E2+%2B+100x+%2B+12000%29+ ALIGN=MIDDLE  ALT=\"+graph%28+400%2C+400%2C+-20%2C+60%2C+-1000%2C+15000%2C+-10x%5E2+%2B+100x+%2B+12000%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );