document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1043672>Question 1043672</A>: <I><SPAN STYLE=\"word-break: break-all;\"> An orange grower finds that she gets an average yield of 40 bushels per tree when she plants 20 trees on an acre of ground. Each time she adds a tree to an acre, the yield per tree decreases by 1 bushel, due to congestion. How many trees per acre should she plant for 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 #658828 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=658828\">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 trees added to 1 acre<BR>\n" );
document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+Y%28n%29+ ALIGN=MIDDLE  ALT=\"+Y%28n%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = the yield in bushels/acre<BR>\n" );
document.write( "------------------------------------------------<BR>\n" );
document.write( "[ yield in bushels/acre ] = [ bushels/tree ] x [ trees/acre ]<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+Y%28n%29+=+%28+40+-+n+%29%2A%28+20+%2B+n+%29+ ALIGN=MIDDLE  ALT=\"+Y%28n%29+=+%28+40+-+n+%29%2A%28+20+%2B+n+%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%28n%29+=+800+-+20n+%2B+40n+-+n%5E2+ ALIGN=MIDDLE  ALT=\"+Y%28n%29+=+800+-+20n+%2B+40n+-+n%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%28n%29+=+-n%5E2+%2B+20n+%2B+800+ ALIGN=MIDDLE  ALT=\"+Y%28n%29+=+-n%5E2+%2B+20n+%2B+800+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The n-value of the vertex ( which is a peak ) <BR>\n" );
document.write( "is given by the formula:<BR>\n" );
document.write( "<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;\" > when the equation has the form:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+Y%28n%29+=+a%2An%5E2+%2B+b%2An+%2B+c+ ALIGN=MIDDLE  ALT=\"+Y%28n%29+=+a%2An%5E2+%2B+b%2An+%2B+c+\"   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+=+%28-20%29%2F%282%2A-1%29+ ALIGN=MIDDLE  ALT=\"+n%5Bmax%5D+=+%28-20%29%2F%282%2A-1%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+=+10+ ALIGN=MIDDLE  ALT=\"+n%5Bmax%5D+=+10+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-------------------------<BR>\n" );
document.write( "The grower started with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+20+ ALIGN=MIDDLE  ALT=\"+20+\"   DISABLED_style= \"max-width:90%; height:auto;\" > tree/acre and adds <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+10+ ALIGN=MIDDLE  ALT=\"+10+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "more for max yield, so she should plant:<BR>\n" );
document.write( "30 trees/acre<BR>\n" );
document.write( "----------------------------------<BR>\n" );
document.write( "check answer:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+Y%2810%29+=+%28+40+-+10+%29%2A%28+20+%2B+10+%29+ ALIGN=MIDDLE  ALT=\"+Y%2810%29+=+%28+40+-+10+%29%2A%28+20+%2B+10+%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%2810%29+=+30%2A30+ ALIGN=MIDDLE  ALT=\"+Y%2810%29+=+30%2A30+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+Y%2810%29+=+900+ ALIGN=MIDDLE  ALT=\"+Y%2810%29+=+900+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Maximum yield is 900 bushels/acre<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+600%2C+-5%2C+50%2C+-200%2C+1200%2C+-x%5E2+%2B+20x+%2B+800+%29+ ALIGN=MIDDLE  ALT=\"+graph%28+600%2C+600%2C+-5%2C+50%2C+-200%2C+1200%2C+-x%5E2+%2B+20x+%2B+800+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );