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 #292509 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=292509\">put this solution on YOUR website!</A><BR><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" );
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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" );
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document.write( "How many trees should be added to maximize the total yield of apples, and what is the maximum yield? <BR>\n" );
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document.write( "Total yield = [(30+x) trees][(400-10x)apples]<BR>\n" );
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document.write( "TY = 30*400 - 300x+400x - 10x^2<BR>\n" );
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document.write( "TY = -x^2+10x+1200<BR>\n" );
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document.write( "Max occurs when x = -b/(2a) = -10/(2*-1) = 5 trees (# of trees to add)<BR>\n" );
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document.write( "TY(5) = -5^2+10*5 + 1200 = 1225<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "stan H.<BR>\n" );
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document.write( " \r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );