document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=617719>Question 617719</A>: <I><SPAN STYLE=\"word-break: break-all;\"> There is one homework question I am stuck on and cannot understand what I am doing wrong. We are worknig on graph shifts. The question is,<BR>\n" );
document.write( "At a certain vineyard it is found that each grape vine produces about 10 pounds of grapes in a season when about 800 vines are planted per acre. For each additional vine that is planted, the production of each vine decreases by about 1 percent. So the number of pounds of grapes produced per acre is modeled byA(n)=(800+n)(10-0.01n) where n is the number of additional vines planted Find the number of vines that should be planted to maximize grape production.\r<BR>\n" );
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document.write( "I have come up with A(n)= -0.01(n+100)^2+8100 and put in the answer of 100, 8100, 800 and many others and nothing is right. I don't understand what I am doing wrong. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #388516 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=388516\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
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document.write( "Not sure how you got to\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ -0.01(n\ +\ 100)^2\ +\ 8100\">\r<BR>\n" );
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document.write( "But it is wrong.\r<BR>\n" );
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document.write( "Start with\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ A(n)\ =\ (800\ +\ n)(10\ -\ 0.01n)\">\r<BR>\n" );
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document.write( "And FOIL it:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ A(n)\ =\ 8000\ -\ 2n\ +\ 10n\ -\ 0.01n^2\">\r<BR>\n" );
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document.write( "Collect terms then go to standard quadratic form:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ A(n)\ =\ -0.01n^2\ +\ 2n\ +\ 8000\">\r<BR>\n" );
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document.write( "Note:  If you multiply yours out and collect terms you are only off by the sign on the first degree term, but it is nevertheless incorrect.\r<BR>\n" );
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document.write( "Note that this is a polynomial function of the form <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \rho(x)\ =\ ax^2\ +\ bx\ +\ c\"> the graph of which is a parabola.  Since it has a negative lead coefficient, the parabola opens downward.  Therefore, the vertex of the parabola is the maximum of the function.  Recall that the <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\">-coordinate of the vertex of <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \rho(x)\ =\ ax^2\ +\ bx\ +\ c\"> is given by <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE x_v\ =\ \frac{-b}{2a}\">\r<BR>\n" );
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document.write( "So calculate <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \frac{-2}{2(-0.01)}\"> to find the number of vines <i><b>in excess of 800</b></i> that should be planted to maximize the yield.  Don't forget to add the answer to 800 to get the answer to the question posed by the problem.\r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi}\ +\ 1\ =\ 0\"><BR>\n" );
document.write( "My calculator said it, I believe it, that settles it<BR>\n" );
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