document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=4788>Question 4788</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the number of units that produces a maximum revenue for \r<BR>\n" );
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document.write( "R = 800x - 0.01x^2\r<BR>\n" );
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document.write( "where R is the total revenue (in dollars) for a cosmetics company and x is the number of units produced. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #2287 by </B><A HREF=/tutors/aboutme.mpl?userid=rapaljer><B>rapaljer(4671)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rapaljer><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=rapaljer><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=2287\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> This equation represents a parabola that opens downward, so the vertex of the parabola will be the point at which maximum revenue occurs.  As in the last question that I posted, the vertex occurs at x = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-b%29+%2F%282a%29 ALIGN=MIDDLE  ALT=\"%28-b%29+%2F%282a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, where a = coefficient of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2 ALIGN=MIDDLE  ALT=\"x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and b = coefficient of x.  In this case a= -0.01 and b= 800.  \r<BR>\n" );
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document.write( "Maximum revenue occurs at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%28-b%29%2F%282a%29+=+%28-800%29%2F%282%2A%28-0.01%29%29=+800%2F0.02+ ALIGN=MIDDLE  ALT=\"x=%28-b%29%2F%282a%29+=+%28-800%29%2F%282%2A%28-0.01%29%29=+800%2F0.02+\"   DISABLED_style= \"max-width:90%; height:auto;\" >= 40,000 units.\r<BR>\n" );
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document.write( "To find the maximum revenue, substitute x= 40,000 into the original equation for R and it turns out that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R+=+800%2A40000+-+0.01%2A40000%5E2 ALIGN=MIDDLE  ALT=\"R+=+800%2A40000+-+0.01%2A40000%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > or $16,000,000.  \r<BR>\n" );
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document.write( "R^2 at SCC  </SPAN>\n" );
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