document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=465289>Question 465289</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me to solve this problem. The demand equation for a manufacturer's product is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p=%2880-q%29%2F4 ALIGN=MIDDLE  ALT=\"p=%2880-q%29%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >, 0 &#8804; q &#8804; 80 , where q is the number of units and p is the price  per unit. At what value of q will there be the maximum revenue? What is the maximum revenue? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #318843 by </B><A HREF=/tutors/aboutme.mpl?userid=richard1234><B>richard1234(7193)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=richard1234><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=richard1234><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=318843\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Assuming all the economic demand is met and q items are sold, the amount of revenue will be pq, or\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE q(\frac{80-q}{4}) = -\frac{q^2}{4} + 20q\">\r<BR>\n" );
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document.write( "This is a quadratic opening downward, so the maximum revenue occurs at the \"vertex\" or at q = -20/(-1/2) = 40 (also halfway between 0 and 80). The revenue will be\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE -\frac{40^2}{4} + 20(40) = 400\"> </SPAN>\n" );
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