document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=767975>Question 767975</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Demand Equation The price (in dollars) and the quantity x sold of a certain product obey the demand equation p= -1/10x+150, 0&#8804;x&#8804;1500\r<BR>\n" );
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document.write( "Revenue is x*p.<BR>\n" );
document.write( "(a) Express the revenue R as a function of x.<BR>\n" );
document.write( "(b) What quantity x maximizes revenue? What is the maximum revenue?\r<BR>\n" );
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document.write( "***PLEASE SHOW STEPS!!<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #467983 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=467983\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=++p=+%28-1%2F10%29%2Ax%2B150+ ALIGN=MIDDLE  ALT=\"++p=+%28-1%2F10%29%2Ax%2B150+\"   DISABLED_style= \"max-width:90%; height:auto;\" >,  0&#8804;x&#8804;1500 <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+R+=+p%2Ax+ ALIGN=MIDDLE  ALT=\"+R+=+p%2Ax+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+R+=+%28+%28-1%2F10%29%2Ax+%2B+150+%29%2Ax+ ALIGN=MIDDLE  ALT=\"+R+=+%28+%28-1%2F10%29%2Ax+%2B+150+%29%2Ax+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+R+=+%28+-1%2F10+%29%2Ax%5E2+%2B+150x+ ALIGN=MIDDLE  ALT=\"+R+=+%28+-1%2F10+%29%2Ax%5E2+%2B+150x+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "This is a parabola with a maximum since<BR>\n" );
document.write( "the coefficient of the <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;\" > term is minus.<BR>\n" );
document.write( "Compare the equation with the general form:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+ax%5E2+%2B+b%2Ax+%2B+c+ ALIGN=MIDDLE  ALT=\"+y+=+ax%5E2+%2B+b%2Ax+%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=+a+=+-1%2F10+ ALIGN=MIDDLE  ALT=\"+a+=+-1%2F10+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+b+=+150+ ALIGN=MIDDLE  ALT=\"+b+=+150+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+c+=+0+ ALIGN=MIDDLE  ALT=\"+c+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----------<BR>\n" );
document.write( "The x-coordinate of the maximum is at <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-b%2F%282a%29+=+-150+%2F+%28+2%2A%28-1%2F10%29%29+ ALIGN=MIDDLE  ALT=\"+-b%2F%282a%29+=+-150+%2F+%28+2%2A%28-1%2F10%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-b%2F%282a%29+=+150+%2F+%281%2F5%29+ ALIGN=MIDDLE  ALT=\"+-b%2F%282a%29+=+150+%2F+%281%2F5%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-b%2F%282a%29+=+750+ ALIGN=MIDDLE  ALT=\"+-b%2F%282a%29+=+750+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "This is the value of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > that maximizes revenue<BR>\n" );
document.write( "Plug this back into the equation<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+R%5Bmax%5D+=+%28+-1%2F10+%29%2Ax%5E2+%2B+150x+ ALIGN=MIDDLE  ALT=\"+R%5Bmax%5D+=+%28+-1%2F10+%29%2Ax%5E2+%2B+150x+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+R%5Bmax%5D+=+%28+-1%2F10+%29%2A750%5E2+%2B+150%2A750+ ALIGN=MIDDLE  ALT=\"+R%5Bmax%5D+=+%28+-1%2F10+%29%2A750%5E2+%2B+150%2A750+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+R%5Bmax%5D+=+-562500%2F10+%2B+112500+ ALIGN=MIDDLE  ALT=\"+R%5Bmax%5D+=+-562500%2F10+%2B+112500+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+R%5Bmax%5D+=+-56250+%2B+112500+ ALIGN=MIDDLE  ALT=\"+R%5Bmax%5D+=+-56250+%2B+112500+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+R%5Bmax%5D+=+56250+ ALIGN=MIDDLE  ALT=\"+R%5Bmax%5D+=+56250+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The maximum revenue is $56,250\r<BR>\n" );
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