document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=60986>Question 60986</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Sharon's revenue \"R\" (in dollars) on the sale of \"x\" fruitcakes is determined by the formula R=50x-x^2. Her cost in \"C\" (dollars) for producing the x fruitcakes is given by the formula C=2x+40. For what values of x is Sharon's profit positive? (Profit=revenue-cost)  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #41902 by </B><A HREF=/tutors/aboutme.mpl?userid=Nate><B>Nate(3500)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Nate><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=41902\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> When your profit is zero, you receive as much money as you spent. So you want a profit greater than zero.<BR>\n" );
document.write( "Profit > 0<BR>\n" );
document.write( "Revenue - Cost > 0<BR>\n" );
document.write( "50x - x^2 - 2x - 40 > 0<BR>\n" );
document.write( "-x^2 + 48x - 40 > 0<BR>\n" );
document.write( "<TABLE  BORDER=1>\n" );
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document.write( " <TR><TD  ALIGN=MIDDLE>Solved by <A  rel=nofollow HREF=http://wiki.algebra.com/index.php/Tutoring_-_pluggable_solvers>pluggable</A> solver: <A  rel=nofollow HREF=quadratic.solver>SOLVE quadratic equation with variable</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT>Quadratic equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ax%5E2%2Bbx%2Bc=0 ALIGN=MIDDLE  ALT=\"ax%5E2%2Bbx%2Bc=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > (in our case <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1x%5E2%2B48x%2B-40+=+0 ALIGN=MIDDLE  ALT=\"-1x%5E2%2B48x%2B-40+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >) has the following solutons:<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  For these solutions to exist, the <U>discriminant</U> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac ALIGN=MIDDLE  ALT=\"b%5E2-4ac\"   DISABLED_style= \"max-width:90%; height:auto;\" > should not be a negative number.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  First, we need to compute the discriminant <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac ALIGN=MIDDLE  ALT=\"b%5E2-4ac\"   DISABLED_style= \"max-width:90%; height:auto;\" >: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac=%2848%29%5E2-4%2A-1%2A-40=2144 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%2848%29%5E2-4%2A-1%2A-40=2144\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=2144 is greater than zero. That means that there are two solutions: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5B12%5D+=+%28-48%2B-sqrt%28+2144+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28-48%2B-sqrt%28+2144+%29%29%2F2%5Ca\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D+=+%28-%2848%29%2Bsqrt%28+2144+%29%29%2F2%5C-1+=+0.848326194419549 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%2848%29%2Bsqrt%28+2144+%29%29%2F2%5C-1+=+0.848326194419549\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B2%5D+=+%28-%2848%29-sqrt%28+2144+%29%29%2F2%5C-1+=+47.1516738055805 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%2848%29-sqrt%28+2144+%29%29%2F2%5C-1+=+47.1516738055805\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <BR>\n" );
document.write( "    Quadratic expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1x%5E2%2B48x%2B-40 ALIGN=MIDDLE  ALT=\"-1x%5E2%2B48x%2B-40\"   DISABLED_style= \"max-width:90%; height:auto;\" > can be factored:<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1x%5E2%2B48x%2B-40+=+-1%28x-0.848326194419549%29%2A%28x-47.1516738055805%29 ALIGN=MIDDLE  ALT=\"-1x%5E2%2B48x%2B-40+=+-1%28x-0.848326194419549%29%2A%28x-47.1516738055805%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 0.848326194419549, 47.1516738055805.\n" );
document.write( "Here's your graph:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-1%2Ax%5E2%2B48%2Ax%2B-40+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-1%2Ax%5E2%2B48%2Ax%2B-40+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
document.write( "</TABLE><BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2848+-+sqrt%2848%5E2+-+160%29%29%2F2+%3C+x+%3C+%2848+%2B+sqrt%2848%5E2+-+160%29%29%2F2 ALIGN=MIDDLE  ALT=\"%2848+-+sqrt%2848%5E2+-+160%29%29%2F2+%3C+x+%3C+%2848+%2B+sqrt%2848%5E2+-+160%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );