document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=763065>Question 763065</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The profit, P, of a video company in thousands of dollars, is given by <BR>\n" );
document.write( "P = -5x^2 + 550x -5000, where x is the amount spent on advertising in thousands of dollars.<BR>\n" );
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document.write( " Determine the amount spent on advertising that will result in a profit of $0.In other words, you will determine the amount that must be spent on advertising in order for the company to “ break even.” </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #464539 by </B><A HREF=/tutors/aboutme.mpl?userid=ramkikk66><B>ramkikk66(644)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ramkikk66><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=464539\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> P = -5*x^2 + 550*x - 5000\r<BR>\n" );
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document.write( "When P = 0\r<BR>\n" );
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document.write( "-5*x^2 + 550*x - 5000 = 0\r<BR>\n" );
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document.write( "Dividing by -5,\r<BR>\n" );
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document.write( "x^2 - 110x + 1000 = 0\r<BR>\n" );
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document.write( "(x - 100)*(x - 10) = 0\r<BR>\n" );
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document.write( "x = 100 or 10\r<BR>\n" );
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document.write( "Profit is 0 when the spend is 100000 dollars or 10000 dollars.\r<BR>\n" );
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document.write( "See the quadratic solution below as well\r<BR>\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%2B-110x%2B1000+=+0 ALIGN=MIDDLE  ALT=\"1x%5E2%2B-110x%2B1000+=+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" );
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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" );
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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=%28-110%29%5E2-4%2A1%2A1000=8100 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%28-110%29%5E2-4%2A1%2A1000=8100\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=8100 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--110%2B-sqrt%28+8100+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28--110%2B-sqrt%28+8100+%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-%28-110%29%2Bsqrt%28+8100+%29%29%2F2%5C1+=+100 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%28-110%29%2Bsqrt%28+8100+%29%29%2F2%5C1+=+100\"   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-%28-110%29-sqrt%28+8100+%29%29%2F2%5C1+=+10 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%28-110%29-sqrt%28+8100+%29%29%2F2%5C1+=+10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "    Quadratic expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1x%5E2%2B-110x%2B1000 ALIGN=MIDDLE  ALT=\"1x%5E2%2B-110x%2B1000\"   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%2B-110x%2B1000+=+1%28x-100%29%2A%28x-10%29 ALIGN=MIDDLE  ALT=\"1x%5E2%2B-110x%2B1000+=+1%28x-100%29%2A%28x-10%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 100, 10.\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%2B-110%2Ax%2B1000+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-110%2Ax%2B1000+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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document.write( " </SPAN>\n" );
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