document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=995708>Question 995708</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Help is urgently needed.\r<BR>\n" );
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document.write( "The profit P(in millions of pesos) for a manufacturer of tablets can be modeled by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+P=-4x%5E3%2B12x%5E2%2B16x+ ALIGN=MIDDLE  ALT=\"+P=-4x%5E3%2B12x%5E2%2B16x+\"   DISABLED_style= \"max-width:90%; height:auto;\" > where x is the number of tablets produced (in millions). Currently, the company produces 3 million tablets and makes a profit of 48,000,000 pesos. What lesser number of tablets could the company produce and still make the same profit? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #614388 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=614388\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> to find out the point where profit is equal to 0, just set the equation equal to 0 and solve.\r<BR>\n" );
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document.write( "you get:\r<BR>\n" );
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document.write( "-4x^3 + 12x^2 + 16x = 0\r<BR>\n" );
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document.write( "factor out the gcf to get:\r<BR>\n" );
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document.write( "(-4x) * (x^2 - 3x - 4) = 0\r<BR>\n" );
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document.write( "factor x^2 - 3x - 4 to get:\r<BR>\n" );
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document.write( "(-4x) * (x-4) * (x+1) = 0\r<BR>\n" );
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document.write( "set each of these factors equal to 0 and solve for x to get:\r<BR>\n" );
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document.write( "x = 0, x = 4, x = -1.\r<BR>\n" );
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document.write( "x represents number of tablets.\r<BR>\n" );
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document.write( "x = 0 leads to a profit of 0 but that's trivial.<BR>\n" );
document.write( "x = -1 is invalid because number of tablets can't be negative.<BR>\n" );
document.write( "only valid answer is that profit is 0 when x = 4.\r<BR>\n" );
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document.write( "you have 3 zero crossing points and you want to see whether profit is positive or negative between them.\r<BR>\n" );
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document.write( "the only intervals that are valid are the intervals between x = 0 and x = 4, and the interval where x is greater than 4.\r<BR>\n" );
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document.write( "it turns out that x is positive in the interval between x = 0 and x = 4 only.\r<BR>\n" );
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document.write( "it is negative otherwise.\r<BR>\n" );
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document.write( "if you look at the graph, you will see that the same profit is made when x = 2 and when x = 3.\r<BR>\n" );
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document.write( "that can be seen by drawing a horizontal line at y = 48 and the intersection will be at x = 2 and x = 3.\r<BR>\n" );
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document.write( "the grpah of your equation is shown below along with the line of y = 48.\r<BR>\n" );
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document.write( "results on the graph are in millions.\r<BR>\n" );
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document.write( "when x = 2 million, you make a 48 million profit.<BR>\n" );
document.write( "when x = 3 million, you make a 48 million profit.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2015/101102.jpg\" alt=\"$$$\" </>\r<BR>\n" );
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document.write( " </SPAN>\n" );
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