document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1130474>Question 1130474</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The profit P, in thousands of dollars, that a manufacturer makes is a function of the number N of items produced in a year, and the formula is as follows:<BR>\n" );
document.write( "P= -0.2N^2 + 3.6N - 9\r<BR>\n" );
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document.write( "(a) Determine the two break-even points for this manufacturer-that is, the two production levels at which the profit is zero.\r<BR>\n" );
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document.write( "(c) How many items should they produce to get this maximum point?\r<BR>\n" );
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document.write( "Please show me how you get the answer, thank you. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #747138 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=747138\">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%28N%29+=+0+ ALIGN=MIDDLE  ALT=\"+P%28N%29+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" > ( zero profit )<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-.2N%5E2+%2B+3.6N+-+9+=+0+ ALIGN=MIDDLE  ALT=\"+-.2N%5E2+%2B+3.6N+-+9+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+N+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ ALIGN=MIDDLE  ALT=\"+N+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+a+=+-.2+ ALIGN=MIDDLE  ALT=\"+a+=+-.2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+b+=+3.6+ ALIGN=MIDDLE  ALT=\"+b+=+3.6+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+c+=+-9+ ALIGN=MIDDLE  ALT=\"+c+=+-9+\"   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=+N+=+%28-3.6+%2B-+sqrt%28+3.6%5E2-4%2A%28-.2%29%2A%28-9%29+%29%29%2F%282%2A%28-.2%29%29+ ALIGN=MIDDLE  ALT=\"+N+=+%28-3.6+%2B-+sqrt%28+3.6%5E2-4%2A%28-.2%29%2A%28-9%29+%29%29%2F%282%2A%28-.2%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=+N+=+%28-3.6+%2B-+sqrt%28+12.96+-+7.2+%29%29%2F%28%28-.4%29%29+ ALIGN=MIDDLE  ALT=\"+N+=+%28-3.6+%2B-+sqrt%28+12.96+-+7.2+%29%29%2F%28%28-.4%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=+N+=+%28-3.6+%2B-+sqrt%28+5.76+%29%29%2F%28%28-.4%29%29+ ALIGN=MIDDLE  ALT=\"+N+=+%28-3.6+%2B-+sqrt%28+5.76+%29%29%2F%28%28-.4%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=+N+=+%28+-3.6+%2B+2.4+%29%2F+%28-.4+%29+ ALIGN=MIDDLE  ALT=\"+N+=+%28+-3.6+%2B+2.4+%29%2F+%28-.4+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+N+=+%28-1.2%29%2F%28-.4%29+ ALIGN=MIDDLE  ALT=\"+N+=+%28-1.2%29%2F%28-.4%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+N+=+3+ ALIGN=MIDDLE  ALT=\"+N+=+3+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+N+=+%28+-3.6+-+2.4+%29+%2F+%28-.4%29+ ALIGN=MIDDLE  ALT=\"+N+=+%28+-3.6+-+2.4+%29+%2F+%28-.4%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+N+=+6%2F.4+ ALIGN=MIDDLE  ALT=\"+N+=+6%2F.4+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+N+=+15+ ALIGN=MIDDLE  ALT=\"+N+=+15+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The two break even points are<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+N+=+3+ ALIGN=MIDDLE  ALT=\"+N+=+3+\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+N+=+15+ ALIGN=MIDDLE  ALT=\"+N+=+15+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-------------------------------------<BR>\n" );
document.write( "check:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-.2N%5E2+%2B+3.6N+-+9+=+0+ ALIGN=MIDDLE  ALT=\"+-.2N%5E2+%2B+3.6N+-+9+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-.2%2A15%5E2+%2B+3.6%2A15+-+9+=+0+ ALIGN=MIDDLE  ALT=\"+-.2%2A15%5E2+%2B+3.6%2A15+-+9+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-.2%2A225+%2B+54+-+9+=+0+ ALIGN=MIDDLE  ALT=\"+-.2%2A225+%2B+54+-+9+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-45+%2B+54+-+9+=+0+ ALIGN=MIDDLE  ALT=\"+-45+%2B+54+-+9+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+0+=+0+ ALIGN=MIDDLE  ALT=\"+0+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "OK<BR>\n" );
document.write( "You can check other solution<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );