document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1124737>Question 1124737</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Help me solve this problem:\r<BR>\n" );
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document.write( "The profit function for a company is P(x) = 36x^2 + 1875x – 6500 where Profit is in dollars, and x represents the number of widgets manufactured.\r<BR>\n" );
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document.write( "(a) The profit function is a quadratic function. Does the function open up or down?  \r<BR>\n" );
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document.write( "(b)  Find the vertex of the profit function P(x) using algebra. Show algebraic work.\r<BR>\n" );
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document.write( "(c)  State the maximum profit and the number of widgets which yield that maximum profit.\r<BR>\n" );
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document.write( " The maximum profit is _______________    when ____________ widgets are produced and sold.\r<BR>\n" );
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document.write( "(d) What are the minimum start-up costs? Justify your answer.<BR>\n" );
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document.write( "(e)  Find and interpret the break-even point. Show algebraic work.<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 #741044 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39620)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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=741044\">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=36x%5E2%2B1875x-6500 ALIGN=MIDDLE  ALT=\"36x%5E2%2B1875x-6500\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Opens upward.  Look for zeros or the break-even points, P(x)=0; solve for x.\r<BR>\n" );
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document.write( "Vertex:<BR>\n" );
document.write( "x value,  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1875%2F%282%2A36%29=-1875%2F72=-625%2F24 ALIGN=MIDDLE  ALT=\"-1875%2F%282%2A36%29=-1875%2F72=-625%2F24\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Roots-Zeros\r<BR>\n" );
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document.write( "discriminant <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1875%5E2%2B4%2A36%2A6500=4451625=3%2A3%2A3%2A5%2A5%2A5%2A1319=9%2A25%2A15%2A1319 ALIGN=MIDDLE  ALT=\"1875%5E2%2B4%2A36%2A6500=4451625=3%2A3%2A3%2A5%2A5%2A5%2A1319=9%2A25%2A15%2A1319\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%28-1875%2B3%2A5%2Asqrt%2815%2A1319%29%29%2F72 ALIGN=MIDDLE  ALT=\"x=%28-1875%2B3%2A5%2Asqrt%2815%2A1319%29%29%2F72\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%28-625%2B5%2Asqrt%2819785%29%29%2F24 ALIGN=MIDDLE  ALT=\"x=%28-625%2B5%2Asqrt%2819785%29%29%2F24\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "x <BR>\n" );
document.write( "is about 3.262.<BR>\n" );
document.write( "Only nonzero whole number is allowed.<BR>\n" );
document.write( "No profit at 3 units<BR>\n" );
document.write( "Any profit begins at 4 units for x.<BR>\n" );
document.write( "Profit only increases for any whole number x greater than 4 units.<BR>\n" );
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