document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1011848>Question 1011848</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Suppose that the cost function for a particular item is given by the equation <BR>\n" );
document.write( "C(x) = 2x2 &#8722; 360x + 16,420,<BR>\n" );
document.write( " where x represents the number of items. How many items should be produced to minimize the cost? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #627621 by </B><A HREF=/tutors/aboutme.mpl?userid=Fombitz><B>Fombitz(32388)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Fombitz><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=Fombitz><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=627621\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You can determine the minimum by either putting it into vertex form (algebraic method) or by taking the derivative (calculus method).<BR>\n" );
document.write( "Vertex:<BR>\n" );
document.write( "Convert to vertex form by completing the square.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%28x%29=2%28x%5E2-180x%29%2B16420 ALIGN=MIDDLE  ALT=\"C%28x%29=2%28x%5E2-180x%29%2B16420\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%28x%29=2%28x%5E2-180x%2B8100%29%2B16420-2%288100%29 ALIGN=MIDDLE  ALT=\"C%28x%29=2%28x%5E2-180x%2B8100%29%2B16420-2%288100%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%28x%29=2%28x-90%29%5E2%2B16420-16200 ALIGN=MIDDLE  ALT=\"C%28x%29=2%28x-90%29%5E2%2B16420-16200\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%28x%29=2%28x-90%29%5E2%2B220 ALIGN=MIDDLE  ALT=\"C%28x%29=2%28x-90%29%5E2%2B220\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So now the function is in vertex form.<BR>\n" );
document.write( "The minimum of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%28x%29=220 ALIGN=MIDDLE  ALT=\"C%28x%29=220\"   DISABLED_style= \"max-width:90%; height:auto;\" > occurs when <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=90 ALIGN=MIDDLE  ALT=\"x=90\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( ".\r<BR>\n" );
document.write( "\n" );
document.write( "Derivative:<BR>\n" );
document.write( "Find the derivative and set it equal to zero.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=dC%2Fdx=4x-360=0 ALIGN=MIDDLE  ALT=\"dC%2Fdx=4x-360=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x=360 ALIGN=MIDDLE  ALT=\"4x=360\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=90 ALIGN=MIDDLE  ALT=\"x=90\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Then,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%2890%29=2%2890%29%5E2-360%2890%29%2B16420 ALIGN=MIDDLE  ALT=\"C%2890%29=2%2890%29%5E2-360%2890%29%2B16420\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%2890%29=16200-32400%2B16420 ALIGN=MIDDLE  ALT=\"C%2890%29=16200-32400%2B16420\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%2890%29=220 ALIGN=MIDDLE  ALT=\"C%2890%29=220\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );