document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=466509>Question 466509</A>: <I><SPAN STYLE=\"word-break: break-all;\">  Bob owns a watch repair shop. He has found that the cost of operating his shop is given by C(x) = 4x2-296x+85 , where c is cost and x is the number of watches repaired. How many watches must he repair to have the lowest cost?     </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #319820 by </B><A HREF=/tutors/aboutme.mpl?userid=ccs2011><B>ccs2011(207)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ccs2011><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=ccs2011><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=319820\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Goal is to minimize C(x)<BR>\n" );
document.write( "minimum occurs when slope is zero<BR>\n" );
document.write( "Differentiate C(x) and set it equal to 0<BR>\n" );
document.write( "Differentiate polynomial using power rule:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28d%2Fdx%29+x%5En+=+nx%5E%28n-1%29 ALIGN=MIDDLE  ALT=\"%28d%2Fdx%29+x%5En+=+nx%5E%28n-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "C'(x) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8x+-+296+=+0 ALIGN=MIDDLE  ALT=\"8x+-+296+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now solve for x<BR>\n" );
document.write( "Add 296 to both sides<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8x+=+296 ALIGN=MIDDLE  ALT=\"8x+=+296\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Divide by 8 on both sides<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+37 ALIGN=MIDDLE  ALT=\"x+=+37\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Lowest cost occurs at x = 37 </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );