document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=167387>Question 167387</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A manufacturer estimates that the total cost of producing x items per day is given by the function C(x)=0.01x^2-4x+1500 with C in dollars.  How many items should be produced each day so that the cost will be a minimum? What will be the minimum cost? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #123285 by </B><A HREF=/tutors/aboutme.mpl?userid=nerdybill><B>nerdybill(7384)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=nerdybill><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=nerdybill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=123285\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> C(x)=0.01x^2-4x+1500 <BR>\n" );
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document.write( "Since the coefficient associated with the x^2 term is \"positive\" (think happy face), the parabola will open upward like a U.  Knowing this, if we find the vertex, we'll find the minimum.<BR>\n" );
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document.write( "The axis of symmetry is the line x = -b/2a<BR>\n" );
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document.write( "x = -(-4)/2(0.01)<BR>\n" );
document.write( "x = 4/0.02<BR>\n" );
document.write( "x = 200 (items produced to minimize cost)<BR>\n" );
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document.write( "To find the cost, plug the value above back into:<BR>\n" );
document.write( "C(x)=0.01x^2-4x+1500 <BR>\n" );
document.write( "C(200)=0.01(200)^2-4(200)+1500 <BR>\n" );
document.write( "C(200)=400-800+1500 <BR>\n" );
document.write( "C(200)=-400+1500 <BR>\n" );
document.write( "C(200)=$1100 (minimum cost)<BR>\n" );
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