document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=435471>Question 435471</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The cost C  (in dollars) of manufacturing x chairs at Maya's Furniture Factory is given by the function C(x)=0.6x^2-336x+57,718 . What is the minimum cost of manufacturing chairs? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #301389 by </B><A HREF=/tutors/aboutme.mpl?userid=lwsshak3><B>lwsshak3(11628)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=lwsshak3><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=301389\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The cost C (in dollars) of manufacturing x chairs at Maya's Furniture Factory is given by the function C(x)=0.6x^2-336x+57,718 . What is the minimum cost of manufacturing chairs?<BR>\n" );
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document.write( "What we need to do here is change this quadratic equation which represents a parabola which opens upwards into the standard form, y=(x-h)^2+k, with (h,k) being the (x,y) coordinates of the vertex. The y-value would be the minimum cost in this case. An alternative method is the use the formula, x=-b/2a, with x being the x coordinate of the vertex. To find the minimum, just plug this x-value into the original equation and solve for C(x).  I will do both methods.<BR>\n" );
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document.write( "0.6x^2-336x+57,718<BR>\n" );
document.write( "completing the square, factoring out 0.6)<BR>\n" );
document.write( ".6(x^2-560x+57718)<BR>\n" );
document.write( "(560/2)^2=78400<BR>\n" );
document.write( ".6(x^2-560x+78400)+57718-47040<BR>\n" );
document.write( ".6(x-280)^2+10678<BR>\n" );
document.write( "ans:<BR>\n" );
document.write( "The minimum cost is $10678 when 280 chairs are made.<BR>\n" );
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document.write( "Alternate method:<BR>\n" );
document.write( "a=.6<BR>\n" );
document.write( "b=-336<BR>\n" );
document.write( "x=-b/2a=-(-336)/2*.6=336/1.2=280<BR>\n" );
document.write( "C(x)=0.6x^2-336x+57,718=.6(280)-336(280)+57718<BR>\n" );
document.write( "      =47040-94080+57718=10678\r<BR>\n" );
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document.write( "In this case the second method might be easier. You should learn both methods, however. </SPAN>\n" );
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