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 #319822 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=319822\">put this solution on YOUR website!</A><BR><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.<BR>\n" );
document.write( "...<BR>\n" );
document.write( "To answer the question, you need an equation like y=A(x-h)^2+k, with (h,k) being the (x,y) coordinates of the vertex, the values of which gives the number of watches Bob must repair to have the lowest cost.<BR>\n" );
document.write( "..<BR>\n" );
document.write( "C(x) = 4x2-296x+85<BR>\n" );
document.write( "completing the square: (factor out 4, then take half of the coefficient of the x-term and square it=(74/2)^2=37^2, then add it in to complete the square.)<BR>\n" );
document.write( "C(x)=4(x^2-74x+37^2)+85-4(37^2)<BR>\n" );
document.write( "C(x)=4(x-37)^2+85-5476<BR>\n" );
document.write( "C(x)=4(x-37)^2-5391<BR>\n" );
document.write( "This is a parabola with vertex at (37,-5391)<BR>\n" );
document.write( "ans:<BR>\n" );
document.write( "Bob must repair 37 watches to have the lowest operating cost\r<BR>\n" );
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document.write( "See graph below as a visual check on the answer<BR>\n" );
document.write( "..<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+400%2C+400%2C+-100%2C100%2C+-8000%2C+1000%2C4%28x-37%29%5E2-5391%29+ ALIGN=MIDDLE  ALT=\"+graph%28+400%2C+400%2C+-100%2C100%2C+-8000%2C+1000%2C4%28x-37%29%5E2-5391%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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