document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1031235>Question 1031235</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The B & J co. wants to produce items at a minimum cost to the company. The cost of the items is modeled by the function C(x) = x^2 - 140 x + 5700, where x is the number of items produced. \r<BR>\n" );
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document.write( "A.) How many items should the company produce to keep the cost to a minimum?\r<BR>\n" );
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document.write( "B.) What is the minimum cost?\r<BR>\n" );
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document.write( "C.) When would the company have a cost of $0? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #646010 by </B><A HREF=/tutors/aboutme.mpl?userid=josmiceli><B>josmiceli(19441)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josmiceli><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=josmiceli><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=646010\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+C%28x%29+=+x%5E2+-+140x+%2B+5700+ ALIGN=MIDDLE  ALT=\"+C%28x%29+=+x%5E2+-+140x+%2B+5700+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(a)<BR>\n" );
document.write( "When the equation has the form:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+a%2Ax%5E2+%2B+b%2Ax+%2B+c+ ALIGN=MIDDLE  ALT=\"+y+=+a%2Ax%5E2+%2B+b%2Ax+%2B+c+\"   DISABLED_style= \"max-width:90%; height:auto;\" > , then the<BR>\n" );
document.write( "x-value of the vertex ( max or min ) is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5Bmin%5D+=+-b%2F%282a%29+ ALIGN=MIDDLE  ALT=\"+x%5Bmin%5D+=+-b%2F%282a%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----------------------<BR>\n" );
document.write( "In this case:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+a+=+1+ ALIGN=MIDDLE  ALT=\"+a+=+1+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+b+=+-140+ ALIGN=MIDDLE  ALT=\"+b+=+-140+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5Bmin%5D+=+-%28-140%29+%2F+%282%2A1%29+ ALIGN=MIDDLE  ALT=\"+x%5Bmin%5D+=+-%28-140%29+%2F+%282%2A1%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5Bmin%5D+=+70+ ALIGN=MIDDLE  ALT=\"+x%5Bmin%5D+=+70+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "70 items should be produced to make<BR>\n" );
document.write( "cost a minimum<BR>\n" );
document.write( "-------------------------<BR>\n" );
document.write( "(b)<BR>\n" );
document.write( "Plug <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5Bmin%5D+ ALIGN=MIDDLE  ALT=\"+x%5Bmin%5D+\"   DISABLED_style= \"max-width:90%; height:auto;\" > into equation to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+C%5Bmin%5D+ ALIGN=MIDDLE  ALT=\"+C%5Bmin%5D+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+C%5Bmin%5D+=+70%5E2+-+140%2A70+%2B+5700+ ALIGN=MIDDLE  ALT=\"+C%5Bmin%5D+=+70%5E2+-+140%2A70+%2B+5700+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+C%5Bmin%5D+=+4900+-+9800+%2B+5700+ ALIGN=MIDDLE  ALT=\"+C%5Bmin%5D+=+4900+-+9800+%2B+5700+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+C%5Bmin%5D+=+800+ ALIGN=MIDDLE  ALT=\"+C%5Bmin%5D+=+800+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The minimum cost is $800<BR>\n" );
document.write( "------------------------<BR>\n" );
document.write( "When does <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+C%28x%29+=+0+ ALIGN=MIDDLE  ALT=\"+C%28x%29+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" >?<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5E2++-+140x+%2B+5700+=+0+ ALIGN=MIDDLE  ALT=\"+x%5E2++-+140x+%2B+5700+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5E2+-+140x+=+-5700+ ALIGN=MIDDLE  ALT=\"+x%5E2+-+140x+=+-5700+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "complete the square<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5E2+-+140x+%2B+%28+-140%2F2+%29%5E2+=+-5700+%2B+%28+-140%2F2+%29%5E2+ ALIGN=MIDDLE  ALT=\"+x%5E2+-+140x+%2B+%28+-140%2F2+%29%5E2+=+-5700+%2B+%28+-140%2F2+%29%5E2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5E2+-+140x+%2B+4900+=+-5700+%2B+4900+ ALIGN=MIDDLE  ALT=\"+x%5E2+-+140x+%2B+4900+=+-5700+%2B+4900+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28+x+-+70+%29%5E2+=+-800+ ALIGN=MIDDLE  ALT=\"+%28+x+-+70+%29%5E2+=+-800+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "I can't take the square root of<BR>\n" );
document.write( "both sides and get a real answer,<BR>\n" );
document.write( "so the cost can never be zero<BR>\n" );
document.write( "----------------------------<BR>\n" );
document.write( "Here's the plot of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+C%28x%29+ ALIGN=MIDDLE  ALT=\"+C%28x%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+400%2C+400%2C+-20%2C+140%2C+-240%2C+2400%2C+x%5E2+-+140x+%2B+5700+%29+ ALIGN=MIDDLE  ALT=\"+graph%28+400%2C+400%2C+-20%2C+140%2C+-240%2C+2400%2C+x%5E2+-+140x+%2B+5700+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );