document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1165819>Question 1165819</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Mr. Lim orders chairs from a factory to sell. When he orders a batch of x chairs, the cost of each chair, $y is given by y = x2  -  14x + 80.<BR>\n" );
document.write( "a. Find x such that the cost of each chair is the same as when Mr. Lim<BR>\n" );
document.write( "ordered 5 chairs.\r<BR>\n" );
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document.write( "b. Find the number of chairs in a batch he needs to orders such that the cost<BR>\n" );
document.write( "per chair is less than $45. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #852036 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=852036\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "Here are alternative methods for solving each of the two parts of the problem.<br><BR>\n" );
document.write( "The graph of the cost function is a parabola, with its minimum value when the number of chairs ordered is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-%28-14%29%29%2F2=7 ALIGN=MIDDLE  ALT=\"%28-%28-14%29%29%2F2=7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "a. Find x such that the cost of each chair is the same as when Mr. Lim<BR>\n" );
document.write( "ordered 5 chairs.<br><BR>\n" );
document.write( "Since the graph is symmetric about the axis of symmetry x=7, the cost will be the same for 9 chairs as it is for 5 chairs.<br><BR>\n" );
document.write( "ANSWER: 9 chairs can be ordered for the same cost as 5 chairs<br><BR>\n" );
document.write( "b. Find the number of chairs in a batch he needs to orders such that the cost<BR>\n" );
document.write( "per chair is less than $45.<br><BR>\n" );
document.write( "The minimum cost, when 7 chairs are ordered, is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7%5E2-14%287%29%2B80=31 ALIGN=MIDDLE  ALT=\"7%5E2-14%287%29%2B80=31\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Because the leading term of the cost function is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2 ALIGN=MIDDLE  ALT=\"x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, the cost will differ from the minimum cost of $31 by n^2 when x differs from 7 by n.  We need the cost to be less than $45, which differs from the minimum cost of $31 by $14.  Since 3^2 is less than 14 and 4^2 is greater than 14, the number of chairs that can be ordered for less than $45 can differ from 7 by at most 3.<br><BR>\n" );
document.write( "ANSWER: Between 4 and 10 chairs can be ordered for a cost less than $45<br><BR>\n" );
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