document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1202457>Question 1202457</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 3. A company is trying to minimize their costs. Their accountant comes up with the formula C = 15x2-18x+24, where C equals the cost and x equals the number of hours a machine runs to help them achieve this.\r<BR>\n" );
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document.write( "What are their break even points?\r<BR>\n" );
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document.write( "What value would minimize the cost?<BR>\n" );
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document.write( "If the machine runs for six hours how much would that cost the company?<BR>\n" );
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document.write( "If the cost is $500, how long was the machine running for?<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #837303 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52781)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><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=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=837303\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
document.write( "3. A company is trying to minimize their costs. Their accountant comes up with the formula <BR>\n" );
document.write( "C = 15x2-18x+24, where C equals the cost and x equals the number of hours a machine runs <BR>\n" );
document.write( "to help them achieve this.<BR>\n" );
document.write( "(a) What are their break even points?\r<BR>\n" );
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document.write( "(b) What value would minimize the cost?\r<BR>\n" );
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document.write( "(c) If the machine runs for six hours how much would that cost the company?\r<BR>\n" );
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document.write( "(d) If the cost is $500, how long was the machine running for?<BR>\n" );
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document.write( "(a)  To answer (a), solve this quadratic equation\r\n" );
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document.write( "        C(x) = 0,  or  15x^2-18x+24 = 0.\r\n" );
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document.write( "     It is standard quadratic equation. Solve it either using the quadratic formula OR \r\n" );
document.write( "     using factoring if it works.  According to the meaning of \"x\", only positive roots are acceptable.\r\n" );
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document.write( "(b)  The value of \"x\", which minimizes the cost, is  <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;\" > = \" <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-b%2F%282a%29 ALIGN=MIDDLE  ALT=\"-b%2F%282a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > \",\r\n" );
document.write( "     which gives x-coordinate of the vertex.\r\n" );
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document.write( "     Substitute here b= -18, a= 15 and get  \r\n" );
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document.write( "         <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;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-%28-18%29%2F%282%2A15%29 ALIGN=MIDDLE  ALT=\"-%28-18%29%2F%282%2A15%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=18%2F30 ALIGN=MIDDLE  ALT=\"18%2F30\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%2F10 ALIGN=MIDDLE  ALT=\"6%2F10\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 0.6 hours = 36 minutes.\r\n" );
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document.write( "(c)  To answer (c), substitute x= 6 hours into the formula for C, and get the value.\r\n" );
document.write( "     It is more than simple exercise.\r\n" );
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document.write( "(d)  To answer (d), you should solve this quadratic equation\r\n" );
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document.write( "        15x^2 -18x + 24 = 500  dollars.\r\n" );
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document.write( "     Again, it is simple mechanical exercise, and you can complete it on your own.\r\n" );
document.write( "</PRE>\r<BR>\n" );
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document.write( "Partly solved; regarding the rest, you have full instructions.\r<BR>\n" );
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document.write( "On finding the maximum/minimum of a quadratic function see the lessons\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/HOW-TO-complete-the-square-of-a-quadratic-function-to-find-its-minimum-maximum.lesson>HOW TO complete the square to find the minimum/maximum of a quadratic function</A>\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/Briefly-on-How-to-complete-the-square-of-a-quadratic-function-to-find-its-minimum-maximum.lesson>Briefly on finding the minimum/maximum of a quadratic function</A>\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/HOW-TO-complete-the-square-to-find-the-vertex-of-a-quadratic-function.lesson>HOW TO complete the square to find the vertex of a parabola</A>\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/Briefly-on-finding-the-vertex-of-a-parabola.lesson>Briefly on finding the vertex of a parabola</A>\r<BR>\n" );
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document.write( "Consider these lessons as your textbook, &nbsp;handbook, &nbsp;tutorials and &nbsp;(free of charge) &nbsp;home teacher.\r<BR>\n" );
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document.write( "Learn the subject from there once and for all.\r<BR>\n" );
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document.write( "Surely and obviously, that wording in this post is far from to be perfect, <BR>\n" );
document.write( "so I need to make my own hypotheses about the meaning of used words in this post.\r<BR>\n" );
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document.write( "It is so typical for numerous illiterate posts at this forum, <BR>\n" );
document.write( "that I just tired to discuss, to edit and/or to disprove them.\r<BR>\n" );
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document.write( "Every second post is nonsense or semi-delusions.\r<BR>\n" );
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