document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1209141>Question 1209141</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Carly just opened her own nail salon. Based on experience, she knows that her daily profit, P, in dollars, can be modelled by the relation P=-15x^2+240x-640, where x is number of clients per day. How many clients should she book each day to maximize her profit?\r<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 #847725 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52909)</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=847725\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
document.write( "Carly just opened her own nail salon. Based on experience, she knows that her daily profit, P, <BR>\n" );
document.write( "in dollars, can be modelled by the relation P=-15x^2+240x-640, where x is number of clients <BR>\n" );
document.write( "per day. How many clients should she book each day to maximize her profit?<BR>\n" );
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document.write( "<PRE STYLE=\"white-space: pre-wrap; white-space: -moz-pre-wrap; white-space: -pre-wrap; white-space: -o-pre-wrap; word-wrap: break-word;\">\r\n" );
document.write( "The given function is a quadratic function.\r\n" );
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document.write( "Since the coefficient at x^2 is negative, the parabola is downward and has a maximum.\r\n" );
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document.write( "The maximum value is achieved  a  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c%5Bmax%5D ALIGN=MIDDLE  ALT=\"c%5Bmax%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;\" >,  where \"a\" is the coefficient at x^2\r\n" );
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document.write( "and \"b\" is the coefficient at x.  In your case,\r\n" );
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document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5Bmax%5D ALIGN=MIDDLE  ALT=\"x%5Bmax%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-240%2F%28-2%2A%28-15%29%29 ALIGN=MIDDLE  ALT=\"-240%2F%28-2%2A%28-15%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=240%2F30 ALIGN=MIDDLE  ALT=\"240%2F30\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 8.\r\n" );
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document.write( "Hence, the profit is maximum if Carly books 8 clients per day.    <U>ANSWER</U>\r\n" );
document.write( "</PRE>\r<BR>\n" );
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document.write( "Solved.\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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