document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1204337>Question 1204337</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A company finds that it can make a profit of P dollars each month by selling<BR>\n" );
document.write( "x patterns, according to the formula<BR>\n" );
document.write( "P(x)=-.002x^2+5.5x-1400. How many patterns must it sell each month to have a maximum profit? <BR>\n" );
document.write( "To attain maximum profit they must sell<BR>\n" );
document.write( "patterns.\r<BR>\n" );
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document.write( "What is the maximum profit? <BR>\n" );
document.write( "The max profit is $\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 #840507 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52797)</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=840507\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
document.write( "A company finds that it can make a profit of P dollars each month by selling<BR>\n" );
document.write( "x patterns, according to the formula<BR>\n" );
document.write( "P(x)=-.002x^2+5.5x-1400. How many patterns must it sell each month to have a maximum profit? <BR>\n" );
document.write( "To attain maximum profit they must sell<BR>\n" );
document.write( "patterns.\r<BR>\n" );
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document.write( "What is the maximum profit? <BR>\n" );
document.write( "The max profit is $<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( "They want you find the maximum of the quadratic function  P(x) = ax^2 + bx + c = -0.002x^2 + 5.5x - 1400.\r\n" );
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document.write( "The general theory says that the maximum is attained at  <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=-b%2F%282a%29 ALIGN=MIDDLE  ALT=\"-b%2F%282a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-5.5%2F%282%2A%28-0.002%29%29 ALIGN=MIDDLE  ALT=\"-5.5%2F%282%2A%28-0.002%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5.5%2F0.004 ALIGN=MIDDLE  ALT=\"5.5%2F0.004\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 1375.\r\n" );
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document.write( "To get the value of the maximum profit, substitute this value <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;\" > = 1375 into the formula for the profit.\r\n" );
document.write( "You will get\r\n" );
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document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%5Bmax%5D ALIGN=MIDDLE  ALT=\"P%5Bmax%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > = -0.002*1375^2 + 5.5*1375 - 1400 = 2381.25  dollars.\r\n" );
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document.write( "<U>ANSWER</U>.  <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;\" > = 1375 patterns.\r\n" );
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document.write( "         <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%5Bmax%5D ALIGN=MIDDLE  ALT=\"P%5Bmax%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 2381.25  dollars.\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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