document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1197165>Question 1197165</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The cost of production of an item is represented with the following equation: C(x) = 7x + 10. The revenue function for this item was determined to be R(x) =  -  2x2 + 59x. What is the maximum amount of profit that can be made at the point where the number of items is the greatest to maximize profit? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #830301 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=830301\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \r<BR>\n" );
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document.write( "The cost of production of an item is represented with the following equation: \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%28x%29+=+7x+%2B+10 ALIGN=MIDDLE  ALT=\"C%28x%29+=+7x+%2B+10\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The revenue function for this item was determined to be: \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R%28x%29+=+-+2x%5E2+%2B+59x+ ALIGN=MIDDLE  ALT=\"R%28x%29+=+-+2x%5E2+%2B+59x+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "What is the maximum amount of profit that can be made at the point where the number of items is the greatest to maximize profit?\r<BR>\n" );
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document.write( "Profit is revenue minus cost.  This means there is a function, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28x%29 ALIGN=MIDDLE  ALT=\"P%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, that is profit. <BR>\n" );
document.write( " <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28x%29+=+R%28x%29+-+C%28x%29 ALIGN=MIDDLE  ALT=\"P%28x%29+=+R%28x%29+-+C%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28x%29+=-+2x%5E2+%2B+59x++-+%287x+%2B+10%29 ALIGN=MIDDLE  ALT=\"P%28x%29+=-+2x%5E2+%2B+59x++-+%287x+%2B+10%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28x%29+=-+2x%5E2+%2B+59x++-+7x+-10 ALIGN=MIDDLE  ALT=\"P%28x%29+=-+2x%5E2+%2B+59x++-+7x+-10\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28x%29+=-2x%5E2+%2B+52x+-+10 ALIGN=MIDDLE  ALT=\"P%28x%29+=-2x%5E2+%2B+52x+-+10\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "the maximum amount of profit that can be made at the vertex (parabola is opening down)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28x%29+=-2x%5E2+%2B+52x+-+10 ALIGN=MIDDLE  ALT=\"P%28x%29+=-2x%5E2+%2B+52x+-+10\"   DISABLED_style= \"max-width:90%; height:auto;\" >..........write in vertex form\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28x%29+=%28-2x%5E2+%2B+52x%29+-+10 ALIGN=MIDDLE  ALT=\"P%28x%29+=%28-2x%5E2+%2B+52x%29+-+10\"   DISABLED_style= \"max-width:90%; height:auto;\" >......complete square\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28x%29+=-2%28x%5E2+-26x%2Bb%5E2%29-%28-2b%5E2%29+-+10 ALIGN=MIDDLE  ALT=\"P%28x%29+=-2%28x%5E2+-26x%2Bb%5E2%29-%28-2b%5E2%29+-+10\"   DISABLED_style= \"max-width:90%; height:auto;\" >............ coefficient of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=26 ALIGN=MIDDLE  ALT=\"26\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=13 ALIGN=MIDDLE  ALT=\"b=13\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28x%29+=-2%28x%5E2+-26x%2B13%5E2%29%2B2%2A13%5E2-+10 ALIGN=MIDDLE  ALT=\"P%28x%29+=-2%28x%5E2+-26x%2B13%5E2%29%2B2%2A13%5E2-+10\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28x%29+=-2%28x+-13%29%5E2%2B328 ALIGN=MIDDLE  ALT=\"P%28x%29+=-2%28x+-13%29%5E2%2B328\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "=> vertex is at (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=13 ALIGN=MIDDLE  ALT=\"13\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=328 ALIGN=MIDDLE  ALT=\"328\"   DISABLED_style= \"max-width:90%; height:auto;\" >)\r<BR>\n" );
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document.write( " the maximum amount of profit is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28x%29+=328 ALIGN=MIDDLE  ALT=\"P%28x%29+=328\"   DISABLED_style= \"max-width:90%; height:auto;\" > at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=13 ALIGN=MIDDLE  ALT=\"x=13\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
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