document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1204775>Question 1204775</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the price that will maximize profit for the demand and cost functions, where p is the price, x is the number of units, and C is the cost.<BR>\n" );
document.write( "Demand Function	    	Cost Function<BR>\n" );
document.write( "p = 80 − 0.1sqrtx    	C = 35x + 600<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 #841250 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20849)</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=841250\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \r<BR>\n" );
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document.write( "Demand Function \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p%28x%29+=+80+-+0.1sqrt%28x%29+ ALIGN=MIDDLE  ALT=\"p%28x%29+=+80+-+0.1sqrt%28x%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Cost Function\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%28x%29+=+35x+%2B+600 ALIGN=MIDDLE  ALT=\"C%28x%29+=+35x+%2B+600\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "To find the price that will maximize profit, using demand and cost functions, first step is to find the profit 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;\" >. Then, use the first derivative to find the critical points for the profit function. Finally use the critical points to find the price to maximize profit.\r<BR>\n" );
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document.write( "Profit Function:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28x%29+%29+=+R%28x%29+-+C%28x%29+ ALIGN=MIDDLE  ALT=\"P%28x%29+%29+=+R%28x%29+-+C%28x%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >...revenue <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R%28x%29+=x%2Ap%28x%29 ALIGN=MIDDLE  ALT=\"R%28x%29+=x%2Ap%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+%29+=+x%2Ap%28x%29+-+C%28x%29+ ALIGN=MIDDLE  ALT=\"P%28x%29+%29+=+x%2Ap%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+%29+=+x%2A%2880+-+0.1sqrt%28x%29+%29+-+%2835x+%2B+600%29 ALIGN=MIDDLE  ALT=\"+P%28x%29+%29+=+x%2A%2880+-+0.1sqrt%28x%29+%29+-+%2835x+%2B+600%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28x%29+=+80x+-+0.1x%5E%283%2F2%29+-+35x+-600+ ALIGN=MIDDLE  ALT=\"P%28x%29+=+80x+-+0.1x%5E%283%2F2%29+-+35x+-600+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Then find first derivate and set equal to zero:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28d%2Fdx%29%2880x+-+0.1x%5E%283%2F2%29+-+35x+-600+%29=-0.15+%28sqrt%28x%29+-+300%29 ALIGN=MIDDLE  ALT=\"%28d%2Fdx%29%2880x+-+0.1x%5E%283%2F2%29+-+35x+-600+%29=-0.15+%28sqrt%28x%29+-+300%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=-0.15+%28sqrt%28x%29+-+300%29=0 ALIGN=MIDDLE  ALT=\"-0.15+%28sqrt%28x%29+-+300%29=0\"   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=sqrt%28x%29+-+300=0 ALIGN=MIDDLE  ALT=\"sqrt%28x%29+-+300=0\"   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=sqrt%28x%29+=300 ALIGN=MIDDLE  ALT=\"sqrt%28x%29+=300\"   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=x=300%5E2 ALIGN=MIDDLE  ALT=\"x=300%5E2\"   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=x+=+90000 ALIGN=MIDDLE  ALT=\"x+=+90000\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " The maximum profit is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%2890000%29 ALIGN=MIDDLE  ALT=\"P%2890000%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >'.<BR>\n" );
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