document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=129106>Question 129106</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 1. A company that produces cells for solar collectors finds through experience that on the average it can sell x cells per day at a selling price (in dollars) of p(x) = 100 – 0.05x  (p is called the demand function). The cost function C(x) for producing x cells per day is C(x)= 4000 + 60x – 0.01x^2\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "A. Write the revenue function R(x).\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "B. Write the profit function P(x).\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "C. Find the value of x that maximizes profit, and find the maximum profit. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #94373 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=94373\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> a)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The revenue can be found by this general formula:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Revenue=Number of units sold*price of each unit\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So in our case, <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" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<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;\" > Start with the given equation\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R%28x%29=x%2A%28100-0.05x%29 ALIGN=MIDDLE  ALT=\"R%28x%29=x%2A%28100-0.05x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28x%29+=+100+%96+0.05x ALIGN=MIDDLE  ALT=\"P%28x%29+=+100+%96+0.05x\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R%28x%29=100x-0.05x%5E2 ALIGN=MIDDLE  ALT=\"R%28x%29=100x-0.05x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R%28x%29=-0.05x%5E2%2B100x+ ALIGN=MIDDLE  ALT=\"R%28x%29=-0.05x%5E2%2B100x+\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rearrange the terms\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So the revenue function is \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R%28x%29=-0.05x%5E2%2B100x+ ALIGN=MIDDLE  ALT=\"R%28x%29=-0.05x%5E2%2B100x+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<hr>\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "b)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The profit can be found by:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Profit=Revenue-Cost\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\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" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28x%29=%28-0.05x%5E2%2B100x%29-%284000+%2B+60x-0.01x%5E2%29 ALIGN=MIDDLE  ALT=\"P%28x%29=%28-0.05x%5E2%2B100x%29-%284000+%2B+60x-0.01x%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R%28x%29=-0.05x%5E2%2B100x+ ALIGN=MIDDLE  ALT=\"R%28x%29=-0.05x%5E2%2B100x+\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%28x%29=4000+%2B+60x+%96+0.01x%5E2 ALIGN=MIDDLE  ALT=\"C%28x%29=4000+%2B+60x+%96+0.01x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28x%29=-0.05x%5E2%2B100x-4000-60x+%2B+0.01x%5E2 ALIGN=MIDDLE  ALT=\"P%28x%29=-0.05x%5E2%2B100x-4000-60x+%2B+0.01x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute the negative\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28x%29=-0.04x%5E2%2B40x-4000 ALIGN=MIDDLE  ALT=\"P%28x%29=-0.04x%5E2%2B40x-4000\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<hr>\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "To find the max profit, we need to graph the profit function <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28x%29=-0.04x%5E2%2B40x-4000 ALIGN=MIDDLE  ALT=\"P%28x%29=-0.04x%5E2%2B40x-4000\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+500%2C+500%2C-740%2C1260%2C-10523%2C7649%2C-0.04x%5E2%2B40x-4000%29 ALIGN=MIDDLE  ALT=\"+graph%28+500%2C+500%2C-740%2C1260%2C-10523%2C7649%2C-0.04x%5E2%2B40x-4000%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "And by using the calculators vertex function, we find that the vertex occurs at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=500 ALIGN=MIDDLE  ALT=\"x=500\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Now plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=500 ALIGN=MIDDLE  ALT=\"x=500\"   DISABLED_style= \"max-width:90%; height:auto;\" > into <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28x%29=-0.04x%5E2%2B40x-4000 ALIGN=MIDDLE  ALT=\"P%28x%29=-0.04x%5E2%2B40x-4000\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28x%29=-0.04%28500%29%5E2%2B40%28500%29-4000 ALIGN=MIDDLE  ALT=\"P%28x%29=-0.04%28500%29%5E2%2B40%28500%29-4000\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28x%29=6000 ALIGN=MIDDLE  ALT=\"P%28x%29=6000\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So the maximum profit is $6,000 </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );