document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1046357>Question 1046357</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Marginal cost is the additional cost imposed by the production of one additional item.  Marginal benefit is the additional benefit of producing one additional item. For a certain company, the marginal cost C, in dollars, if you are currently producing n items, is given by C(n)= 8+n, and the marginal benefit B, in dollars, is given by B(n)= 40*0.5^n. Economic efficiency occurs at the production level where marginal cost and marginal benefit are the same.  What production level n gives economic efficiency for this company?\r<BR>\n" );
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document.write( "C(n)= 8 + n<BR>\n" );
document.write( "B(n)= 40 * 0.5^n\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 #661821 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=661821\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
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document.write( "You need to set the two functions equal to each other and then solve for <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large n\">.  The problem with that idea is that you end up with:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ n\ =\ \frac{W_m\left(10240\ln(2)\right)\ -\ 8\ln(2)}{\ln(2)}\">\r<BR>\n" );
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document.write( "Where <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large W_m\left(10240\ln(2)\right)\"> is a Lambert W-Function that requires a mighty ugly Taylor Series expansion to evaluate.\r<BR>\n" );
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document.write( "On the other hand, if you graph the two functions, it looks like they intersect at the point <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large (2,10)\">.\r<BR>\n" );
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document.write( " <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/display-illustration.mpl?tutor=solver91311&illustration_name=economicefficiency_(2).jpg\">\r<BR>\n" );
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document.write( "And lo and behold:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 8\ +\ 2\ =\ 10\">\r<BR>\n" );
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document.write( "And\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 40\left(\frac{1}{2}\right)^2\ =\ 40\left(\frac{1}{4}\right)\ =\ 10\">\r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi}\ +\ 1\ =\ 0\"><BR>\n" );
document.write( "My calculator said it, I believe it, that settles it<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \ \\r\"> </SPAN>\n" );
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