document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=187397>Question 187397</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/032129646X/algebrahomeworkh>Precalculus</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> Hi,<BR>\n" );
document.write( "I'll write the problem word for word in case you can't find it:\r<BR>\n" );
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document.write( "Toy manufacturing: After being in business for t years, a toy manufacturer <BR>\n" );
document.write( "is making x = 5000 + 50t + 10t^2 GI Jimmy toys per year. The sale <BR>\n" );
document.write( "price p in dollars per toy has risen according to the formula <BR>\n" );
document.write( "p = 10 + 0.5t. Write a formula for the manufacturer's yearly revenue as\r<BR>\n" );
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document.write( "a. a function of time t.<BR>\n" );
document.write( "b. a function of price p.\r<BR>\n" );
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document.write( " I've used the formula:<BR>\n" );
document.write( "(R)Revenue = (P)Price per item * (x)Number of items sold,\r<BR>\n" );
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document.write( "and came up with: R(t)=(10+0.5t)*(5000+50t+10t^2) for part a. I'm not sure if this is right or not. Part b I'm not sure either. I had: R(p)=p(5000+50t+10t^2).<BR>\n" );
document.write( "Any help at this point would be really appreciated.<BR>\n" );
document.write( "Thank you,<BR>\n" );
document.write( "Lynn Scott<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 #140471 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=140471\">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 are almost there.  Part a is technically correct, although you should finish it by multiplying the price binomial across the quantity trinomial:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ R(t)=(10+0.5t)(5000+50t+10t^2) = 50000 + 3000t + 25t^2 + 5t^3\">\r<BR>\n" );
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document.write( "The problem with your answer to Part b is that what you are saying is a function of <i>p</i> is actually a function of <i>p</i> <i><b>and</b></i> <i>t</i>.\r<BR>\n" );
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document.write( "What you need to do is take the price function of t:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \  P(t) = p = 10 + 0.5t\">\r<BR>\n" );
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document.write( "and solve it for <i>t</i>,\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \   t = 2p - 20\">,\r<BR>\n" );
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document.write( "and then substitute this expression for <i>t</i> into your function for price, thus:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \  R(p)=p(5000+50(2p-20)+10(2p-20)^2)\">\r<BR>\n" );
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document.write( "Simplifying to a single polynomial expression is left as an exercise for the student.\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" );
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