document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=190669>Question 190669</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If a vendor charges p dollars each for rugby shirts, then he expects to sell 2000-100p shirts at a tournament.\r<BR>\n" );
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document.write( "Find a polynomial R(p) that represents the total revenue<BR>\n" );
document.write( "when the shirts are p dollars each.\r<BR>\n" );
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document.write( "Find R(5), R(10), and R(20).\r<BR>\n" );
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document.write( "So far I have R=(2000-100)P(2000-100^2)<BR>\n" );
document.write( "then I'm lost after that. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #143151 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=143151\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Remember, the revenue is simply the money that a individual/company has made BEFORE any expenses or taxes are accounted for. So this amount of money is solely determined by the amount of products/services that have been sold.\r<BR>\n" );
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document.write( "So basically, the revenue is\r<BR>\n" );
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document.write( "Revenue = (Price Per Product) x (Number of Products Sold)\r<BR>\n" );
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document.write( "In this case, since \"a vendor charges p dollars each for rugby shirts\", this means that the price is simply \"p\" and because \"he expects to sell 2000-100p\", this means that the number of products sold is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2000-100p ALIGN=MIDDLE  ALT=\"2000-100p\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So just multiply the price by the quantity to get\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R%28p%29=p%282000-100p%29 ALIGN=MIDDLE  ALT=\"R%28p%29=p%282000-100p%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=R%28p%29=2000p-100p%5E2 ALIGN=MIDDLE  ALT=\"R%28p%29=2000p-100p%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R%28p%29=-100p%5E2%2B2000p ALIGN=MIDDLE  ALT=\"R%28p%29=-100p%5E2%2B2000p\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rearrange the terms.\r<BR>\n" );
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document.write( "So the polynomial that represents the revenue is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R%28p%29=-100p%5E2%2B2000p ALIGN=MIDDLE  ALT=\"R%28p%29=-100p%5E2%2B2000p\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Find R(5):\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R%28p%29=-100p%5E2%2B2000p ALIGN=MIDDLE  ALT=\"R%28p%29=-100p%5E2%2B2000p\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given equation.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R%285%29=-100%285%29%5E2%2B2000%285%29 ALIGN=MIDDLE  ALT=\"R%285%29=-100%285%29%5E2%2B2000%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p=5 ALIGN=MIDDLE  ALT=\"p=5\"   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=R%285%29=-100%2825%29%2B2000%285%29 ALIGN=MIDDLE  ALT=\"R%285%29=-100%2825%29%2B2000%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5 ALIGN=MIDDLE  ALT=\"5\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=25 ALIGN=MIDDLE  ALT=\"25\"   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=R%285%29=-2500%2B2000%285%29 ALIGN=MIDDLE  ALT=\"R%285%29=-2500%2B2000%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-100 ALIGN=MIDDLE  ALT=\"-100\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=25 ALIGN=MIDDLE  ALT=\"25\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2500 ALIGN=MIDDLE  ALT=\"-2500\"   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=R%285%29=-2500%2B10000 ALIGN=MIDDLE  ALT=\"R%285%29=-2500%2B10000\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2000 ALIGN=MIDDLE  ALT=\"2000\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5 ALIGN=MIDDLE  ALT=\"5\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10000 ALIGN=MIDDLE  ALT=\"10000\"   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=R%285%29=7500 ALIGN=MIDDLE  ALT=\"R%285%29=7500\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms.\r<BR>\n" );
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document.write( "So this means that if the price is $5 a shirt, then he'll expect to make $7,500\r<BR>\n" );
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document.write( "Find R(10):\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R%28p%29=-100p%5E2%2B2000p ALIGN=MIDDLE  ALT=\"R%28p%29=-100p%5E2%2B2000p\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given equation.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R%2810%29=-100%2810%29%5E2%2B2000%2810%29 ALIGN=MIDDLE  ALT=\"R%2810%29=-100%2810%29%5E2%2B2000%2810%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p=10 ALIGN=MIDDLE  ALT=\"p=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=R%2810%29=-100%28100%29%2B2000%2810%29 ALIGN=MIDDLE  ALT=\"R%2810%29=-100%28100%29%2B2000%2810%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10 ALIGN=MIDDLE  ALT=\"10\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=100 ALIGN=MIDDLE  ALT=\"100\"   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=R%2810%29=-10000%2B2000%2810%29 ALIGN=MIDDLE  ALT=\"R%2810%29=-10000%2B2000%2810%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-100 ALIGN=MIDDLE  ALT=\"-100\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=100 ALIGN=MIDDLE  ALT=\"100\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-10000 ALIGN=MIDDLE  ALT=\"-10000\"   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=R%2810%29=-10000%2B20000 ALIGN=MIDDLE  ALT=\"R%2810%29=-10000%2B20000\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2000 ALIGN=MIDDLE  ALT=\"2000\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10 ALIGN=MIDDLE  ALT=\"10\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=20000 ALIGN=MIDDLE  ALT=\"20000\"   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=R%2810%29=10000 ALIGN=MIDDLE  ALT=\"R%2810%29=10000\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms.\r<BR>\n" );
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document.write( "So this means that if the price is $10 a shirt, then he'll expect to make $10,000\r<BR>\n" );
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document.write( "Find R(20):\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R%28p%29=-100p%5E2%2B2000p ALIGN=MIDDLE  ALT=\"R%28p%29=-100p%5E2%2B2000p\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given equation.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R%2820%29=-100%2820%29%5E2%2B2000%2820%29 ALIGN=MIDDLE  ALT=\"R%2820%29=-100%2820%29%5E2%2B2000%2820%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p=20 ALIGN=MIDDLE  ALT=\"p=20\"   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=R%2820%29=-100%28400%29%2B2000%2820%29 ALIGN=MIDDLE  ALT=\"R%2820%29=-100%28400%29%2B2000%2820%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=20 ALIGN=MIDDLE  ALT=\"20\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=400 ALIGN=MIDDLE  ALT=\"400\"   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=R%2820%29=-40000%2B2000%2820%29 ALIGN=MIDDLE  ALT=\"R%2820%29=-40000%2B2000%2820%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-100 ALIGN=MIDDLE  ALT=\"-100\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=400 ALIGN=MIDDLE  ALT=\"400\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-40000 ALIGN=MIDDLE  ALT=\"-40000\"   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=R%2820%29=-40000%2B40000 ALIGN=MIDDLE  ALT=\"R%2820%29=-40000%2B40000\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2000 ALIGN=MIDDLE  ALT=\"2000\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=20 ALIGN=MIDDLE  ALT=\"20\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=40000 ALIGN=MIDDLE  ALT=\"40000\"   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=R%2820%29=0 ALIGN=MIDDLE  ALT=\"R%2820%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms.\r<BR>\n" );
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document.write( "So if the price is $20 per shirt, then he'll break even (he will neither gain or lose money). </SPAN>\n" );
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