document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1195270>Question 1195270</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Suppose the demand price for selling	out a production run of x DVDs is given by	p(x)=-0.0005x^2+60 dollars per DVD. Further suppose the weekly cost of producing these DVDs is given by C(x)=-0.001x^2+18x+4000 dollars	to produce that many DVDs.\r<BR>\n" );
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document.write( "(i) Write the Revenue function R(x). And be sure to state its DOMAIN.\r<BR>\n" );
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document.write( "(ii) Use (i) to write the profit	function P(x). Again, be sure to state its DOMAIN.\r<BR>\n" );
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document.write( "I am very confused as to how to get the domain in these problems because initially I thought it was (-infinity, infinity) for both revenue function and profit function, but my professor said that mathematically this is correct, but since we're talking about the real world it would be something else and it wouldn't make sense to have negative infinity, and I would like an explanation as to how to get the domain. Would the interval be (0, infinity) for both, or is there a method to figuring out the domain in this situation. \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 #827699 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</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=827699\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( " the demand price for selling out a production run of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > DVDs is given by \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p%28x%29=-0.0005x%5E2%2B60 ALIGN=MIDDLE  ALT=\"p%28x%29=-0.0005x%5E2%2B60\"   DISABLED_style= \"max-width:90%; height:auto;\" >  \r<BR>\n" );
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document.write( "the weekly cost of producing  is given by \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%28x%29=-0.001x%5E2%2B18x%2B4000+ ALIGN=MIDDLE  ALT=\"C%28x%29=-0.001x%5E2%2B18x%2B4000+\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "so, we have\r<BR>\n" );
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document.write( "demand price: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+p%28x%29=-0.0005x%5E2%2B60+ ALIGN=MIDDLE  ALT=\"+p%28x%29=-0.0005x%5E2%2B60+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "weekly cost : <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%28x%29=-0.001x%5E2%2B18x%2B4000 ALIGN=MIDDLE  ALT=\"C%28x%29=-0.001x%5E2%2B18x%2B4000\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "i)\r<BR>\n" );
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document.write( "the Revenue function <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R%28x%29 ALIGN=MIDDLE  ALT=\"R%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >:\r<BR>\n" );
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document.write( "Revenue is equal to the number of units sold times the price per unit. To obtain the revenue function, multiply the output level by the price function.\r<BR>\n" );
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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;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R%28x%29=+x%2A%28-0.0005x%5E2%2B60%29 ALIGN=MIDDLE  ALT=\"R%28x%29=+x%2A%28-0.0005x%5E2%2B60%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%28x%29=+-0.0005x%5E3%2B60x ALIGN=MIDDLE  ALT=\"R%28x%29=+-0.0005x%5E3%2B60x\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "DOMAIN:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R+ ALIGN=MIDDLE  ALT=\"R+\"   DISABLED_style= \"max-width:90%; height:auto;\" >(all real numbers)<BR>\n" );
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document.write( "so, domain is all <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+%3E=0 ALIGN=MIDDLE  ALT=\"x+%3E=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "interval notation: \r<BR>\n" );
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document.write( "[<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=infinity ALIGN=MIDDLE  ALT=\"infinity\"   DISABLED_style= \"max-width:90%; height:auto;\" >)\r<BR>\n" );
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document.write( "ii)\r<BR>\n" );
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document.write( "The profit a business makes is equal to the revenue it takes in minus what it spends as costs. To obtain the profit function, subtract costs from revenue.\r<BR>\n" );
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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" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28x%29=-0.0005x%5E3%2B60x+-+%28-0.001x%5E2%2B18x%2B4000%29 ALIGN=MIDDLE  ALT=\"P%28x%29=-0.0005x%5E3%2B60x+-+%28-0.001x%5E2%2B18x%2B4000%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=-0.0005x%5E3%2B60x+%2B0.001x%5E2-18x-4000 ALIGN=MIDDLE  ALT=\"P%28x%29=-0.0005x%5E3%2B60x+%2B0.001x%5E2-18x-4000\"   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=-0.0005x%5E3+%2B+0.001x%5E2+%2B+42x+-+4000 ALIGN=MIDDLE  ALT=\"P%28x%29=-0.0005x%5E3+%2B+0.001x%5E2+%2B+42x+-+4000\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "DOMAIN:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R ALIGN=MIDDLE  ALT=\"R\"   DISABLED_style= \"max-width:90%; height:auto;\" > (all real numbers)\r<BR>\n" );
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document.write( "so, domain is all <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+%3E=0 ALIGN=MIDDLE  ALT=\"x+%3E=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "interval notation: \r<BR>\n" );
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document.write( "[<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=infinity ALIGN=MIDDLE  ALT=\"infinity\"   DISABLED_style= \"max-width:90%; height:auto;\" >)\r<BR>\n" );
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