document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1125309>Question 1125309</A>: <I><SPAN STYLE=\"word-break: break-all;\"> (40 points) A Middle Eastern oil-producing country estimates that the demand for oil (in millions of barrels per day) is D(p) = 9.5 e^(-0.04p), where p is the price of a barrel of oil. To raise its revenues, should it raise or lower its price from its current level of $120 per barrel?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #741602 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=741602\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the equation of D = 9.5 * e^(-.04 * P) tells the demand based on the price per barrel.\r<BR>\n" );
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document.write( "revenue is equal to demand * price.\r<BR>\n" );
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document.write( "demand is presumably in millions of barrels of oil.\r<BR>\n" );
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document.write( "the price is presumably price per barrel.\r<BR>\n" );
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document.write( "since revenue = demand * price, you can determine the reveue by using the following equation.\r<BR>\n" );
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document.write( "y = 9.5 * e^(-.04 * x) * x.\r<BR>\n" );
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document.write( "y is the revenue, in millions of dollars.<BR>\n" );
document.write( "9.5 * e^(-.04 * x) is the demand, in millions of barrels of oil.<BR>\n" );
document.write( "x is the price per barrel.\r<BR>\n" );
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document.write( "note:\r<BR>\n" );
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document.write( "millions of barrels of oil is assumed.<BR>\n" );
document.write( "it could be any unit multiple, such as thousands of barrels of oil, or billions of barrels of oil.<BR>\n" );
document.write( "i assumed millions, because that seems to be a common unit multiple used when talking about daily production of barrels of oil world wide.<BR>\n" );
document.write( "it really doesn't matter, since the revenue curve is unit independent, i.e. the same conclusions can be formed regardless of the units of measure used.\r<BR>\n" );
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document.write( "what i did was graph the equation of y = 9.5 * e^(-.04*x) * x.\r<BR>\n" );
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document.write( "the graph is shown below:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2018/100501.jpg\" alt=\"$$$\" >\r<BR>\n" );
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document.write( "the graph shows that the revenue will get greater as the price of oil goes down until the price becomes 25 dollars a barrel, when the revenue is maximized at 87.371 million dollars (assuming millions of barrels is the unit of measure).\r<BR>\n" );
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document.write( "any price below that will lead to a decrease in revenue from that peak.\r<BR>\n" );
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document.write( "any price above that will leas to a decrease in revenue from that peak.\r<BR>\n" );
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document.write( "based on this graph, the solution is that reducing the price down from 120 a barrel will result in an increase in revenue as long as the price doesn't go below 25 dollars a barrel.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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