document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=320043>Question 320043</A>: <I><SPAN STYLE=\"word-break: break-all;\"> This one was a bit tricky for me, If anyone can help, I will greatly appreciate it. Here goes:<BR>\n" );
document.write( "Demand for pools. Tropical Pools sells an aboveground<BR>\n" );
document.write( "model for p dollars each. The monthly revenue for this<BR>\n" );
document.write( "model is given by the formula<BR>\n" );
document.write( "R(p)= -0.08p2 + 300p.<BR>\n" );
document.write( "Revenue is the product of the price p and the demand<BR>\n" );
document.write( "(quantity sold).<BR>\n" );
document.write( "a) Factor out the price on the right-hand side of the<BR>\n" );
document.write( "formula.<BR>\n" );
document.write( "b) Write a formula D(p) for the monthly demand.<BR>\n" );
document.write( "c) Find D(3000).<BR>\n" );
document.write( "d) Use the accompanying graph to estimate the price at<BR>\n" );
document.write( "which the revenue is maximized. Approximately how<BR>\n" );
document.write( "many pools will be sold monthly at this price?<BR>\n" );
document.write( "e) What is the approximate maximum revenue?<BR>\n" );
document.write( "f) Use the accompanying graph to estimate the price at<BR>\n" );
document.write( "which the revenue is zero<BR>\n" );
document.write( "to solve each problem.\r<BR>\n" );
document.write( "\n" );
document.write( "Price (dollars)<BR>\n" );
document.write( "Revenue (thousands     <BR>\n" );
document.write( "                        300\r<BR>\n" );
document.write( "\n" );
document.write( "                        200\r<BR>\n" );
document.write( "\n" );
document.write( "                        100\r<BR>\n" );
document.write( "\n" );
document.write( "                        0<BR>\n" );
document.write( "                        1000 2000 3000 4000\r<BR>\n" );
document.write( "\n" );
document.write( "                        Price (dollars<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #229290 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=229290\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Demand for pools. Tropical Pools sells an above ground model for p dollars each. <BR>\n" );
document.write( "The monthly revenue for this model is given by the formula<BR>\n" );
document.write( "R(p)= -0.08p^2 + 300p.<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Revenue is the product of the price p and the demand(quantity sold).<BR>\n" );
document.write( ";<BR>\n" );
document.write( "a) Factor out the price on the right-hand side of the formula.<BR>\n" );
document.write( "R(p)= p(-0.08p + 300).<BR>\n" );
document.write( ":<BR>\n" );
document.write( "b) Write a formula D(p) for the monthly demand.<BR>\n" );
document.write( "Demand is equal the revenue divided by the price<BR>\n" );
document.write( "D(p) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p%28-.08p+%2B+300%29%2Fp ALIGN=MIDDLE  ALT=\"p%28-.08p+%2B+300%29%2Fp\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "cancel p;<BR>\n" );
document.write( "D(p) = -.08p + 300<BR>\n" );
document.write( ":<BR>\n" );
document.write( "c) Find D(3000).<BR>\n" );
document.write( "D(3000) = -.08(3000) + 300<BR>\n" );
document.write( "D(3000) = -240 + 300<BR>\n" );
document.write( "D(3000) = 60 pools when the price is $3000<BR>\n" );
document.write( ":<BR>\n" );
document.write( "d) Use the accompanying graph to estimate the price at<BR>\n" );
document.write( "which the revenue is maximized.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+200%2C+-1000%2C+5000%2C+-50000%2C+400000%2C+-.08x%5E2%2B300x%29+ ALIGN=MIDDLE  ALT=\"+graph%28+300%2C+200%2C+-1000%2C+5000%2C+-50000%2C+400000%2C+-.08x%5E2%2B300x%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "$1900 price for max revenue<BR>\n" );
document.write( ":<BR>\n" );
document.write( " Approximately how many pools will be sold monthly at this price?<BR>\n" );
document.write( "28000/1850 = 147 pools sold<BR>\n" );
document.write( ":<BR>\n" );
document.write( "e) What is the approximate maximum revenue?<BR>\n" );
document.write( "$280,000<BR>\n" );
document.write( ":<BR>\n" );
document.write( "f) Use the accompanying graph to estimate the price at which the revenue is zero<BR>\n" );
document.write( "$3800<BR>\n" );
document.write( ":<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );