document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=204002>Question 204002</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 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)=-0.08p^2 + 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. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #153922 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=153922\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 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)=-0.08p^2 + 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( "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( "D(p) = -0.08p+300<BR>\n" );
document.write( "--------------------------<BR>\n" );
document.write( "c) Find D(3000)= -0.08*3000+300 = 60<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. Approximately how<BR>\n" );
document.write( "many pools will be sold monthly at this price?<BR>\n" );
document.write( "Max occurs when p = -b/2a = -300/(2*-0.08) = 1875<BR>\n" );
document.write( "----------------------------<BR>\n" );
document.write( "e) What is the approximate maximum revenue?<BR>\n" );
document.write( "R(1875) = -0.08(1875)^2+300*1875 = $281,250<BR>\n" );
document.write( "----------------------------\r<BR>\n" );
document.write( "\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( "Comment: No graph appeared in your post.<BR>\n" );
document.write( "================================================<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );