document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1148699>Question 1148699</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A man can rent all of his apartments if he rents them for $500 each per month. However, for each $50 increase in rent he will rent two fewer apartments. To guarantee the best monetary return, how much monthly rent should he charge and how many apartments will he rent out? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #770061 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=770061\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">  A man can rent all of his apartments if he rents them for $500 each per month. <BR>\n" );
document.write( " However, for each $50 increase in rent he will rent two fewer apartments.<BR>\n" );
document.write( " To guarantee the best monetary return, how much monthly rent should he charge and how many apartments will he rent out?<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Let's assume he has 100 apartments, we need to know this.<BR>\n" );
document.write( "let x = no. $50 increases in rent and each two apt decreases<BR>\n" );
document.write( "then<BR>\n" );
document.write( "Rev = total apts * apt rent amt<BR>\n" );
document.write( "f(x) = (100 - 2x)(500 + 50x) <BR>\n" );
document.write( "FOIL<BR>\n" );
document.write( "f(x) = 50000 + 5000x - 1000x - 100x^2<BR>\n" );
document.write( "a Quadratic equation<BR>\n" );
document.write( "f(x) = -100x^2 + 4000x + 50000<BR>\n" );
document.write( "simplify, divide by 100<BR>\n" );
document.write( "-x^2 + 40x + 500 = 0<BR>\n" );
document.write( "max rev occurs on the axis of symmetry x = -b/(2a)<BR>\n" );
document.write( "x = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-40%29%2F%282%2A-1%29 ALIGN=MIDDLE  ALT=\"%28-40%29%2F%282%2A-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "x = +20 ea $50 increases and 40 apt decreases<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Max revenue occurs when he charges 500+20(50) = $1500!! Outrageous!<BR>\n" );
document.write( "He will be renting 100 - 2(20) = 60 apartments<BR>\n" );
document.write( "Revenue then 60 * 1500 = $90000 vs $50000 renting all 100 at 500 per month<BR>\n" );
document.write( ":<BR>\n" );
document.write( "\"But how about the all the hardship you are causing these renters, is there a price on that?\" What good is it, if you gain the whole world and lose your soul!!\" <BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );