document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=112130>Question 112130</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0618314350/algebrahomeworkh></A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> A real estate office handles 50 apartment units. When the rent is $540 per month, all units are occupied. However, for each $30 increase in rent, one unit becomes vacant. Each occupied unit requires an average of $18 per month for service and repairs. What rent should be charged to obtain the maximum profit? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #82102 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=82102\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A real estate office handles 50 apartment units. When the rent is $540 per month, all units are occupied. However, for each $30 increase in rent, one unit becomes vacant. Each occupied unit requires an average of $18 per month for service and repairs. What rent should be charged to obtain the maximum profit?<BR>\n" );
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document.write( "Let x = no. of $30 increases<BR>\n" );
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document.write( "Also x = no. of vacant apartments<BR>\n" );
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document.write( "Y = Revenue \r<BR>\n" );
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document.write( "y = price per apt * no. of apts<BR>\n" );
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document.write( "y = (540+30x) * (50-x); FOIL this<BR>\n" );
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document.write( "y = 27000 - 540x + 1500x - 30x^2<BR>\n" );
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document.write( "y = -30x^2 + 960x + 27000; arranged as a quadratic equation (a parabola)<BR>\n" );
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document.write( "The axis of symmetry will be the value of x for max profit<BR>\n" );
document.write( "x =<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-960%29%2F%282%2A-30%29 ALIGN=MIDDLE  ALT=\"%28-960%29%2F%282%2A-30%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "x =<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-960%29%2F%28-60%29 ALIGN=MIDDLE  ALT=\"%28-960%29%2F%28-60%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "x = 16; no. of increases of $30 and 16 apts vacant<BR>\n" );
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document.write( "Use x = 16 to find the rent for max profit:<BR>\n" );
document.write( "540 + (30*16) = $1020 per month<BR>\n" );
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document.write( "Find the actual profit by subtracting the service fee from the rental of 34 apts:<BR>\n" );
document.write( "(50-16)*(1020 - 18) =<BR>\n" );
document.write( " 34 * 1002 = $34,068<BR>\n" );
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document.write( "Did this help?<BR>\n" );
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