document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=196967>Question 196967</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A club usually sells 1200 shirts a year at $20 each. A survey indicates that for every $2 increase in price, there will be a drop of 60 sales a year. What price they should charge for each shirt to maximize the revenue? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #147733 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=147733\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A club usually sells 1200 shirts a year at $20 each. A survey indicates that<BR>\n" );
document.write( " for every $2 increase in price, there will be a drop of 60 sales a year.<BR>\n" );
document.write( " What price they should charge for each shirt to maximize the revenue?<BR>\n" );
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document.write( "Let x = no. of $2 increases<BR>\n" );
document.write( "also<BR>\n" );
document.write( "Let x = no. 60 shirt sales reductions<BR>\n" );
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document.write( "Price = (20 + 2x)<BR>\n" );
document.write( "No. of shirts = (1200 - 60x)<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Revenue = price * no. of shirts sold, therefore:<BR>\n" );
document.write( "R = (20 + 2x)*(1200 - 60x)<BR>\n" );
document.write( "FOIL<BR>\n" );
document.write( "R = 24000 - 1200x + 2400x - 120x^2<BR>\n" );
document.write( "Arranges as a quadratic equation<BR>\n" );
document.write( "R = -120x^2 + 1200x + 24000<BR>\n" );
document.write( "Find the axis of symmetry to find the price for max revenue: x = -b/(2a)<BR>\n" );
document.write( "In this equation; a=-120; b=1200<BR>\n" );
document.write( "x = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-1200%29%2F%282%2A-120%29 ALIGN=MIDDLE  ALT=\"%28-1200%29%2F%282%2A-120%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=%28-1200%29%2F%28-240%29 ALIGN=MIDDLE  ALT=\"%28-1200%29%2F%28-240%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "x = +5 ea $2 increases<BR>\n" );
document.write( "and<BR>\n" );
document.write( "5*60 = 300 reduction in shirt sales:<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Price for max sales; 20 +2(5) = $30, will sell 1200 - 300 = 900 shirts<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Max revenue: 30 * 900 = $27,000<BR>\n" );
document.write( ";<BR>\n" );
document.write( ":<BR>\n" );
document.write( "How about this? Did this make sense to you?<BR>\n" );
document.write( " </SPAN>\n" );
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