document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1191133>Question 1191133</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A school club makes and sells decorations to raise money. The materials for each decoration cost<BR>\n" );
document.write( "$6, and the club sells them for $10 each. They sell 20 decorations per week. They are considering<BR>\n" );
document.write( "raising the price, so they conduct a survey and find that for every dollar increase, they will lose 2<BR>\n" );
document.write( "sales per week. Set up a function and solve to determine what price they should charge to maximize<BR>\n" );
document.write( "profits. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #822899 by </B><A HREF=/tutors/aboutme.mpl?userid=Boreal><B>Boreal(15235)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Boreal><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=Boreal><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=822899\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Their profit is $4 per sale currently<BR>\n" );
document.write( "for each $1 increase they lose 2 sales.<BR>\n" );
document.write( "profit is 4+x, and sales are 20-2x<BR>\n" );
document.write( "so maximize that profit which is f(x)= 80+12x-2x^2<BR>\n" );
document.write( "x=-b/2a maximum or -12/-4 or 3, and f(3)=80+36-18=$98<BR>\n" );
document.write( "so when x=3 the sale price is $13 (profit is $7) and the sales number is 14 (20-3*2)<BR>\n" );
document.write( "The profit is maximum $98 at $13 per decoration sale price. \r<BR>\n" );
document.write( "\n" );
document.write( "Check<BR>\n" );
document.write( "#---price-#---revenue-- N-CP(number-cost to produce)---Profit<BR>\n" );
document.write( "6---$10---20--$200------$120-----------------------------$80<BR>\n" );
document.write( "6---$11---18---$198----- $108-----------------------------$92<BR>\n" );
document.write( "6---$12---16--$192------$96------------------------------$96<BR>\n" );
document.write( "6---$13---14--$182------$84------------------------------$98<BR>\n" );
document.write( "6---$14---12--$168------$72------------------------------$96 </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );