document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1094144>Question 1094144</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A company can produce a doll at a cost of $5 per dolls. When the company sells the dolls at a price of $40 they can sell 400 dolls each week. It is estimated that for every $0.50 decrease in the price, they can sell 20 more dolls.<BR>\n" );
document.write( "Find the price that will maximize the profit for the company. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #708741 by </B><A HREF=/tutors/aboutme.mpl?userid=josmiceli><B>josmiceli(19441)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josmiceli><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=josmiceli><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=708741\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+P+ ALIGN=MIDDLE  ALT=\"+P+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = profit per week<BR>\n" );
document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+n+ ALIGN=MIDDLE  ALT=\"+n+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = the number of $.50 decreases in price<BR>\n" );
document.write( "[ profit ] = [ income ] - [ cost ]<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+P+=+%28+40+-+.5n+%29%2A%28+400+%2B+20n+%29+-+%28+400+%2B+20n+%29%2A5+ ALIGN=MIDDLE  ALT=\"+P+=+%28+40+-+.5n+%29%2A%28+400+%2B+20n+%29+-+%28+400+%2B+20n+%29%2A5+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+P+=+%28+40+-+5+-+.5n+%29%2A%28+400+%2B+20n+%29+ ALIGN=MIDDLE  ALT=\"+P+=+%28+40+-+5+-+.5n+%29%2A%28+400+%2B+20n+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+P+=+%28+35+-+.5n+%29%2A%28+400+%2B+20n+%29+ ALIGN=MIDDLE  ALT=\"+P+=+%28+35+-+.5n+%29%2A%28+400+%2B+20n+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+P+=+14000+-+200n+%2B+700n+-+10n%5E2+ ALIGN=MIDDLE  ALT=\"+P+=+14000+-+200n+%2B+700n+-+10n%5E2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+P+=+-10n%5E2+%2B+500n+%2B+14000+ ALIGN=MIDDLE  ALT=\"+P+=+-10n%5E2+%2B+500n+%2B+14000+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+P+=+-n%5E2+%2B+50n+%2B+1400+ ALIGN=MIDDLE  ALT=\"+P+=+-n%5E2+%2B+50n+%2B+1400+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-------------------------------------<BR>\n" );
document.write( "The n-value of the maximum is at:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+n%5Bmax%5D+=+-b%2F%282a%29+ ALIGN=MIDDLE  ALT=\"+n%5Bmax%5D+=+-b%2F%282a%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+a+=+-1+ ALIGN=MIDDLE  ALT=\"+a+=+-1+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+b+=+50+ ALIGN=MIDDLE  ALT=\"+b+=+50+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+n%5Bmax%5D+=+-50%2F%282%2A%28-1%29%29+ ALIGN=MIDDLE  ALT=\"+n%5Bmax%5D+=+-50%2F%282%2A%28-1%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+n%5Bmax%5D+=+25+ ALIGN=MIDDLE  ALT=\"+n%5Bmax%5D+=+25+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+P%5Bmax%5D+=+-10%2A25%5E2+%2B+500%2A25+%2B+14000+ ALIGN=MIDDLE  ALT=\"+P%5Bmax%5D+=+-10%2A25%5E2+%2B+500%2A25+%2B+14000+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+P%5Bmax%5D+=+-6250+%2B+12500+%2B+14000+ ALIGN=MIDDLE  ALT=\"+P%5Bmax%5D+=+-6250+%2B+12500+%2B+14000+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+P%5Bmax%5D+=+20250+ ALIGN=MIDDLE  ALT=\"+P%5Bmax%5D+=+20250+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The maximum weekly profit is $20,250<BR>\n" );
document.write( "The price that will maximize the profit is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+40+-+.5n+ ALIGN=MIDDLE  ALT=\"+40+-+.5n+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+40+-+.5%2A25+ ALIGN=MIDDLE  ALT=\"+40+-+.5%2A25+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+40+-+12.5+=+27.5+ ALIGN=MIDDLE  ALT=\"+40+-+12.5+=+27.5+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "$27.50 per doll<BR>\n" );
document.write( "------------------------------------------<BR>\n" );
document.write( "check:<BR>\n" );
document.write( "Here's the plot:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+400%2C+400%2C+-10%2C+60%2C+-2000%2C+25000%2C+-10x%5E2+%2B+500x+%2B+14000+%29+ ALIGN=MIDDLE  ALT=\"+graph%28+400%2C+400%2C+-10%2C+60%2C+-2000%2C+25000%2C+-10x%5E2+%2B+500x+%2B+14000+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );