document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1107128>Question 1107128</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Giselle wants to run a tutoring program over the summer. She comes up with the following profit function: P(x)=-2x^2+100x=25 where x represents the price of the program.  Between what two prices should she charge to make a profit? How much should she charge her students if she wants to make the most profit? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #722187 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=722187\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The function is -2x^2+100x-25=0, and positive is profit.<BR>\n" );
document.write( "Can graph it<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C300%2C-15%2C70%2C-200%2C1500%2C-2x%5E2%2B100x-25%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C300%2C-15%2C70%2C-200%2C1500%2C-2x%5E2%2B100x-25%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Need zeros to show the range of values<BR>\n" );
document.write( "multiplying by -1 get 2x^2-100x+25=0<BR>\n" );
document.write( "x=(1/4)(100+/-sqrt(10000-200); sqrt(9800)=98.99<BR>\n" );
document.write( "x=(1/4)(198.99)=49.75 and x=(1/4)(1.01) or 0.25, round to $0.26, exact is $0.2525.<BR>\n" );
document.write( "Maximum is at vertex. and x=-b/2a=-100/4=$25<BR>\n" );
document.write( "Between $0.25 and $49.75, maximum at $25. </SPAN>\n" );
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