document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=922713>Question 922713</A>: <I><SPAN STYLE=\"word-break: break-all;\"> P(x) = -560x^2 + 5488x - 2695<BR>\n" );
document.write( "where P(x) is the weekly profit in dollars when the price of a cup of<BR>\n" );
document.write( "espresso is x dollars.<BR>\n" );
document.write( "a) What is the weekly profit when the price per cup is $2.75?<BR>\n" );
document.write( "b) What is the total weekly overhead expense which must be covered before<BR>\n" );
document.write( " any profit is made?<BR>\n" );
document.write( "Using an algebraic method, determine exact answers for parts c & d. You<BR>\n" );
document.write( "should use the graph of the function to check your answers.<BR>\n" );
document.write( "c) What is the price of a cup of espresso which will maximize weekly<BR>\n" );
document.write( " profits?<BR>\n" );
document.write( "d) What is the expected maximum weekly profit? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #559715 by </B><A HREF=/tutors/aboutme.mpl?userid=ewatrrr><B>ewatrrr(24785)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ewatrrr><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=ewatrrr><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=559715\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> P(x) = -560x^2 + 5488x - 2695<BR>\n" );
document.write( "a) What is the weekly profit when the price per cup is $2.75?<BR>\n" );
document.write( "P(2.75) = -560x^2 + 5488x - 2695 = $8162<BR>\n" );
document.write( " b) What is the total weekly overhead expense which must be covered before<BR>\n" );
document.write( " any profit is made?  $2695<BR>\n" );
document.write( " Using an algebraic method, determine exact answers for parts c & d. You<BR>\n" );
document.write( " should use the graph of the function to check your answers.<BR>\n" );
document.write( " c) What is the price of a cup of espresso which will maximize weekly<BR>\n" );
document.write( " profits? $4.90<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-5488%2F2%2A-560 ALIGN=MIDDLE  ALT=\"-5488%2F2%2A-560\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 4.9<BR>\n" );
document.write( "P(x) = -560(x -4.90)^2 x^2 + 10750.60<BR>\n" );
document.write( " d) What is the expected maximum weekly profit?<BR>\n" );
document.write( "$10,750.60 </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );