document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=277463>Question 277463</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me solve this problem: Suppose you have a lemonade stand, and when you charge $2 per cup of lemonade you sell 120 cups. But when you raise your price to $3 you only sell 60 cups. Write an equation for the number of cups you sell as a function of the price you charge. Denote \"C\" for the number of cups, and \"P\" for the price you charge. Assume the function is linear.<BR>\n" );
document.write( "Continuing our lemonade stand question:<BR>\n" );
document.write( "We all know that local revenue (TR) is a function of the price we charge (P) multiplied by the item quantity sold (in our case-Cups),i.,e.,TR=Price*Cups.<BR>\n" );
document.write( "Please write the equation for your TR by inputting your answer from the function you have calculated. What price would you maximize your TR? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #201992 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=201992\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Suppose you have a lemonade stand, and when you charge $2 per cup of lemonade you sell 120 cups. But when you raise your price to $3 you only sell 60 cups. Write an equation for the number of cups you sell as a function of the price you charge. Denote \"C\" for the number of cups, and \"P\" for the price you charge. Assume the function is linear.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "You have two points relating price and cups sold: (2,120) and (3,60)<BR>\n" );
document.write( "Equation you want: C = mp + b where p is price and C is # of cups.<BR>\n" );
document.write( "---<BR>\n" );
document.write( "slope = m = (120-60)/(2-3) = -60<BR>\n" );
document.write( "---<BR>\n" );
document.write( "60 = -60*3 + b<BR>\n" );
document.write( "b = 4*60<BR>\n" );
document.write( "b = 240<BR>\n" );
document.write( "-------------------<BR>\n" );
document.write( "Equation: # of cups sold = -60p + 240<BR>\n" );
document.write( "---------------------\r<BR>\n" );
document.write( "\n" );
document.write( "Continuing our lemonade stand question:<BR>\n" );
document.write( "We all know that local revenue (TR) is a function of the price we charge (P) multiplied by the item quantity sold (in our case-Cups),i.,e.,TR=Price*Cups.<BR>\n" );
document.write( "Please write the equation for your TR by inputting your answer from the function you have calculated. What price would you maximize your TR?<BR>\n" );
document.write( "--------------<BR>\n" );
document.write( "Total Revenue = -60p^2 + 240p<BR>\n" );
document.write( "--<BR>\n" );
document.write( "This is a quadratic equation with a = -60 and b = 240<BR>\n" );
document.write( "Maximum occurs when p = -b/2a = -240/(-120) = 2<BR>\n" );
document.write( "----<BR>\n" );
document.write( "Maximum sales occurs when the price is $2.<BR>\n" );
document.write( "===============================================<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );