document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=228146>Question 228146</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 2.    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.  \r<BR>\n" );
document.write( "\n" );
document.write( "a.    Write an equation for the number of cups you sell as a function of the price you charge.  \r<BR>\n" );
document.write( "\n" );
document.write( "b.    Denote \"C\" for number of cups, and \"P\" for the price you charge.\r<BR>\n" );
document.write( "\n" );
document.write( "c.    Assume the function is linear.\r<BR>\n" );
document.write( "\n" );
document.write( " \r<BR>\n" );
document.write( "\n" );
document.write( "3.    Continuing our lemonade stand question:\r<BR>\n" );
document.write( "\n" );
document.write( "a.    We all know that total revenue (TR) is a function of the price we charged (P) multiplied by the item quantity sold (in our case – Cups), i.e., TR = Price * Cups\r<BR>\n" );
document.write( "\n" );
document.write( "b.    Please write the equation for your TR by inputting your answer from the function you have calculated in question #2.\r<BR>\n" );
document.write( "\n" );
document.write( "c. What price would maximize your TR?\r<BR>\n" );
document.write( "\n" );
document.write( " \r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #169426 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=169426\">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. <BR>\n" );
document.write( "a. Write an equation for the number of cups you sell as a function of the price you charge.<BR>\n" );
document.write( "You have two points relating cups sold and price: (120,2)(60,3)<BR>\n" );
document.write( "slope = (2-3)/(120-60) = -1/60<BR>\n" );
document.write( "Since 2 = (-1/60)*120+b, b = 2+2 = 4<BR>\n" );
document.write( "Equation: <BR>\n" );
document.write( "P = (-1/60)c + 4<BR>\n" );
document.write( "-------------------------- <BR>\n" );
document.write( "b. Denote \"C\" for number of cups, and \"P\" for the price you charge. <BR>\n" );
document.write( "c. Assume the function is linear.<BR>\n" );
document.write( "========================================================================= \r<BR>\n" );
document.write( "\n" );
document.write( "3. Continuing our lemonade stand question: <BR>\n" );
document.write( "a. We all know that total revenue (TR) is a function of the price we charged (P) multiplied by the item quantity sold (in our case – Cups), i.e., TR = Price * Cups <BR>\n" );
document.write( "b. Please write the equation for your TR by inputting your answer from the function you have calculated in question #2.<BR>\n" );
document.write( "TR = c<BR>\n" );
document.write( "TR = (-1/60)c^2 + 4c<BR>\n" );
document.write( "Note: This is a quadratic with a = (-1/60) and b = 4<BR>\n" );
document.write( "-------------------------- <BR>\n" );
document.write( "c. What price would maximize your TR? <BR>\n" );
document.write( "Max occurs when c = -b/2a = -4/(-2/60) = 120 cups<BR>\n" );
document.write( "P(120) = $2 so a price of $2 gives you maximum revenue.<BR>\n" );
document.write( "======================================================<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );