document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=33152>Question 33152</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0534373526/algebrahomeworkh>College Algebra</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> A soft-drink vendor at a popular beach analyzes his sales records, and finds that if he sells x cans of soda pop in one day, his profit (in dollars) is given by:\r<BR>\n" );
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document.write( "P(x) = -0.001x^2 + 3x - 1800\r<BR>\n" );
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document.write( "What is his maximum profit per day, and how many cans must he sell for maximum profit?\r<BR>\n" );
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document.write( "Thank you very much! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #19566 by </B><A HREF=/tutors/aboutme.mpl?userid=mukhopadhyay><B>mukhopadhyay(490)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=mukhopadhyay><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=19566\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> P(x) is a quadratic function representing a function for parabola.<BR>\n" );
document.write( "The parabola P(x) opens downward; implying the maximum value of the function (for profit) is attained at its vertex.<BR>\n" );
document.write( "The x-coordinate of the vertex is found from -b/2a (for f(x) = ax^2+bx+c);<BR>\n" );
document.write( "In this example a=-.001 and b=3<BR>\n" );
document.write( "Thus, x-coordinate of the vertex is 3/.002 = 1500;<BR>\n" );
document.write( "P(x) for x=1500 is -.001(225*10^4) + 4500 - 1800 = -2250 + 4500 - 1800 = 450<BR>\n" );
document.write( "Answer: The vendor should sell 1,500 cans of soda to make the highest profit of $450.00. </SPAN>\n" );
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