document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1030987>Question 1030987</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The area of a certain rectangular pen is given by the formula: A(w) = 14w - w^2 ... where w represents the width in feet. a) Determine the width that produces the maximum area. b) What is the length of the pen (find the area with your answer to part a)? c) Of all rectangles, which particular type gives the maximum area? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #645716 by </B><A HREF=/tutors/aboutme.mpl?userid=Alan3354><B>Alan3354(69443)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Alan3354><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=Alan3354><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=645716\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The area of a certain rectangular pen is given by the formula: <BR>\n" );
document.write( "A(w) = 14w - w^2 ... where w represents the width in feet. <BR>\n" );
document.write( "a) Determine the width that produces the maximum area. <BR>\n" );
document.write( "It's the vertex of the parabola.<BR>\n" );
document.write( "A(w) = 14w - w^2<BR>\n" );
document.write( "The vertex is on the Axis of Symmetry, w = -b/2a<BR>\n" );
document.write( "w = -14/-2 = 7<BR>\n" );
document.write( "A(7) = 98 - 49 = 49 sq feet<BR>\n" );
document.write( "b) What is the length of the pen (find the area with your answer to part a)?<BR>\n" );
document.write( "A(7) = 98 - 49 = 49 sq feet<BR>\n" );
document.write( "L = 7 feet, w = 7 feet<BR>\n" );
document.write( "-------------<BR>\n" );
document.write( "c) Of all rectangles, which particular type gives the maximum area?<BR>\n" );
document.write( "A square (for a given perimeter). </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );