<PRE><B>Question 322751</B>
A rectangular field is to be enclosed by a fence and  Ithen divided into two
 small plots by a fence parallel to one of the sides. 
If there is 1800 m of fencing available, find the dimensions of the field that will give the maximum area.
:
2L + 3W = 1800
2L = 1800-3W
Divide both sides by 2
L = (900-1.5W)
:
Area = L * W
Replace L with (900-1.5W)
A = W(900-1.5W)
A = -1.5W^2 + 900W
Find the axis of symmetry, x=-b/(2a); in this equation: a=-1.5, b=900
W = {{{(-900)/(2*-1.5)}}}
W = {{{(-900)/(-3)}}}
W = +300 m is the width for max area
then
L = 900 - 1.5(300)
L = 450 m is the length
and
300 * 450 = 135,000 sq/m is max area</PRE>