Question 453862
A rectangular field having an area of 2700 m^2 is to be enclosed by a fence, and
 an additional fence is to be used to divide the field in the middle.
 The cost of the fence down the middle is $24 per running meter, and the fence
 along the sides cost $36 per running meter. 
Estimate the dimensions of the field so that the total cost of the fencing material is least.
:
the area
L * W = 2700
L = {{{2700/W}}}
:
The perimeter
p = 2L + 2W + W; (3rd width down the middle)
Cost = 36(2L) + 36(2W) + 24W
C = 72L + 72W + 24W
C = 72L + 96W
Replace L with {{{2700/W}}}
C = 72*{{{2700/W}}} + 96W
C = {{{194400/W}}} + 96W
Graph this:
{{{ graph( 300, 200, -20, 80, -1000, 15000, 96x+(194400/x)) }}}
:
looks like min cost occurs when the width is 45 meters
then
length = 2700/45 = 60 meters
therefore
36(2*60) + 36(2*45) + 24(45) = $8640 is the min cost