Question 296318
A rectangular field is to be enclosed with a fence.
 One side of the field is against an existing fence, so that no fence is needed on that side.
 If material for the fence cost $2 per foot for the two ends and $4 per foot for
 the side parallel to the existing fence, find the dimensions of the field of
 the largest area that can be enclosed for 1,000.
:
Let L = length of the $2 sides
Let W = length of the $4 side
:
2(2L) + 4W = 1000
4L + 4W = 1000
Simplify, divide by 4
L + W = 250
L = (250-W)
:
Area:
A = L*W
Replace L with (250-W)
A = (250-W) * W
A = -W^2 = 250W
Find the axis of symmetry: a=-1; b=250, will give max area
W = {{{(-250)/(2*-1)}}}
W = +125 ft, length of $4 side
then
L = 250-125 = 125 ft, length of the $2 sides
:
Max area:  all three sides = 125 ft
:
:
Check 2(2*125) + 4(125) = $1000