Question 1130473
Bill wants to build a rectangular garden against one side of his house.
 He bought 240 feet of fence.
 what is the dimension of the rectangular garden must be to maximize the area?
:
The perimeter of the fence only, three sides
L + 2w = 240
L = -2w + 240
:
Area
A = L*w
replace L with (-2w+240)
A = w(-2w+240)
A = -2w^2 + 240w
Max area occurs on the axis of symmetry. Find this using formula: x = -b/(2a)
In the above equation a=-2; b=240
w = {{{(-240)/(2*-2)}}}
w = 60 ft width will give max area
find L
L = -2(60) + 240
L = 120 ft is the length
:
Garden dimensions of 120 by 60 will give max area. (7200sq/ft)