Question

I am confused on how to solve this problem?

We need to enclose a field with a rectangular fence. We have 500 ft of
fencing material and a building is on one side of the field and so won’t need any fencing.
Determine the dimensions of the field that will enclose the largest area.

Answer 1

Solutions ne Since need to enclose a field with a rectangular fence, let length of such Rectangular fence ben a breath be y y & 2soft Takes the 250 ft n. K si shape of Square Since we have total 500 ft of fencing material. So ty= 0 Now, let Area of such Rectangular field = A= xy - need to maximise the area provided provided ty=500 : he So let 500- x y = Now substitute Equ (111) in Equ, he A = xy = x(500-4) = 500 x- x2 Now differentiating Equ (*) , wrt &, wegeti

500 - 2x ** d dr Now put da 500- 2xco ) x=500 250 dx 2 na 250 eget, maximum area for dA=o; - 2 co dx duz Now, let us differentiate Equ (**) wit x. again, d3 weshall get axim rence; for largest Area Eln= 250 And so from earl, y = 5000 dimensions are (n.y) = (250, 250) Pruel 250 (y=250 -500 n = 500 - 200 = 2