Question

A farmer plans to enclose a rectangular pasture adjacent to a river. (see figure). The pasture must contain 320,000 square meters in order to provide enough grass for the herd. What dimensions will require the least amount of fencing if no fencing is needed along the river?
x = m
y = m


Plz help...thnks

Answer 1

Since length x width = area
we have length=area/width

Let
w=width of the pasture, and
320000/w=length (parallel to river) of pasture
Total length of fencing
F=twice width + length
=2w + 320000/w

Find derivative of F with respect to w and equate to zero to find w.
i.e.
Solve for w in
dF/dw=0