a farmer wants to make a rectangular pasture with 80000 squre meters. if the pasture lies along a river and he feneces the remaning three sides,what dimension shoud he use to minimize the amount fence needed

1 answer

Taking the length as x, and the width as y,

Length of fence = x + y + x = 2x + y

Now, the area has been fixed.
=> xy = k = 80,000
=> y = k/x

Function to minimize = f(x) = Length
= 2x + y
= 2x + (k/x)

f'(x) = d(2x + (k/x))/dx
= 2 - k/(x^2)

Equating f'(x) with zero,
=> 2 - k/(x^2) = 0
=> 2 = k/x^2
=> x^2 = k/2 = 80000/2 = 40000

Hence, x = +200/-200
But length cannot be negative, so x = 200

=> x = 200, y = (80000/200) = 400