Question

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

Answers

Arora
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

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