Question

A farmer wants to fence an area of 24 million square feet in a rectangular field and then divide it in half with a fence parallel to one of the sides of the rectangle. What should the lengths of the sides of the rectangular field be so as to minimize the cost of the fence?
smaller value? and larger value?

Answer 1

Let x = width (with a middle fence parallel to this side)
24000000/x = length

P = length of the fence

P = 3x + 2(24000000/x)

P = 3x + (48000000/x)

dP/dx = 3 - 48000000/x²

for minimum P , dP/dx=0

3 - 48000000/x² = 0

3 = 48000000/x²

3x² = 48000000

x² = 16000000

x = 4000 ft <----width

24000000/x = 6000 ft <----length