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?

Question

anonymous · Answer

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anonymous · Answer

$$P=3x+2y$$
$$xy=24\iff y=\frac{24}{x}$$
$$P(x)=3x+\frac{48}{x}$$ minimize that one

anonymous · Answer

assuming side length of the field is x and y
 the perimeter including the divider is 2x + 3y = L
 the area is xy = 24000000
 so the problem is to find L's minimum with constraint of xy = 24000000
 solution is x = 5948 y = 4034 L = 23998