A farmer wants to fence an area of 6 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?

Question

Mathematics

Naima Castro

5 February, 16:41

A farmer wants to fence an area of 6 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?

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Chuckles · Answer 1

3x + 2y A = xy = 6,000,000 y = 6,000, 000/x L = 2x + 12,000,000/x 3 - (12,000,000/x^2) = 0 3 = 12, 000,000/x^2 sqrt x^2 = sqrt 4,000,000 x = 2,000 and y = 3,000