Question

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. Find the dimensions of the rectangle he should use to minimize the cost of fencing. List the dimensions in non-decreasing order.

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

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