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

24,000,000 = LW
24,000,000/L = W

Perimeter = 3 widths + 2 lengths

Y = 3(24,000,000/x) + 2x
Find the minimum on this graph on the TI83. (You could also do the first derivative and solve it for x.)

The minimum perimeter is when the 2 lengths are 6,000 feet and the 3 widths are each 4,000 feet.