A farmer wants to fence off a rectangular field of area 15000 square feet using barbed wire fencing. SInce the opposite of the road is a corn-field, he wants a two-strand fence along the road, and one strand on each of the other three sides. What are the dimensions of the field which minimize the amount of fence used?

Question

Steve · Answer

if the 2-strand dimension is x, then we have

f(x) = 2x + x + 2(15000/x)
df/dx = 3 - 30000/x^2
min fence when df/dx = 0, at x = 100

so, the field is 100x150

as usual, the fencing is divided equally among the dimensions.

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f(x) = fencing(x) !