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?

1 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) !