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The production

$$f(x_i,...,x_n)=\min\{x_i,...,x_n\}$$

is pretty straight forward and usually with smaller size data sets and can usually be picked up on rather quickly in an intuitive sense.

However if one has a very large set of data with a firm that produces $n$ products, how does one go about analyzing the production process and say that such a relationship exists in production of a given good?

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