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A generator is to be installed in a factory to supply power to $$n$$ machines located at positions $$( x _ { i } , y _ { i } ) , i = 1,2 , \ldots , n$$ . Where should the generator be located to minimize the sum of the squares of its distances from the machines?
$$\text { at } ( \overline { x } , \overline { y } ) \text { where } \overline { x } = ( \sum _ { i = 1 } ^ { n } x _ { i } ) / n , \overline { y } = ( \sum _ { i = 1 } ^ { n } y _ { i } ) / n$$