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Algebra
Question

A generator is to be installed in a factory to su...

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?

Answer

\(\text { at } ( \overline { x } , \overline { y } ) \text { where } \overline { x } = ( \sum _ { i = 1 } ^ { n } x _ { i } ) / n , \overline { y } = ( \sum _ { i = 1 } ^ { n } y _ { i } ) / n\)

Solution
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