Analytical Solution for the Generalized Fermat-Torricelli Problem

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We present explicit analytical solution for the problem of minimization of the function F(x,y)= ∑ⱼ₌₁³ mⱼ √(x-xⱼ)²+(y-yⱼ)², i.e. we find the coordinates of stationary point and the corresponding critical value of F(x,y) as functions of mⱼ,xⱼ,yⱼⱼ₌₁³. In addition, we also discuss inverse problem of finding such values of m₁,m₂,m₃ with the aim for the corresponding function F to posses a prescribed position of stationary point.