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For the Weber problem of construction of the minimal cost planar weightednetwork connecting four terminals with two extra facilities, the solution byradicals is proposed. The conditions for the existence of the network in theassumed topology and the explicit formulae for coordinates of the facilitiesare presented. The obtained results are utilized for investigation of thenetwork dynamics under variation of parameters. Extension of the results to thegeneral Weber problem is also discussed.

Geometry and Analytics of the Multifacility Weber Problem