In this paper is presented the mathematical model for the optimization of a radial electric network, taking into account the cost of investment in an electric line, the cost of line losses and the cost of load supplied from a source and constraints. The constraints are for sources, for loads and for the power lines. The purpose of the paper is to determine the optimal configuration (graph) of a test system that comprises three sources, two loads and six power lines. The optimal graph for the test system is determined based on the optimization results.