The method of minimization of function which represents the sum of modules of the binomial being the differences of an independent variable and a set of these numbers is considered. Such function determines the sum of the distances measured by length of an arch of some set line from the points belonging to this line to some point (on the same line). Need of minimization of this function can arise for solution of the following question. On the thoroughfare (the railroad, the highway, the river, etc.) there are operating manufacturing enterprises, and it is necessary to deliver their products for further processing to the enterprise which is planned to be located on this highway. It is required to define location of this enterprise proceeding from a condition of the smallest transportation costs.