In the process of multivariate design of machining technology, one of the important tasks is to select the optimal cutting conditions at the final transitions of the forming process, providing a given quality of the surfaces on the workpiece made of the appropriate material. At the same time, to describe most of the design procedures of the machining process, there are problems associated with the algorithm for choosing the solution method, the response function and the range of acceptable solutions at all stages of processing. In this paper, as an algorithm for solving the problem, we propose the use of the known method of extreme planning of the experiment, which allows to obtain a mathematical model of the investigated multifactorial process with incomplete knowledge of its optimization mechanism. In the process of implementation of this algorithm in real production conditions on the basis of a priori information, the research area was chosen and the main levels of factors and intervals of their variation in this area were established. Then a full factorial experiment was carried out and its results were processed on the basis of a linear polynomial taking into account linear effects and interaction effects. As a result of testing the polynomial confidence intervals were determined for all regression coefficients by four parallel experiments at the same values of factors. In the second phase, were evaluated the adequacy of most mathematical models of the Fisher test. In the end, the transition from the coded values of the factors in the mathematical model to their natural values was carried out. Using the final model with natural values of the factors, a numerical experiment was conducted, which determined the optimum region with the most unfavorable treatment mode. Such a study allows to simplify the procedure for assigning the processing mode of the workpiece at the final stage in the conditions of the current production, while ensuring the specified quality of the machined surfaces and maintaining the productivity of the forming process. This technique is the subject of consideration in this work.