Quantitative validation of the utility function of secondary schools depending on the costs incurred and determination of its key parameters

This paper examines the general form of the utility function of secondary educational schools in the current year, which is a function dependent on three variables: spending on equipment and consumables in the current year, spending on the staffing of schools in the current year, as well as the total budget of the school. In this work, we assume that the school solves the problem of maximizing its usefulness calculated on the average score of the Unified State Exam (or percent of students with high exam results) in the current year, as well as using real data of educational results and spending of school budgets. The most probable type of this utility function, as well as its parameters is determined in St. Petersburg. The work is one of the first attempts to apply mathematical modeling to the field of large systems management in education.