ANALYSIS OF THE PROBLEMS OF MAXIMIZING PRODUCTION VOLUME IN THE CONDITIONS OF LIMITED BUDGET IN THE ACTIVITIES OF ENTERPRISES USING MATHEMATICAL METHODS
Keywords:
Keywords: production function, Cobb-Douglas model, optimization, Lagrangian method, labor and capital, budget constraint, marginal productivity, economic and mathematical modeling.Abstract
Annotation: This scientific article analyzes the problems of maximizing production volume in the conditions of limited budget in the activities of enterprises using mathematical methods. The relevance of the research is that in a modern competitive market, the allocation of resources (labor and capital) based on empirical or intuitive factors leads to economic inefficiency for enterprises. The Cobb-Douglas production function and the Lagrange multiplier method (conditional extremum) were used as a solution to the problem. The mathematical calculations and the results obtained show that the optimal proportion of resources is directly related to their prices and the level of elasticity in production. The scientific and practical contribution of the study is that a specific mathematical algorithm and the optimal point for the distribution of limited financial resources between capital and labor were calculated on the example of a local textile enterprise.
