Optimization of the production processes of the industrial enterprise

Optimizing production capacities and finding new ways to reduce labour and capital costs in producing goods requires modern approaches to building production functions, finding their extremes and providing recommendations for production changes. There are several well-known production functions, including Cobb-Douglas, Bertrand, Leontiev, and Weibull. Still, their use requires careful selection for specific production and further search for constituent functions, such as the cost or production functions. To optimize the production process of manufacturing metal products, the task is to choose the production function and find its extremes. After analyzing the given functions, it was found that the optimal function for describing this production is functions based on exponential models, which allow describing non-linear processes and are flexible enough to adapt to different types of production. The work considers ways of optimizing industrial enterprise production processes. It proposes using an approach based on the Weibull equations to estimate labour and capital costs for product production. The search for local extrema of the production function was carried out. Based on the modelling results, recommendations were given regarding the optimal indicators of labour and capital costs. It was determined that the optimal product release plan is the consumption of 0.007 million person-hours and 0.024 million hryvnias. It is also possible to study this function for a minimum and determine at which point, with the ratio of labour and capital costs, there is a minimum production