ECONOMIC-MATHEMATICAL METHODS AND MODELS IN MANAGEMENT OF ECONOMIC ACTIVITY OF AGRICULTURAL ENTERPRISES

The paper summarizes the most common mathematical methods used in the analysis, planning, organization, and management of economic activities of agricultural enterprises. It is determined that mathematical methods in combination with qualitative, logical methods of analysis contribute to the correct assessment of production efficiency or assessment of individual economic phenomena. It is a set of methods that turns analysis into truly scientific means of production management. It is proved that the most important universal method of research of economic activity of the enterprise is the method of modeling and construction of mathematical model of economic object. The study of economic processes in agricultural enterprises with the help of economic and mathematical modeling allows to assess the level of efficiency of the enterprise for the past period and to predict the effect of the implementation of certain management measures. Particular attention is paid to the principle of classification of economic and mathematical models on various grounds used in agricultural production during management decisions. The optimization models which make the widest group of models are considered and are intended for a choice of an optimum variant which will provide the maximum efficiency of the enterprise. Different approaches to the choice of basic parameters for building models to determine the resource potential are presented. It is revealed that during modeling it is necessary to follow the system approach, considering not only separate components and their interrelations, but also all system as a whole. It is advisable to use a system of models of parameters, characteristics, con-dition, and behavior in the external environment of interconnected economic processes, taking into account the complex structure of the organization, which will increase the adequacy and accuracy of results obtained in management decisions by managers of agricultural enterprises. It is established that economic-mathematical modeling allows to effectively solve specific economic problems and practical problems in the field of enterprise management in order to minimize the negative economic consequences.

Management decisions are the result of analysis, fore casting and evaluation of the situation, choosing the best alternative to achieve the goal. At the same time, it is the result of the management's choice of course of action, aimed at solving the problem in the current or projected situation [1].
Decisionmaking technology is a set of actions consis ting of individual stages, procedures, operations. Under such conditions, economic and mathematical methods and mode ling are important tools for making managerial decisions.

Випуск 1 (3), 2022
Землеробство та рослинництво: теорія і практика Mathematical methods accelerate economic analy sis, contribute to a fuller consideration of the impact of performance factors and increase the accuracy of cal culations. Analysis using economic and mathematical methods allows to predict the further development of an economic process, which will increase the efficien cy of agricultural production. Economicmathematical methods are a set of mathematical methods (mathemati cal statistics, probability theory, mathematical program ming, etc.), used to solve various economic problems in science and practice [2; 3].
The aim of the study -deepening the essence and highlighting the varieties of the most common mathema tical methods and models, which are used in the analysis, planning, organization, and management of economic activities of agricultural enterprises and substantiation of different approaches to the choice of parameters for building models for determining resource potential. That is why the study of the use of economic and mathemati cal methods and models in the management of economic activity of agricultural enterprises is relevant in the cur rent environment.
Materials and methods of research. The material of the study was the work of domestic scientists on the use of economic and mathematical methods and mo dels in enterprise management. The following methods and techniques were used to achieve this goal: selective (when selecting economicmathematical methods and models for analysis), comparative (in the study of cost management concepts, to find similarities and differen ces between them), abstractlogical (during the forma tion of conclusions), system analysis (for the correct choice of system tools in order to solve the problem) and genera lization (to generalize the results of research of domestic scientists and the formation of logical con clusions).
Results and discussion. Mathematical methods of analysis contribute to a reasonable assessment of the efficiency of production or individual econo mic phenomena only in organic unity with qualitative, logical methods of analysis. It is the combination of quantitative and qualitative methods that transforms analysis into truly scientific means of production management. Analyzing the economic activity of enterprises often combine balance sheet and factor methods. It is noted that the balance sheet method is used as a way to compare interrelated indicators of economic activity in order to determine and calcu late their mutual influence, as well as the calculation of reserves to improve production efficiency. Factor analysis is a method of finding and classifying fac tors by identifying causal relationships, affecting the change of specific indicators of economic activity. Methods of multiple and pair correlation analysis, which are used to study the relationships of correla tionrelated variables, have become widespread in economic analysis. [4].
A number of economic and mathematical methods are based on the concept of normal distribution law. Therefore, for the correct application of economic and statistical methods requires verification of the norma lity of the laws of distribution of variables. One of the methods of multidimensional analysis is cluster ana lysis, which is used to group (cluster) certain objects by a set of features. Grouping of economic objects is important for the identification of similar enterprises in order to develop general standards for planning and evaluation of objects based on the results of economic activity [5].
The most important universal method of studying the economic activity of the enterprise is the method of mo deling. Modeling and construction of a mathematical model of an economic object make it possible to con centrate the economic analysis of production processes to mathematical analysis and effective decisionmaking. Therefore, the revision of theoretical and methodologi cal principles and the development of promising areas of economic and mathematical modeling and outlining effec tive mechanisms for their application in solving practical problems and problems becomes especially important [6].
The model is usually different from the object of study, but, of course, has similarities with this object, es pecially in terms of those characteristics that are to be studied and predicted [7].
There are various economic and mathematical mod els used in research. The most common are the laws of correlation and regression analysis, production functions and systems of economic equations. For the most part, current research in economics and management focuses on data analysis using a single tool.
The application of mathematical modeling of eco nomic and production processes allows you to effective ly use the available resource base in the process of achie ving the strategic goals of the agricultural enterprise and take into account significant sources of uncertainty and minimize negative economic consequences [8; 9].
Development of models should be carried out accor ding to a certain algorithm. First formulate the purpose Економіка 81 Землеробство та рослинництво: теорія і практика Випуск 1 (3), 2022 of modeling, then express a hypothesis that represents a qualitative description of the system, choose the type of model and mathematical methods of its description depending on the goal. The final stage is to create a mo del and test it for the reliability of the description of the process, object or phenomenon [10].
An important point of the simulation is a clear defi nition of the criterion according to which the different solutions will be compared. In economic analysis, such criteria may be: the highest profit, the lowest production costs, maximum equipment load, labor productivity, etc. If the results do not correspond to the real production conditions, it is necessary to make an economic analy sis of the reasons for noncompliance. This may be the lack of reliability of information, and the inconsistency of mathematical methods to the characteristics of the economic object being studied. Once the cause is iden tified, adjustments are made to the model and the prob lemsolving process is repeated [11].
The study of economic processes in agricultural en terprises with the help of economic and mathematical modeling makes it possible to assess the level of effi ciency of the enterprise for the past period and predict the effect of the implementation of certain management measures [12].
Economic and mathematical models used in agricul tural production are classified according to various cha racteristics: • by the general purpose: theoretical and analytical (to study the general properties and patterns of economic processes), applied (for solving specific economic problems); • by the degree of aggregation: microeconomic (ref lect the activities of agricultural enterprises), mac roeconomic (reflect the functioning of the econo my as a whole); • by a specific purpose: optimization models (nee ded to choose the best option available), simulation models (necessary for the use of computer simu lation of processes), gaming models (required for the object of simulation in the uncertainty of the parameters studied); • by the time factor: statistical, dynamic [8; 13].
• by the approach to the object, there are normative models that reflect the processes of purposeful re gulation, and descriptive models that allow analy sis to explain the facts being investigated; • by the way of expressing the relationships between the characteristics to be determined, external con ditions, internal parameters distinguish structural models that reflect the internal organization of the economic process (its constituent elements, their relationships, links with input and output informa tion), and functional models that simulate the ope ration of the process [14].
The broadest group of models that can be developed using mathematical programming methods are optimi zation models. Such models are designed to select the optimal (best) option from a variety of options, which will best meet market conditions and ensure maximum efficiency of the enterprise [15].
The optimization economic and mathematical model is based on the limitations of the agricultural enterprise. Constraints are in the form of linear inequalities or equa tions. The economic meaning of restrictions is diverse and depends on the content of the tasks. The most typi cal of the restrictions are: restrictions on the volume of production; restrictions on production resources. Con straints of the first and second types in the problem can be many: for each type of material, fuel, energy, equip ment, number of employees, financial resources, capacity of enterprises, etc. Therefore, the most important factor influencing the quality of strategic analysis in agriculture is to determine the limitations of the enterprise and the correctness of their reflection in the form of equations and inequalities [16].
For the stable development of each agricultural en terprise the key is to provide the necessary amount of material and technical resources. At the same time, it is important to conduct timely economicmathematical and statistical analysis of their presence. Given the limited availability of material and monetary resources, there is an urgent need for a more thorough study of econo mic indicators based on the use of mathematical methods of research and development of complex economic and mathematical models [8].
Rational use of production assets is one of the most important tasks, the solution of which helps to increase the efficiency of agricultural production. In solving eco nomic problems, taking into account the provision of the enterprise with resources is of particular importance, be cause any type of resource at a particular time is limited. The main principle of optimal development of agricul ture is to ensure the maximum effect with the rational use of limited resources [17].

Землеробство та рослинництво: теорія і практика
With this in mind, consider the model of resource op timization as an important tool for determining the re source potential and management of economic activity of the enterprise.
In general, the problem of rational use of resources is formulated as follows: the company produces n types of products, using m types of resources; the matrix of spe cific resource costs has the form: A = // a ij // (i = 1, m; j = 1, n), where a ij -the number of units of the i-th type of resources, spent on the production of the j-th type of pro duct unit; resource reserves are expressed as b i (i = 1, m), profit -c j ( j = 1, n), and the desired planned production of the j-th type x j ( j = 1, n). Then the objective function, which expresses the requirement to maximize the total profit Z, takes the form: (1) Constraints that reflect the fact that resource costs cannot exceed their inventories are: Variables are also subject to nonnegative conditions: The solution to the problem is to determine the nonnegative values of the variables х 1 , х 2 , ..., х n , which satisfy the system of basic constraints and give the max imum of the target function [18].
When building an economicmathematical model must be taken into account: characteristics of changing external conditions, a certain set of internal parameters that are necessary and can in accordance with the pur pose of modeling to characterize a particular economic process, as well as the parameters or characteristics of the process to be obtained [19; 20].
Different experts choose different parameters as de terminants and offer different approaches to building models. To determine the resource potential for the poo ling of disparate resources into one indicator, some eco nomists take as a basis the resource indices obtained by the ratio of the actual value of each resource to its ave rage as a whole, or their scores, other economists − their valuations, others take into account the cost of working time (direct and indirect), fourth − the number of wor kers, both actually employed in agriculture and required for the manufacture of fixed and current assets. At the same time, it should be borne in mind that agriculture is an open system, so its modeling should follow a system atic approach, considering not only the individual com ponents and their relationships, but also the system as a whole [14].
Economic and mathematical modeling is one of the most effective ways to form optimal parameters for the manage ment of agricultural enterprises. The choice of management decisionmaking model depends on the specific situation and is determined by a combination of factors, which affect this situation and this management decision.
In the management of economic activity of the en terprise economic and mathematical modeling should be used to solve problems such as: 1) determining the range of products, as well as optimizing production for a certain long period; 2) distribution of available material and financial resources by type of activity; 3) determining the price that will provide the required (or optimal) level of profit; 4) determining the size of allocations for the purchase of equipment and its equip ment; 5) determining the needs for loans to be attracted, etc. [21].
In agriculture, there are typical models that are expe rimentally verified and bring high effects. Such models include the optimization of the structure of sown areas, the use of arable land and fertilizers, reclamation mea sures, the combination and specialization of agricultural sectors. The use of tools of mathematical methods and models makes it possible to better justify the process of making managerial decisions, which is necessary for optimal planning and search for reserves to improve the efficiency of production activities of agricultural enter prises [8]. Economic and mathematical model, even carefully calculated, is not able to fully adequately reflect the pat terns of agricultural production. Therefore, it is advisable to use a system of models, parameters, characteristics, state and behavior in the external environment of inter connected economic processes taking into account the complex structure of the organization, which will in crease the adequacy and accuracy of the results obtained during management decisions by managers of agricultu ral enterprises.

Conclusions
Mathematical methods and models are a tool for ana lyzing and managing the economic activity of the enter prise. They allow to effectively solve specific economic problems and practical problems in the field of enterprise management in order to minimize the negative economic consequences.