OPTIMAL PRODUCTION PLAN FOR A CONFECTIONERY FACTORY USING THE SIMPLEX METHOD

Аннотация

Simplex method – linear programming issues effective solution for used strong is an algorithm . Simplex schedule using iterative calculations done increased , optimal solution This is found in method resources distribution , production release planning and logistics in the fields wide is used . This in my article confectionery factory from resources effective use andmaximum benefit to take issuelinear programming and simplex method usinganalysis as I'm leaving . Key words :Simplex method , linear programming , optimal plan , goal function , constraint conditions , pivot element , simplex table , production release optimization , resources distribution , maximum profit , mathematics modeling , linear equations , organization efficiency , economic optimization , product working production , confectionery factory , costs reduction ,mathematics programming ,executableiterations ,business planning. Introduction. Processes research and optimal management – decision acceptance to doandsystems tooptimizescientific fields oriented .​ 1-Process research resources effective distribution for mathematician models , linear programming ,games​ theory andnetworks optimizationsuch as from methods uses . 2- Optimal management systems the most good management strategies determination with He is engaged in his work . main methods Pontryagin's Maximum principle and Bellman's dynamic programming . Literature analysis Confectionery optimal factory operation release plan according to literature analysis working release processes optimization , resources effective distribution and profit maximum to the level to deliver according to various methods to determine help gives . L. Kantorovich's " Mathematical programming and economic analysis " (1959 ) working release optimal plan in processes to compose and resources distribution methods statement G. Dantzig " Linear programming and his/her in the book " Applications " (1963) simplex method and make it real release to the conditions application​ issues covered . R. Dorfman, P. Samuelson and R. Solow " Linear programming and economic analysis " (1958 ) optimal planning , constraints and goal function based on decision acceptance to do discussion IG Bashmakov's "Optimal production " release systems " (2005 ) modern working release processes to optimize related theoretical and practical approaches showing​ Also , GN page1190 INTERNATIONAL JOURNAL OF ARTIFICIAL INTELLIGENCE ISSN:2692-5206,ImpactFactor:12,23 AmericanAcademicpublishers,volume05,issue04,2025 Journal: https://www.academicpublishers.org/journals/index.php/ijai Nemchinov 's " Linear economic models " (1972) book economic in systems linear programming and analysis methodsto use dedicated . Research methodology This research confectionery optimal factory operation release plan to compose according to linear programming methods to apply Research​ ​ methodology empirical and theoretical analysis own​ inside Research​ ​ during literature analysis optimal performance through release plan formation according tothere is scientific sources is studied . Various mathematician modeling methods , including simplex​ method , graphic method and dual method using working release processes optimization opportunities analysis Comparative​ ​ analysis through various economic models compared and their confectionery products working release to the process compatibility is determined . In this working release resources limited , product types benefit level and demand conditions into account is obtained . Experimental analysis and theoretical basically of the optimal plan formulated to practice implementation to be completed to study aimed at to be , to work release size increase and expenses reduce according to recommendations working Qualitative​ ​ analysis methodological aspects , work release process conditions and the results quality in terms of to evaluate is based on . Research methodology working release plan thorough planning , resources effective distribution and maximum benefit to take for scientific approaches to determine These methods are aimed at using working release process furtherimprovement andeconomic efficiency increase possible. Analysesandresults Simplex method general if the borders equations and goal of functions equations canonical to look has if not optimization linear issues solution for is used . In this case equations system 's appearance​ as follows . a x + a x +...+ a x =b 11 1 12 2 1n n 1 a x + a x +...+ a x =b 21 1 22 2 2n n 2 ( 1) a x + a x +...+ a x =b m1 1 m2 2 mn n m с x + с x +...+ с x - z =0 1 1 2 2 n n Simplex (method )in 2steps is divided . Stage 1-Delimiterequations and goal functions canonical to lookto bring Stage 2 - Optimization of the objective function obtained as a result of stage 1 using thesimplexalgorithm . Step1we build. Artificial in stage 1 changes​ input way with , such as variables all to equations are entered , equations to the system canonical appearance is given . Basis in character variable