Linear programming methods and their application in economics

Tema ovog završnog rada su metode linearnog programiranja te njihova primjena u ekonomiji. Linearno programiranje je područje matematike koje se bavi problemom optimizacije sustava uz zadana ograničenja. Probleme iz realnog života možemo modelirati problemima iz linearnog programiranja te pronaći optimalna rješenja u ovisnosti o ograničenjima koja su dana. Razvijeni su mnogi algoritmi za rješavanje ovakvih problema. Linearno programiranje ima široku primjenu u mikroekonomiji i upravljanju tvrtkama u planiranju, proizvodnji, tehnologiji, prijevozu i ostalim područjima . Iako se problemi u poslovanju poduzeća neprestano mijenjaju, većina ih ima u cilju maksimizirati profit i minimizirati troškove uz ograničene resurse, pa se većina problema može promatrati kao problem linearnog programiranja i riješiti nekom od poznatih metoda. U ovom radu se razmatraju problemi iz realnog svijeta koji se rješavaju svođenjem na probleme linearnog programiranja. Proučavaju se metode linearnog programiranja te navode problemi na kojima se ilustrira upotreba razmatranih metoda. U ovom radu je predstavljena analiza osjetljivosti koja opisuje kako promjena ulaznih parametara kod nekog problema matematičkog programiranja utječe na promjene skupa mogućih rješenja.The topic of this final paper are linear programming methods and their application in economics. Linear programming is a branch of mathematics that addresses the problem of system optimization within given constraints. Linear programming problems help us model real-life problems and find optimal solutions depending on the given constraints. So far, many algorithms have been developed that address the problem of solving these issues. Linear programming is used in microeconomics and business management in terms of planning, manufacturing, technology, transportation and other fields. Although business management issues are constantly changing, most companies aim to maximize profits and minimize costs with limited resources, so most problems can be referred to as linear programming problems and solved by using some of the known and accepted methods. Real-world problems that are reduced to linear programming problems are discussed in this paper. Linear programming methods are studied and problems are given that illustrate the use of the methods considered. This paper presents a sensitivity analysis that studies the effect of changes in the input parameters of a mathematical programming problem on changes to a set of possible solutions