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В работе представлены различные методы расчёта усилий в фермах. Анализируются подходы для вычисления усилий в фермах: метод вырезания узлов, метод Риттера, графический метод на основе диаграмм Максвелла-Кремоны, численный метод. На основе полученных усилий в результате подбираются сечения растянутых и сжатых стержней при конструктивном расчёте. Показано, что численный расчёт, в отличие от аналитических и графических методов, учитывает не только продольные усилия в стержнях, но также изгибающий момент и поперечную силу., The paper presents various methods for calculating forces in trusses. Approaches for calculating forces in trusses are analyzed: knot cutting method, Ritter method, graphical method based on Maxwell-Cremona diagrams, numerical method. On the basis of the forces obtained, the sections of tensioned and compressed rods are selected as a result of the structural analysis. We demonstrate that the numerical calculation, in contrast to analytical and graphical methods, takes into account not only the longitudinal forces in the rods, but also the bending moment and the transverse force.

U završnom radu definirani proizvodni problem je riješen pomoću tri metode: analitička, grafička i Simplex te pomoću računalnog programa MS Excel. Cilj rada je organizirati optimalnu petodnevnu proizvodnju dva proizvoda: ogradnog stupa i vodilice za klizne elemente s postizanjem maksimalne dobiti. Prema prikupljenim podacima iz poduzeća problem je definiran, raščlanjen i zatim modeliran. Modelirani problem je riješen navedenim metodama i računalnim programom. Primijenjene metode su uspoređene te su objašnjene poveznice među njima., In this bachelor thesis, the productional problem is defined and it is solved by using three methods: analytical, graphical and Simplex as well as with the tool Solver in the computer program MS Excel. Objective of this thesis is to organize optimal production of two products, the fence post and the guide for sliding elements, in period of five days with aim for the maximal earnings. According to the gathered data from the company the problem is defined, analyzed and then it is modeled. The modeled problem is solved by mentioned methods and with the computer program. Applied methods are compared and links between them are explained.

U ovom završnom radu definiran je proizvodni problem koji je riješen različitim metodama. S obzirom da se radi o problemu linearnog programiranja, ograničenja i funkcija cilja su linearne funkcije. Najprije je, pomoću prikupljenih podataka, definiran problem te je postavljen matematički model i kanonski oblik matematičkog modela. Nakon toga, modeli su riješeni grafičkom, analitičkom i simplex metodom, a sve u cilju dobivanja optimalnog rješenja. Također, optimalno rješenje je dobiveno i primjenom računala, točnije uporabom programa WinQSB, što je opisano u petom poglavlju. Usporedba navedenih metoda pokazana je u zaključku., In this bachelor thesis, the production problem is being defined to be solved later using different methods. Considering that the topic is problem of linear programming, constraints and objective function are linear equations. Using collected data, after the problem is defined, mathematical model and canonical form of mathematical model are set. Afterwards, models are being solved by graphic, analytic and simplex method, focusing on achievement of optimal solution. The integer solution is achieved using a computer, i.e. WinQSB programme, described in chapter five. All mentioned methods are compared in the conclusion.

U ovom završnom radu prikazane su različite metode rješavanja proizvodnog problema linearnog programiranja. Uz pomoć prikupljenih podataka postavljen je matematički model i kanonski oblik matematičkog modela. Nakon rješavanja grafičkom, analitičkom i simplex metodom, dobiveno je optimalno rješenje koje daje maksimalnu dobit nakon proizvodnje dva proizvoda. U ovom slučaju, za rješavanje uz pomoć računala primijenjen je alat Rješavač u MS Excel-u. Da bi varijable bile cijeli brojevi, postavljeno je novo ograničenje za cjelobrojnost varijabli. U zaključku je opisana usporedba ove četiri metode te je analizirano optimalno rješenje., In this bachelor thesis, different methods of solving the production problem of linear programming are presented. With the collected data, the mathematical model and the canonical model are formulated. After using graphical, analytical and simplex methods, an optimal solution is obtained that gives maximum profit after the production of two products. In addition, the Solver tool in MS Excel was used to solve the formulated mathematical model. To make the variables integers, a new constraint is defined for the variables. In conclusion, a comparison of used methods is performed and the optimal solution analysed.

U ovom završnom radu cilj je donijeti optimalnu odluku za problem iz proizvodnje jednog poduzeća koje se bavi proizvodnjom rukohvata stubišta i rukohvata bazena. Problem je moguće riješiti pomoću različitih metoda linearnog programiranja. Za definirani problem iz proizvodnje postavljen je matematički model te kanonski oblik matematičkog modela. Rješavanje pomoću grafičke, analitičke i simplex metode prikazano je u četvrtom poglavlju. Kako bi se dobilo cjelobrojno rješenje, problem je riješen i primjenom računalnih programa. U završetku je dana usporedba svih metoda rješavanja., In this bachelor thesis, the goal is to obtain an optimal solution for the production problem of a company engaged in the production of stair handrails and pool handrails. The problem can be solved using various linear programming methods. For the defined production problem, mathematical model is formulated and solved by graphical, analytical and simplex methods, which is presented in the fourth chapter. In order to obtain an integer solution, the problem is solved by the use of computer programs. A comparison of all models and solutions is given at the end of the thesis.

RESUMO A biomassa polidispersa tem como uma de suas principais características as variações das dimensões e dos formatos de suas partículas. Os métodos de determinação do diâmetro médio por peneiramento, amplamente utilizados devido a sua relativa simplicidade e baixo custo, quando aplicados a materiais heterogêneos, como a biomassa polidispersa, podem levar a resultados equivocados. Assim, com o objetivo de obter resultados mais precisos, foram avaliados três métodos de determinação do diâmetro médio de partículas de biomassa polidispersa, baseados na técnica de fracionamento por peneiramento mecânico: um de forma analítica (Diâmetro de Sauter) e outros dois por meio de análise gráfica das funções de distribuição das partículas (Função de Densidade de Distribuição Mássica e Função Cumulativa/Aumentativa de Distribuição). O método baseado na análise gráfica da função da distribuição da densidade mássica (FDDM) foi o mais eficiente para a análise do bagaço de cana, pois permitiu identificar as diferentes populações existentes e identificar com clareza as dimensões características, mostrando assim ser uma poderosa ferramenta para a análise granulométrica de biomassas polidispersas. ABSTRACT Polydispersed biomass has as one of the main features variations in particle dimension and size. Mean diameter determination methods by screening are widely used due to their relative simplicity and low cost. However, when applied for heterogeneous materials such as polydispersed biomass, they can lead to misleading results. Thus, we evaluated three methods for determining mean diameter of polydispersed biomass particles, aiming at most accurate results. The methods are based on size fractionation by mechanical sieving: one analytical (Sauter diameter) and two by graphical analysis of particle distribution functions (Mass Distribution Density - MDD and Cumulative/ Augmentative Distribution - CAD). The method based on graphical analysis of mass distribution density (MDD) was the most efficient for sugarcane bagasse analysis, once it enabled detecting different populations and clearly identifying their respective characteristic dimensions. Therefore, it is a powerful tool for particle size analysis of polydispersed biomass.