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master's thesis
Linearno programiranje
Zagreb: University of Zagreb, Faculty of Science, 2019. urn:nbn:hr:217:036141
Lukačević, Antonio
University of Zagreb
Faculty of Science
Department of Mathematics

Institutional repository: Repository of the Faculty of Science

Cite this document

Lukačević, A. (2019). Linearno programiranje (Master's thesis). Zagreb: University of Zagreb, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:036141

Lukačević, Antonio. "Linearno programiranje." Master's thesis, University of Zagreb, Faculty of Science, 2019. https://urn.nsk.hr/urn:nbn:hr:217:036141

Lukačević, Antonio. "Linearno programiranje." Master's thesis, University of Zagreb, Faculty of Science, 2019. https://urn.nsk.hr/urn:nbn:hr:217:036141

Lukačević, A. (2019). 'Linearno programiranje', Master's thesis, University of Zagreb, Faculty of Science, accessed 27 November 2024, https://urn.nsk.hr/urn:nbn:hr:217:036141

Lukačević A. Linearno programiranje [Master's thesis]. Zagreb: University of Zagreb, Faculty of Science; 2019 [cited 2024 November 27] Available at: https://urn.nsk.hr/urn:nbn:hr:217:036141

A. Lukačević, "Linearno programiranje", Master's thesis, University of Zagreb, Faculty of Science, Zagreb, 2019. Available at: https://urn.nsk.hr/urn:nbn:hr:217:036141

Metadata
TitleLinearno programiranje
AuthorAntonio Lukačević
MentorMarko Erceg (mentor)
Committee memberMarko Erceg (predsjednik povjerenstva)
Committee memberMarcela Hanzer (član povjerenstva)
Committee memberBoris Širola (član povjerenstva)
Committee memberJosip Tambača (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Science
(Department of Mathematics)
Zagreb
Defense date and country2019-11-27, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract
U ovom radu proučavani su osnovni problemi linearnog programiranja. Cilj je bio, za promatranu funkciju cilja, pronaći optimalnu (minimalnu ili maksimalnu) vrijednost na skupu područja rješenja zadanog linearnim nejednakostima. Rješavanju problema linearnog programiranja, pristupili smo na tri načina: geometrijski, algoritamski (simpleks metoda) i algebarski (teorija dualnosti). Optimalnu vrijednost problema linearnog programiranja, kod geometrijske metode, određivali smo na dva načina: korištenjem linije konstantne vrijednosti i provjeravanjem vrijednosti funkcije cilja u vrhovima područja rješenja. Kako geometrijska metoda nije pogodna za rješavanje velikih problema, tada smo problemu pristupili algoritamski, simpleks metodom. Korake simpleks metode organizirali smo simpleks tablicom. Teorem dualnosti je dokazan konstruktivno, koristeći simpleks metodu, te geometrijski pomoću teorije nejednakosti. Sve metode u radu su potkrijepljene primjerima.
Abstract (english)
This thesis studies the main problems of linear programming. The aim of the observed cost function was to find the optimal (minimum and maximum) value of the solution area set defined by linear inequalities. We approached the problem of linear programming in three methods: geometric, algorithmic (simplex method) and algebraic (dualty theorem). We determined linear programming optimal value, according to geometric method, in two ways: using constant value line and by verifying the cost function value at the corners of the solution area. As the geometric method is not suitable for solving big problems, we approached the problem in algorithmic mode, using simplex method. Simplex method steps were organized by simplex tableau. The duality theorem is proved constructively, using the simplex method, and geometrically using the theory of inequality. All presented methods in thesis are supported by examples.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:217:036141
Study programmeTitle: Mathematics Education; specializations in: Mathematics Education
Course: Mathematics Education
Study programme type: university
Study level: graduate
Academic / professional title: magistar/magistra edukacije matematike (magistar/magistra edukacije matematike)
Type of resourceText
File originBorn digital
Access conditionsOpen access
Terms of useLicence In copyright icon
Created on2020-07-09 10:59:12