| Sažetak | Cilj istraživanja je utvrditi način na koji linearno programiranje može biti rješenje problema ishrane u svakodnevnom životu na primjeru rekreativnog sportaša te koliko su kvalitetna rješenja koja može ponuditi. U tu svrhu se utvrđuje što je linearno programiranje, od kojih se problema sastoji, koji teoremi vrijede i kako se rješava. Zatim se problem ishrane svrstava unutar tog opusa i predstavlja se praktični problem.
Problem linearnog programiranja može biti problem maksimuma ili problem minimuma, odnosno cilj je ili maksimizirati ili minimizirati funkciju cilja. Problem maksimuma se sastoji od m varijabli i n ograničenja, odnosno problem minimuma se sastoji od n varijabli i m ograničenja. Takvi problemi se pojavljuju svakodnevno u poslovanju, bilo proizvodnje, trgovine, marketinga ili menadžmenta. Svaki originalni problem ima svoj dual, te vrijede određeni teoremi. Optimalno rješenje originalnog problema i duala će imati istu vrijednost, te ako postoji optimalno rješenje originalnog problema, ono postoji i za njegov dual. Prvi način rješavanja takvih problema je grafička metoda, koja ipak vrijedi samo za sustave s dvije nepoznanice. Drugi način rješavanja je pomoću principa oslabljene komplementarnosti, u kojem slučaju se standardni problem mora prevesti u kanonski oblik pomoću dopunskih varijabli. Treći oblik je simpleks metoda, iterativni proces koji poboljšava rješenje u svakom koraku. Prvo se postavlja početno rješenje, pa se testovima utvrđuje radi li se o optimalnom rješenju te ako se ne radi, metoda daje upute, odnosno postoje kriteriji koji se prate, kako doći do njega.
Utvrđuju se specifičnosti svakog pojedinca iz skupina rekreativnih sportaša, poput dobi, spola, visine i težine, pod određenim pretpostavkama. Na temelju toga se izrađuje reprezentativna nutriciona matrica s vrstama hrane, minimalnim zahtjevima i cijenama. Određeni artikli će biti skuplji i manje vrijedni, pa su uvršteni samo ako se želi postići što veća raznolikost prehrane. Uočava se razlika u troškovima s obzirom na vrstu spola i raznolikosti prehrane te se utvrđuje da će troškovi prehrane rasti što je osoba teža, viša i što želi raznolikiju prehranu. Zaključuje se da je linearno programiranje sposobno ponuditi primjenjivo rješenje u takvom slučaju, ali je ipak najbolje primjenjivo u objektivnim slučajevima kad treba izraditi plan prehrane za veću postrojbu gdje je subjektivni faktor minimiziran. |
| Sažetak (engleski) | The goal of the research is to show how linear programming can be solution to the diet issue in everyday life, for example in the recreational athlete, and how quality those solutions really are. In that purpose, it is defined what i linear programming, which issues it is compiled of, which theorems apply and how it´s solved. After that, diet issue is put inside of that context and practical problem is presented.
The problem of the linear programming can be a problem of maximum or minimum, as the goal is to maximize or minimize the goal function. Maximum problem is made of m variables and n limitations while minimum problem is made of n variables and m limitations. Problems like that are common everday business production, on the market, in marketing or management. Every original problem has its own dual, while some theorems apply. The optimal solution to the original problem and dual problem will have the same value and if there is an optimal solution to the original problem, there will also be one for dual problem. The first way to solve that kind of problem is graphic method which is only worth for systems with only two unknown variables. The second way is through a principle of impaired complementarity, in which case standard problem must be translated to canonical form with the help of additional variables. The third way is the simplex method, iterative process which improves solution in every step of the way. Firstly, it sets the starting solution, after that there are several tests which will determine if the solution is optimal one or not, and if it isn´t, the method will give instruction, based on certain criteria, how to improve it.
Specifics of every individual from the group of recreational athletes are determined based on age, sex, height and weight under specific circumstances. Based on this information, the representative nutritional matrix with type of food, minimum nutritional requirements and prices of food is created. Some food will be more expensive and with less nutritional value so they are included only if greater diversity is desired. The difference in costs based on type of sex and diversity of food intake is noticable, so it´s concluded that the costs of food will grow if the person is taller, heavier and wants more diverse food intake. In conlusion, linear programming can be used to find a quality solution for diet issue, but it´s best served in objective situations when diet plan needs to created for the larger unit where subjective factors are minimized. |
