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Mathematics programmers - Nakonechny S.I.

4.2. Analisz rozv'yakіv conjugation of economical and mathematical problems

A simplex table has been put in place to optimize the design of the direct tasks. The optimal plan of direct problems is known through , And the optimal plan is y *.

X * = (0; 0; 35; 45; 0; 30; 0), max Z = 285;

Y * = (4; 0; 3) x = (1/2, 0; 2);

Min F = 250/2 + 160 = 285 = max Z.

The basic principles of the optimal plan for direct tasks are to sign the vibrokitnva vidpovіdnykh vidovіv products. Otzhe, vypuskie proizvodstvі vidіv A ta V not perebachaetsya ( x 1 = x 2 = 0), and C і D - planuetsya at kіlostіі vіdpііdno 35 th 45 od.

Додаткові змінні optimum to the plan of the direct tasks х 5, х 6, х 7 to characterize the linters (unincorporated обсяги) resources in the form 1, 2 ta 3. Oskilki х 6 = 30, then tse means, other resource vikoristovuyutsya in the process of vibrobitvtva produktsii not ponynistyu. The first that third resource for the optimal plan of the vibrobitvita will be vikoristani povnistju, bo x 5 = x 7 = 0.

For such a plan, vibrobitvita produktsii pіdpriєmstvo otrimalo b naybіlsh virhichu osoyagom 285 mind. Od.

З розділу ІІІ відомо, що між змінними пряї та двоїстої задач існує відповідність to the mind:

The optimal plan for the two tasks is to optimize the system of resource allocation, and to be vikorostovuyutsya vibrobitvtsi.

Basic zmіnnі dvuhistoї problemi for the induced schema to follow the addictive zmіnnym straightforward, to characterize the invocations of non-conserved resources. Otzhe, otrimani znachennya zmіnnih at 1, at 2 ta at 3 mozhna vikoristati for vidnosnoї kіlkіsnoї otsіinki podrobnosti vidpovіdnikh vidіv resursiv. Thus, for 1 = 1/2 and у 3 = 2 for a zero point, and resource 1 for that 2 (for the values ​​of the add-ons of right-angled direct problems), be revived. Двоїста оцінка у 2 = 0 і Відповідний type resource does not vіnіkostyu vіkoristvuyatsya for the optimal plan vibrobitntsva produkcii. Tse pidtverdzhuyutsya takozh transversal analizom dodatkovyh zmіnikh optimal to the plan of direct problems. Moreover, for the third theorem, it is doubly obvious: the activity is basically the optimal for the plan of the two tasks, 0, then the zyna (zbilshchenya abo zmenshennya) the oath of the resource and the resource should be reduced to the value of the value of the function by the value y . Якщо уі = 0, then the value of the tsil'ovoy funkіії zalisyaetsya nezіmіnim.

The augmentation, at 1 = 1/2, means that if the stock of the first resource is equal to one wit alone ( b 1 = 250 + 1 = 251), then the value of the maximal function is Z zlisshitsya i nishih novikovi obstavin na 1 = 1/2 mind . Od. І stanovitime max Z = 285 +1/2 = 285.5 mind. Od. Analogously zlislenshnya for one wits oditnitsu third resource ( b 3 = 80 + 1 = 81) cite for your new minds to zlislenshnya tsil'ovoy funktsii on 3 = 2 mind. Od., Scho stanowimme max Z = 285 +2 = 287 mind. Od. Lisha, ignorant zmіni otnagu other resource niak not vplivatimut on znachennosti tsil'ovoy funktsii, oskilki u 2 = 0.

Додаткові змінні optimum to the plan of the two tasks to meet the basic tasks of the direct tasks, to isolate the vibrobitvtva's ovaries from the skin type of the product, in the 4, 5, 6, and 7 takozh at the pivniy sposib majut characterize the vibrobnitsu vidpovidnih vidіv produkcii. Behind the rules of motivating two-pronged tasks, it is obvious that the optimal way to accomplish the tasks of the two tasks is to show off, to increase the resource of resources, to transfer the price of food products. Otzhe, stink vidnosno characterize zbitkovіst vibrobitnitsva vidpііdnіh vidіv produktsії.

Додаткові змінні двоїстої задачі розоіщнія в оцінковом ряку remainnнії simplex tables at the stackers " х 1" - " х 4". Їх optimum value: у 4 = 5; Y 5 = 5/2; Y 6 = 0; At 7 = 0. To that of vitrati on vibrobitntsu productions Aіі В перевищують їх ціну відповідно on 5 ta 5/2 mind. Od., And for produkcii C і D such перевищення it is not enough. Tse pidtverdzhuyutsya takozh spekdnіm analizom basic zmіnih optimal to the plan of direct problems, oskilki for the optimal plan dotsilno vogotovlati sama produktju vidiv S i D.

Rozrahovana optimal system otsinok zabezpechuє naimenshu zagalnu vartіst usіh resursiv, scho vikoristovuytsya on pіdpriemstvі: min F = 285 mind. Od.