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Mathematics programmers - Nakonechny S.I.

3.3.3. The third theorem of binary

Yak Bulo z'yasovano in poperednomu paragrafі, іsnuvannya dvoїstih zmіnnih umozhlivlyuє zіstavlennya vitrat on virobnitstvo i tsіn on produktsіyu on pіdstavі chogo obґruntovuєtsya visnovok about dotsіlnіst chi nedotsіlnіst virobnitstva skin produktsії mind. Krіm tsogo, the value dvoїstoї otsіnki harakterizuє zmіnu values ​​tsіlovoї funktsії scho zumovlena malimi zmіnami vіlnogo member vіdpovіdnogo obmezhennya. Дане твердження формулюється у вигляді такої теореми.

Theorem ( third theorem of binary ) . Components of the optimal plan for the two tasks Дорівнють значенням частинних похідних від цільової функції For some arguments , Abo

(3.28)

Beforehand . Roshglyanemo task linіynogo programvannya, filed in the canonical form:

(3.29)

(3.30)

(3.31)

To the problem, the problem to problems (3.29) - (3.31) can be formulated as follows: know the optimal plan , For what is the significance of the meaning

(3.32)

For the mind:

(3.33)

Причому умова невід'ємності змінних Відсутня.

Significantly - an optimal plan for the two tasks, - the optimal plan of problems (3.29) - (3.31). For the first theorem, it is twofold:

,

Abo

. (3.34)

Оскільки досліджується питання впливу зміни значен On F, then the linear function (3.34) can be viewed as a function of arguments . Тоді частинні похідні за змінними Budet dorivnyuati components of the optimal plan for the two tasks :

. (3.35)

However, the source of solidification is fairer for that if the components of the optimal plan Zalishayutsya postiynimi, and okkilki for the first theorem of the bicentenary , Then the value of the binary otsinok will be unlimited for the purpose of the post-organizational structure of the optimal plan for the tasks that are to be tapped.

Otzhe, rіvnostі (3.35) to cope with the Lisha for the unknown zmіn , Іnakshe suttєva zmіna minds pochatkovoї zadachі (Rule Chastain Sistemi obmezhen (3.30) is the tsіlovoї funktsії (3.32)) are given to zmіni basis in optimal planі pryamoї zadachі and mean i to іnshogo rozv'yazku dvoїstoї .

The economical part of the third theorem is binary . Dvoїstі otsіnki Je unіkalnim іnstrumentom, yaky daє zmogu zіstavlyati neporіvnyannі rechі. Obviously, it is impossible to simplify the definition of quantities, which can be used to explain the behavior of a person. Yakscho take yak butt virobnichu task, tsіkavim Je power: yak zmіnyuvatimetsya values ​​tsіlovoї funktsії (Mauger vimіryuvatisya in penny odinitsyah) for zmіni obsyagіv rіznih resursіv (mozhut vimіryuvatisya tonnes, m2, people / year toscho ha.).

Vikoristovuyuchi dvoїstostі third theory, it is easy to viznachiti vpliv zmіnu values ​​tsіlovoї funktsії zbіlshennya chi zmenshennya obsyagіv okremih resursіv: chislovі values ​​dvoїstih otsіnok pokazuyut on yak value zmіnyuєtsya tsіlova funktsіya for zmіni obsyagu vіdpovіdnogo danіy otsіntsі resource .

Otzhe, for the name of the ignorant zmіn (3.29) - (3.31) is a new problem, de Resigned to . Significantly through The optimal plan for the new tasks. For viznachennya Not potrybno rozv'yazuvati new problem lennyi programvannya, and dostagno cope with the formula , De - the optimal plan of problems (3.29) - (3.31).