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pep 2.6 p oope eoopx ox aoe ooe oo oy e eee 20 e. aeoo eeca A, e eee 30 e. eeca B e eee 6 e.

eeca C. aae aee eeca coepa a a opa. Coepae e aex eec 1 aoo o opa peeo ceye ae.

Taa 2.poy Coepae aex eec, e.

A B C I 10 25 II 15 30 Coca eo pao, oecea oyee eoxooo oeca aex eec p ax eex apaax, ec ea 1 opa I a cocae - 100 p. II a - 300 p.

Peee Ooa epe x1 coepae opa a I eo paoe ooo (), epe x2 coepae opa a II. Toa eo paoe ooo ye coepac 10x1 + 15x2 e. eeca A, 25x1 + 30x2 e. eeca B 2x+ 10x2 e. eeca C. aaa ye e ceyy aeaecy opypoy:

C = 100x1 + 300x2 min, p ycox 10x1+15x2 20, 25x1+30x2 30, 2x1+10x2 6, x1, x2 0.

M ceece ep oyeo aa. Taoo a aa aa "aaa o ee". aa aoo a cpeac ae p cocae cax pax cece, oope o yoeop opeee peoa, apep, cec ye pax apo, ea .. oy e y coc paec ae aa o pacpoe aepaa, p o oo pyc oxo cooc eoxooo aepaa.

B pe yaay aay oo pe cec-eoo c eee cycceoo aca. Paccop opoee o apa.

pep 2.6 (npooeue) Caaa o p ooee epeee peopaoa aoecoy y yoae yoa a 1, o epe aae aca. oyae aay.

C = -100x1 - 300x2 max, p ycox 10x1 + 15x2 - x3 = 20, 25x1 + 30x2 - x4 = 30, 2x1 + 10x2 - x5 = 6, xi 0, (i = 1,5 ).

aee , o ocpoe epoaaoo aca eoxoo ec ee cyccee epeee x6, x7, x8. oyae aay.

C = -100x1 - 300x2 - 1000x6 - 1000x7 - 1000x8 max, p ycox 10x1 + 15x2 - x3 + x6 = 20, 25x1 + 30x2 - x4 + x7 = 30, 2x1+10x2 - x5 + x8 = 6, xi 0, (i = 1,8 ).

Teep oo coca epy cec-ay oy peee.

ae, o oyeo aae 3 opae 8 epeex.

B eceoc opao oee ooo, c o pe oeca eoxox ce, epe paccope oceo aa. eo ee pe cec-eoo, a ae a peee cxoo aa ocee cecae pee oceo aa.

pep 2.6 (npooeue) ocea aaa ye e cey opao:

C = 20y1 + 30y2 + 6y3 max, p opaex 10y1 + 25y2 + 2y3 100, 15y1 + 30y2 + 10y3 300, y1, y2 0.

Bo a pae, e ooee epeee y4, y5 0, pa x a ac peae aay cec-eoo. ae, o oyea aaa ee oo opae 5 epeex.

pep axoe pee ocee cec-a oceo aa paccope paee.

Tea 3 OHOMO-MATEMATECE MOE OPMPOBAH OTMAHX AHOB POBOCTBA p ye eoo popapoa ye oop e a pepax, o ee aa oa e ooe ooecoe aee. B acoc coc aa, oopx peyec a ae e ao oece yo yca, o acpoa p oe yca poy ..

p o pecypc peoaac cpoo opae.

Paccope ocao x aa o oee paec yo pe, x oo ye e p eaa ypoe oax yee eo oxo o oooc eocpeceoo paecoo pee. Cpay ceye aa a a ax eaa ypoe. o eoooc opac p oee aeca aa pooca oo o oaaee ( eceoc ceye cooa e x aop), a ae - o eceoc cya xapaep ox apaepo opeex ocao aa, apep, ax a opopacxo cao-aco a ooee e e pacxo aepaa .. aeca a pae cyaoc (coxacoc) x apaepo oeo ee eoaoc ae eooc ex ao, oope oye peyae pee aa .

Oao p opeeeo pa paccapaex e oxoo oo ycpa oe eoca cooecyx oee [5, 9].

3.1 Moe e yea c yeo peayeoc aa Bo epx e pa oe, o e cop a eoca, e cooa oa ao eoopx aoee cocox ex coooe eo aec eca coepaeo epceo. ooy ececeo, o pe ee pae cooecye cxe pee ceo ceye eapoa oee eo opee, o ceac ceae.

Ha pae apoa pooc oo oop o ceye oee opeo oaoo oe cce ex coooe.

= 1X1 + 2X2+... nXn max, (3.1) n C X i,i = 1,2,...,m, j = 1,2,...,n; (3.2) tij j j=n H X T, = 1,2,...,0; (3.3) tij j j=n M X R, = 1,2,...,0; (3.4) tij j j=n X ; (3.5) j j j =n C X C ; (3.6) j j j =d X Dj, j = 1,2,...,n. (3.7) j j ec aee coyc ceye ooae:

Xj - oe pooca oapo poy j-o a apyeo oy aypao epe; j - oaea ea p o peaa e e j-o a, M - co py aoaeeoo exooecoo oopyoa C exax pep (oopoe eecoopao ya aece opae); tij apa pya cao-acax, a ey poy j-o a p ooe ee a cex oepax, oex a oopyoa i- py; i - ooo pace o paoeo pee oopyoa i- py; 0 - co cex poeccoaoapoax py paox-ceo ocoo pooce, eocpeceo e cax c ocyae exooecoo oopyoa H ocox exax; tj - apa opo-acax paoeo pee - py paoxceo a ey poy j-o a; T - ooo pace o paoeo pee opo-acax paoeo pee - py paox-ceo; 0 -co cex opaex o poocex pecypco, yaex ao aae M apoa; tj - apa poocex pecypco -o a a ey poy j-o a; R - epx paa pacxoo -o a pecypco; , C j j cooeceo coocaa pa ae ooa ea e j-o a; , C - aaa paa yca oapo poy a pep apyeo oy coocax px ae oox eax; d, Dj j cooeceo epx pa oea pooca poy j-o a (epx paa, a pao, oe oycoea yco ca poy oooc cooaeoo pooca; e paa - xoce c pep c py pep opaa).



ooec cc pepao y (3.1) yco(3.2) - (3.7) peeo aeaeco oe oee. Oe , o oye oee aeceoo oooo aa pooca eecoopaee o cooae oopepao aeaeco oe. ooeo pep (3.1) oe o paccope oa ax pepe, a oe pooca coocax eax, ceecooc poy .. Bce pep ocaoo eo pa e opy coy eee oe. Ceye caa, o paec oopepay aay pea ceee e, e cocoo, oopepao, ooy ypoe e ye ocaaac a o acee.

peea oe (3.1) - (3.7) ec eo oe peea ceceoo. Oao oa coep cee p eaa, oope pe ee paecoy cooa ceye oac ycpa.

Bo-epx a ec o, o oe oe pecypco caec eee. o e cea cooecye peaoc, apep, cyae oe coo peaeoc eoopoo poya, oeo, oa ae oo oca a ce ooex apa peep x yee. poe oo cece oo coca paccapaeo oe ec o, o eopeec oe ooe e ac ooo aa yoeopeo ce yco opae.

B aece xoa yaax pyoce oo peo cooae ceye oe.

0 n m (1) (2) (2) (3) = X -W Yi(1) + Y + Y(3) max, (3.8) j j Ci C C j =1 i=1 =1 = n C X i + Yi(1),i = 1, 2,..., m, j = 1, 2,..., n; (3.9) tij j j =n H X T + Y(2), = 1, 2,...,0; (3.10) tij j j =n M X R + Y(3), = 1, 2,..., 0; (3.11) tij j j =n X ; (3.12) j j j =n C X C ; (3.13) j j j =d X Dj, j = 1, 2,..., n, (3.14) j j Yi(1) 0,Y(2) 0,Y(3) 0, cex i,,. (3.15) ec coyc ceye ooee epeee.

Yi(1) - eoca o paoeo pee cao-acax a oopyoa i- py; Y(2) - eoca o paoeo pee opo-acax - py paoxceo; Y(3) - eoca oe -o a pecypco.

Aa e ceye ooee oe.

Ci(1) - oea aoc e eocaeo oa paoeo pee cao( acax a oopyoa i- py; C2) - oea aoc e eocaeo oa ( paoeo pee opo-acax - py paox-ceo; C3) - oea aoc e eocaeo oea -o a pecypco.

aae oe oo oy o c oo pee cepo, .e. c cooae eoo cepx oeo o a-y py cocoo, apep, o opya ceyeo a.

1 1 ( ( Ci(1) =,(i = 1, m), C2) =,( = 1,0), C3) =,( = 1, 0).

i T R Bao o cc aee oea W. o oe ec ocaoo o ooe co paae, a , "pa", oop aaaec a ey oxoa cyae pee p apoa exc oeo pecypco. c-ooa o e ocoaec a peooe, o p yee eoopoo pecypca pep pxoc a eoope "cepxapa" cae, apep, co cpoeco ox poocex ooce peo a paoy ox apo ..

Haoee e aeco oe (3.8) - (3.15) ec o, o ee peee cyecye cea, .e. aec xo o a pooca yoeop ce ccee yco.

3.1 Moe c yeo cyaoc apaepo py ae eocao oe (3.1) - (3.7) ec o, o ce ee apaep peoaac eeppoa (.e. e cya, cpoo aa). o oeo oxo coacyec c ooee ee e eco a pae. B eceoc cea oe peoaa eoop cpe ypoe oo oo apaepa. o oocc ypo e, oop coc yye a pe, oy oopyoa, oopoe cya opao xo cpo peoa .. Ta opao co, o, o-epx, a ocpoe o epee eeppoa oe ooc e ye oe oa, a o-opx, o apaep paccapaex a oee ceye ca cya ea.





p o oae opoc: a eo oe eep oxapaepoa oe apaep Bo-epx, ocoac a epao peeo eopee eop epooc, o oy, oyco ca apaep opao pacpeee. A opaoe pacpeeee, a eco, ooc xapaepyec co aeaec oae cepce. Bo-opx, pecaec oo ca ec cpeee aee (.e. aeaecoe oae) x apaepo, apep, p a y ey cooecye ae eeppoax oee. Oea e cepc oe pa cxo peyeo oa apoa pooca a ocoe oex ax a p pox e a ao pep.

co, o p coxacoc (cyaoc) oeo oe, cooecye opae, a a e aee pepao y oo oa oo epooco cce. He oaeo ce apaep ca cya. aee ye ca cya ea c ec C ooc poco oo ceye apaep j, tij, i. Toa oe cooaa, apep, ceya coxaceca oe.

0 n m (1) (2) (3) = M X -W Yi(1) -W Y(2) + Y(3) max, (3.16) j j Ci C C j =1 i=1 =1 = n P C X i + Yi(1) p1,i = 1, 2,..., m, j = 1, 2,..., n; (3.17) tij j i j= n H (2) X T + Y, = 1,2,...,0; (3.18) tij j j=n M X R + Y(3), = 1, 2,..., 0; (3.19) tij j j =n X ; (3.20) j j j =n C X C ; (3.21) j j j =d X Dj, j = 1, 2,..., n, (3.22) j j Yi(1) 0, Y(2) 0, Y(3) 0, cex i,,. (3.23) ec M, P - cooeceo oepaop aeaecoo oa epooc, pi -aaae a eae ypoe epooc oe cooecyeo yco.

Ta opao, , o o-epx ec o eocpeceoo ae yoaa p eoopx ypox poc poyo cea epexo eo cpeey ae p cyaoc oo ypo. Oe, o pepao y oy cooac pye coxacece aao. Hapep, aca epooc oo, o eceoe aee p peoe eoopy aay ey. Oao epexo cpeey oaeoy ae ec oe ecece, oy e o ee ee oo ococo, o oopo ye caao e. Bo-opx, epoocy opy ac opae o pecypca oopyoa. Teep ye oop o o o epooc oe oo opae.

aee , o o aa aoa yoae ece e eocax pecypco ex opae, apaep oopx p ecya. o ceao, ocoy ao cyae e e c cya, coc aeaecoo oa ceye aa oooc.

co (3.18) - (3.23) ooc coxpa co opy. B cyae ec o po peee o eoxooc ca xoe x apaep cya x opa peopaoaoc coepeo aao opao.

oop o pee oe (3.16) - (3.23) ceye caa, o e cyecye eoo oox a ee ( aaox eex oee) ooe peee, p o ope oopo oa acaa. o cao eo co coxacoc o oe. cac ae eo cyae ec oo ae paccapaey oe ee eeppoa aeo.

3.2 eeppoa ae coxaceco oe C (1) Ooa epe t, , Y - aeaece oa cooecyx ij i i 2 2 C cyax e, ij, i(), 2( (1) ) - cepc cooeceo cyax e tij, i Y i, Yi(1).

Ooa epe (j = 1,.., n) - aeaecoe oae cyao e j.

j Toa oyc coco eoc oepaopa aeaecoo oa e, o ce cyae e cae eac oyae, o yoay (3.16) aee cey 0 n m (1) (1) (2) (2) (3) = X -W Y -W Y + Y(3) max, (3.24) j i i j C C C j =1 i=1 =1 = (1) e C =. eo oooc ac o oepaopa ae-aecoo oa i i ec a ococo pacca-paeoo pep aeca.

Ooceo cyao e Yi(1) oo caa, o oa pae n C 0, p X < i tij j (1) j =ceye ae: Y =.

i n n C C X - i, p X i tij j tij j j =1 j = C Moo yaa epooc x ae p ecx apaepax tij i aax X. aee Yi(1) = 0 ye pac c epooc j n C 0 - - i x t t X ij z0 -t2 j n 1 j=,ec F(x) = P1 = P C X - i < 0 = F(z0) = e dt,e z0 = tij j e dt n 2 2 - ij X + i() j=j j=epaa y aacca, eoope ae oopo pee poe.

oee oe a e ae oo a apep [6, 7, 8] pyx ax.

Toa cepc e Yi(1) oo peo ca pao n 2 2 2( (1) ) = P1 0 + 1 - P1 X + i().

ij j i Y j= aee coc opaoo pacpeee eco, o ycoe n P C X i + Yi(1) p1, i = 1, 2,..., m, j = 1, 2,..., n;

tij j i j = aeo yco n n C (1) -1 2 2 2 + Y ij i i - F ( p1) X + i() + i(Y ), i = 1, 2,..., m, (3.25) t X j i ij j j=1 j=-e F ( p1), i = 1, 2,..., m - ae y opao epao y aacca, i oope oo axo o e e aa.

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