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Teep eco oe (3.16) - (3.23) oyae aey eeppoay oe (3.24), (3.25), (3.18) - (3.23). p o ao, o oyea oe e ec eo e ca e oe peea cec-eoo.

Oao c oo epaooo (aooo) poecca oopa aa oo a ee peoe peee. aec - a oopoo apapoaa a a eaea epooc eo oe, oao oe e oa. p cooa BM aay oo pe co co yoo oo ooc. p pyo cee paec pecaec oo peo oyc a oee eee aece c o pe ae pepao y.

3.3 pep cooa oe c yeo aeoc cocae aa pooca Ha pep ycaec p a poy. peoaaea ea p o peaa c e e j-o a, j = 1,3 :

1 = 15, 2 = 25, 3 = 20.

apa pya cao-acax, a ooee c e poy j-o a a oopyoa i-o py, i = 1,2, cac opao pacpeee cya ea. x cpee ae cepc xapapepyc apa:

2 6 C 0,1 0,25 0,, ij = t =.

ij 3 7 4 0,15 0,3 0, ooo pace o paoeo pee oopyoa i-o py, caec cyao eo c xapaepca:

32 =, i() =.

i 40 apa opo-acax paoeo pee - py paox-ceo, = 1,2, a cy e poy j-o a o eo o:

10 35 20 H tj =, T 340.

14 65 25 = Caec eecoopa opa pacxo oo ooo pecypca, apa oopoo a cy e j-o a epx paa pacxoa aac ea M t = 8 11 7, R = 260.

j Coocaa pa ae ooa ea c e j-o a xapaepyec cooeceo eopa, = 24 34 30, C = 22 32 28.

j j = 200, C = 180 - aaa paa yca oapo poy a pep apyeo oy cooeceo px ae coocax oox eax.

d1 = 5, D1 = 10 - cooeceo epx pa oea pooca poy 1-o a ( c. .), pyo poy ax opae e.

Coca eeppoa ae aeaeco coxaceco oe oppoa oaoo pooceoo aa c yeo aeoc. p epooc oe aa o cooa oopyoa p1 = 0,95, i = 1,2.

i peo oyc a o oooc oca acy p.

Peee pe ey paoo oea W = 1000. o aa -axo F (0,95) = 1,645. Toa coooe eep-poaoo aea coxaceco oe c yeo peayeoc e .

Ha acy pepao y:

= 15X1 + 25X + 20X 2 1 1 1 1 (3) -1000 Y1(1) + Y2(1) + Y1(2) + Y2(2) + Y max, 32 40 230 340 p opaex o:

- oopyoa (1) 2 2 2 2X1 + 6X + 3X 32 + Y -1,645 0,1X1 + 0,25X + 0,16X + 3 + 1(Y ), 2 3 2 (1) 2 2 3X1 + 7X + 4X 40 +Y -1,645 0,15X1 + 0,3X + 0,2X + 4 + 2(Y ) ;

2 3 2 2 - paoey pee 10X1 + 35X + 20X 230 + Y1(2), 2 14X + 65X + 35X 340 + Y2(2) ;

1 2 - aepa pecypca 8X1 +11X + 7X 260 + Y1(3), 2 - oey cooeceo aox coocax ea 24X1 + 34X + 30X 200, 2 22X1 + 32X + 28X 180;

2 - o oey aypao pae 5 X1 10.

pcy oopy oycoo aa.

a 1 yc apep X1 = 5, X = 5, X = 5.

2 o oey aox coocax ea, a a e o oey aypao pae a ec oyc 24 5 + 34 5 + 30 5 = 440 200, 22 5 + 32 5 + 28 5 = 410 180, 5 X1 10.

ocae eep Y1(1) n C 0 - - t X ij i z0 - t j 1 j = P1 = F(z0) = e dt,e z0 = = n 2 - ij X + i() j j =32 - 25 - 65 - 35 = = - = -1,46.

15,0,152 + 0,2552 + 0,1652 + o aa axo P1 = F(-1,46) = 0,072.

Teep axo, o 1(Y ) = (1- 0,072) 0,152 + 0,2552 + 0,1652 + 3 = 14,6.

Y1(1) 40 - 35 - 75 - 45 P1 = F(z0),e z0 = = - = -1,48.

20,0,1552 + 0,352 + 0,252 + o aa axo P1 = F(-1,48) = 0,069.

Toa 2(Y ) = (1- 0,069) 0,1552 + 0,352 + 0,252 + 4 = 18,85.

Toa (1) Y = -32 + 25 + 65 + 35 +1,645 0,152 + 0,2552 + 0,1652 + 3 +14,6 = = -32 + 45 + 9,06 = 22,06, (1) Y = -40 + 3 5 + 7 5 + 4 5 +1,645 0,15 52 + 0,3 52 + 0,2 52 + 4 + 18,85 = = -40 + 70 +10,3 = 40,3, 105 + 355 + 205 230 +Y1(2), Y1(2) = 95, 145 + 655 + 355 340 +Y2(2), Y2(2) = 230, 85 +115 + 75 260 +Y1(3), Y1(3) = 0.

Haxo eep aee yoaa = 155 + 255 + 205 1 1 1 1 -1000 22,06 + 40,3 + 95 + 230 + 0 = 350 - 2761 = -2419.

32 40 230 340 B, o oye peya e oe cac yo-eope.

Oeo, ceye ye yc 2-o 3-o poyo.

a 2 Paccop a X1 = 5, X = 2, X3 = 2.

o oey aox coocax ea, a a e o oey aypao pae a ec oyc 245 + 34 2 + 30 2 = 248 200, 225 + 32 2 + 28 2 = 230 180, 5 X1 10.

ocae Y1(1) 32 - 25 - 6 2 - 3 2 P1 = F(z0),e z0 = = = 1,4.

7,0,152 + 0,25 22 + 0,16 22 + P1 = F(1,4) = 0,92.

Teep axo, o 1(Y ) = (1- 0,92) 0,152 + 0,25 22 + 0,16 22 + 3 = 0,5712.

Y2(1) 40 - 35 - 7 2 - 4 2 P1 = F(z0),e z0 = = = 0,31, 9,0,1552 + 0,3 22 + 0,2 22 + P1 = F(0,31) = 0,62, 2(Y ) = (1- 0,62) 0,1552 + 0,3 22 + 0,2 22 + 4 = 3,7.

Toa (1) Y = -32 + 25 + 6 2 + 3 2 +1,645 0,152 + 0,2552 + 0,1652 + 3 + 0,57 = = -32 + 28 + 4,6 = 0,6, (1) Y = -40 + 3 5 + 7 2 + 4 2 +1,645 0,15 52 + 0,3 22 + 0,2 22 + 4 + 3,7 = = -40 + 37 + 6,03 = 3, 105 + 35 2 + 20 2 = 160 230 +Y1(2), Y1(2) = 0, 145 + 65 2 + 35 2 = 270 340 +Y2(2), Y2(2) = 0, 85 +11 2 + 7 2 = 76 260 +Y1(3), Y1(3) = 0.



Haxo eep aee yoaa = 155 + 25 2 + 20 2 1 1 1 1 -1000 0,6 + 3 + 0 + 0 + 0 = 165 -18,75 - 75 = 72,5.

32 40 230 340 Booo oyeoe aee oo ca oyc. Oao , o ye yc opoo poya ye yc peeo peya epoo yyc.

a 3 Paccop a X1 = 5, X2 = 1, X3 = 3.

o oey aox coocax ea, a a e o oey aypao pae a ec oyc 245 + 341+ 303 = 244 200, 225 + 321+ 283 = 226 180, 5 X1 10.

ocae Y1(1) 32 - 25 - 61- 33 P1 = F(z0),e z0 = = = 0,97.

7,0,152 + 0,2512 + 0,1632 + P1 = F(0,97) = 0,834.

Teep axo, o 1(Y ) = (1- 0,834) 0,152 + 0,2512 + 0,1612 + 3 = 1,85.

Y2(1) 40 - 3 5 - 7 1- 4 3 P1 = F(z0 ),e z0 = = = 0,61, 9,0,15 52 + 0,312 + 0,2 32 + P1 = F(0,61) = 0,73, 2(Y ) = (1- 0,73) 0,15 52 + 0,312 + 0,2 32 + 4 = 2,66.

Toa (1) Y = -32 + 2 5 + 6 1+ 3 3 +1,645 0,1 52 + 0,2512 + 0,16 32 + 3 +1,85 = (1) = -32 + 25 + 4,95 = -2,05, Y = 0, (1) Y = -40 + 3 5 + 7 1+ 4 3 +1,645 0,15 52 + 0,312 + 0,2 32 + 4 + 2,66 = (1) = -40 + 34 + 5,8 = -0,2, Y = 0, 10 5 + 351+ 20 3 = 145 230 + Y1(2), Y1(2) = 0, 14 5 + 651+ 35 3 = 240 340 + Y2(2), Y2(2) = 0, 8 5 +111+ 7 3 = 72 260 + Y1(3), Y1(3) = 0.

Haxo eep aee yoaa = 15 5 + 251+ 20 3 1 1 1 1 -1000 0 + 0 + 0 + 0 + 0 = 160.

32 40 230 340 oyeoe aee aeo peae peye. Hapae ee aa eye aeey eo yye ye e co oe, a a peyx aax. ooy ocaoc a ocyo peyae.

Heoxoo ee pa caa, o peee paccapaex oee, ocoeo cyae peax aa c o oeco epeex opae, pecaec oo c cooae BM. B o cyae eo c oo ecx cex eoo o a paec ooe peee aa oa aa.

Tea 4 EMEHT TEOPP Oa xapaepx ep coo oeceoo coao-ooecoo e coco oeceoc, oocopooc cxoo oo e, a copo, aeex pa epeca, xo a ecox pax ax oe pe a ee eo cxo.

Ta, apep, pxoc cac c pae x, oex oecex epeco. B ycox aoo cce xoca eoxoo coea opacee peoae epec, a ae oac poopeae py pyy epec oex eoc. Ocoe pyoc epe pacpocpae ooee peopeec poopee ey ceoe oo yy eo. Bo cce oo caa, o oe coao-ooecoe ee aeeo epa oa. Cya aaec oumo, ec e yacy copo, epec oopx ooc aco poooo.

Teop p oocc aeaecoy oecee oepoa e ocoo coao-ooeco xapaepa.

4.1 Ocoe o oa acca p Bca aeaeca oe coao-ooecoo e oa oa paa pcye ey ep, .e. o pae epe opaa ceye eo ooe:

a) aepecoae copo;

) ooe ec ao copo;

) epec copo.

a opaoe ocae yaax ooe oa, o p o py epoo ooae.

aepecoae copo yy aee aac poa a, a oeco cex poo ye ooaac epe I. aee opac paccopee cya, oa oeco I oeo. He apya ooc oo pa, o I = {1, 2,..., n}.

oe oooe poa i I ece aaec eo cmpameue.

Moeco cex cpae poa i ooa epe Xi. B ycox oa a po i I pae eoopy co cpae xi Xi peyae eo caaec aop cpae x = (x1, x2,..., xn), aae cumyaue. Moeco cex cya ooa Z.

aepecoaoc poo paaec o, o aoy poy i I o o cya x Z pcaec co, paaee cee yoeope eo epeco o cya. o co aaec upe poa i cya x ooaaec epe Hi(x). Bea Hi(x) aaec yue upa poa i oo ec ece co.

Bx ycox poeae oa coco ope a poo i I eo cpae xi Xi oye coec cya x = (x1, x2,..., xn) eoopoo coa pa Hi(x). Ta opao oeco poo, x cpae x y pa ooc oca eoopy py, o opao aca a = < I,{xi}iI,{Hi}iI >. (4.1) Opeeee pa - o ece opa o, oopo eec o pae epe a poa a oopx cpec oce cocex ee. pa a poecc pecae coo oopao oopc op poa cox cpae.

oce paa peeoo opeee oaae, o py ceye ca e a oopa oe yapa, a a ocoo , o pae epe, oopao, ocyece poecc.





Opeeee pa aaec po c yeo cyo, ec cya cex aee paa y, .e. ec cya pope popax poo paa cye pe ocax poo oeca I.

Booe oop, oea poo i cya x ye yaa pa H(x) e cea ooa paec ae e cea ee cc. Ha o y coaec meopu up c npenomeuu, oee poa, e meopu up c upau. Oao aee aaec paccapaec oo oce, a a eop p c peoe oee coa oa ee eocaoo papaoaa.

Bce p oo pae a a a: oauuoe ecoauuoe. oauue aa oe ooeco oeca I. pa oopo ec poo eoopo oa apae a aca pa ce oa e oceyeo eo paee ey poa oa aac oao. B ecoaoo pe e aoo yaca ec oyee o oooc oeo yaoo pa. Cyecye ceaa eop oaox p aaea oonepamuo meopue, eoope ocoe e oopo yy paccope . 4.6.

Cpe cex ecoaox p c yeo cyo ecece opao eec acc amaoucmuecux up, oopx co poo pao y, a ae x y pa ao cya pa o ee poooo o ay:

H1(X1, X2) = - H1(X1, X2).

o copa yopeee eco, oeca cpae poo 1 aaoceco pe yy oo ooaac epe X Y, a y pa Hi - epe H. aoocecx p c y poa oc ceyee opeeee.

Opeeee yc ao cpae 1-o poa aooo-ao ocaea cooece cpoa eoopo ap A, a ao cpae 2-o poa aoooao ocae cooece coe o ap. Mapy A aa nameo ( ampue up), ec e ee aij pae py 1-o poa (.e.

popy 2-o) p ope 1- poo i- cpae, a 2- - j-.

ooy aaoceca pa ooc ocaec eceo ape cooec c aaec ampuo.

pep 4.1 eoe pepe apye accooy ycy oy oe oe. Cpoc a y oe e oe oo opeee Oao oo peoo, o eo ea xapaepyec pe oo coco (I, II, III). C yeo x coco aapyc p oox apaa yca ao oe (A, , B). a x apao peye cox apa oeceae oeo cee pa e. p (c. p.), oopy oyae pepe p ao oee yca oe cooecye coco cpoca, opeeec ape I II III A 22 23 21 25 B 20 21 Bop o o cce ayeo apaa yca oee oo oa a apy py.

4.2 oe oaoc cpae Teop p a aeaeca ca ee copeeo coco aaec opa yee p, .e. cae coe aae ycao aoe oeee poo ceye ca oa (pay, eecoopa).

Oaoc cpae oeo oo oa o-paoy. To ec o oaoc eop p oaoo pee p e c ooa, apop, aco. Bece c e o c oe, .e.

a apa oaoc oaec ooy oca p oo eyccex aeaecx opypoo. Te ca pae coepaee pecae o oaoc oy po oac aeaec oe.

Oco coepae epa oaoc pee cxoy oecy cxoo oa oo ca ye pecae o oocmu cnpaeuocmu.

Moo, apep, oao cyae ca ay, oopo oopeeo oca cox acyo y pa aoo poo. coe oaoc o cce cya x* p (4.1) opao oo aca a Hi(x) < Hi(x*) x i I, x Z. (4.2) Booc ao cya ca.

Hepyo e, oao, o cyecoae ecoaoo pe cya, oax oo o ocao cce, ec cpaeo pe cee (a oe coaee acyo ecox y). B cyoc, peayeoc oo pa oaoc cooecye caoc ox ep oepyeoo e, oc ee eo yaco.

Ececeo ooy ca pye pecae o oaoc, oe, e co eccope, o ao oee aco peayee.

Oo aoee ooopx op peaa pecae o oaoc oo ca oe paoec, cocoee ceye.

Opeeee Cya aaec paoeco, ec o poo e aepecoa o, o ee apy, .e. ooc o ee.

Ec pa ec aaoceco, o paoeca cya x* ee (x*, y*) opao paoeco cya oo aca H(x, y*) H(x*, y*) H(x*, y), (4.3) p x x X, y Y. e oo, o (4.3) coyec e cpooe epaeco "ee pao - " ceye, o paoecx cya oe ecoo.

Opeeee B cyae aaoceco p cya paoec aaec ceoo moo. Oaaec, o y pa p o cex ee ceox oax pae oo o e aee, oopoe aaec eo up ( aeue up).

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