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Применение экономико-математических методов при решении конкретных аналитических задач

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I?EIAIAIEA YEIIIIEEI – IAOAIAOE*ANEEO IAOIAeIA

I?E ?AOAIEE EIIE?AOIUO AIAEEOE*ANEEO CAAeA*

7.1. A?AOE*ANEEA IAOIAeU

A?aoe/aneea iaoiaeu naycaiu i?aaeaea anaai n aaiiao?e/aneei
ecia?aaeaieai ooieoeeiiaeueiie caaeneiinoe i?e iiiiue eeiee ia
ieineinoe. A?aoeee eniieuecothony aeey auno?iai iaoiaeaeaiey
cia/aiey ooieoeee ii niioaaonoaothua-

io cia/aieth a?aoiaioa, aeey iaaeyaeiiai ecia?aaeaiey
ooieoeeiiaeueiuo caaeneiinoae.

A yeiiiie/aneii aiaeeca i?eiaiythony ii/oe ana aeaeu
a?aoeeia: aeeaa?aiiu n?aaiaiey, aeeaa?aiiu a?aiaiiuo ?yaeia,
e?eaua ?ani?aaeaeaiey, a?aoeee ei??aeyoeeiiiiai iiey, noaoenoe/aneea
ea?oia?aiiu. Iniaaiii oe?i-

ei ?ani?ino?aiaiu a aiaeeca aeeaa?aiiu n?aaiaiey – aeey n?aaiaiey
io/aoiuo iieacaoaeae n ieaiiauie, i?aaeoanoaothueo ia?eiaeia e
ia?aaeiauo i?aaei?ey-

oee. Aeey iaaeyaeiiai ecia?aaeaiey aeeiaieee yeiiiie/aneeo yaeaiee
( a a aiaeeca n aeeiaie/aneeie ?yaeaie i?eoiaeeony eiaoue aeaei
i/aiue /anoi ) en-

iieuecothony aeeaa?aiiu n?aaeieo ?yaeia.

N iiiiuueth eii?aeeiaoiie naoee no?iyony a?aoeee
caaeneiinoe, iai?eia?, o?iaiy ecaea?aeae io iauaia i?iecaaaeaiiie
e ?aaeeciaaiiie i?iae

oeoeee, a oaeaea a?aoeee, ia eioi?uo iiaeii ecia?aaeaoue e
ei??aeyoeeiiiua nayce iaaeaeo iieacaoaeyie. A nenoaia inae
eii?aeeiao ecia?aaeaiea ieacuaaao aeeyiea ?acee/iuo oaeoi?ia ia oio
eee eiie iieacaoaeue.

Oe?iei i?eiaiyaony a?aoe/aneee iaoiae aeey
enneaaeiaaiey i?iecaiaeno aaiiuo i?ioeannia, i?aaiecaoeeiiiuo
no?oeoo?, i?ioeannia i?ia?aiie?iaaiey e o. ae. Iai?eia?, aeey
aiaeeca yooaeoeaiinoe eniieueciaaiey i?iecaiaenoaaiiiai
iai?oaeiaaiey no?iyony ?an/aoiua a?aoeee, a oii /enea a?aoeee
iiiaeanoaaii-

uo oaeoi?ia.

A iaoaiaoe/anee oi?iaeeciaaiiie nenoaia aiaeeca,
ieaie?iaaiey e oi?aaeaiey iniaia ianoi caieiatho naoaaua a?aoeee.
Iie aeatho aieueoie yei-

iiie/aneee yooaeo i?e no?ieoaeuenoaa e iiioaaea i?iiuoeaiiuo e
ae?oaeo i?aaei?eyoee.

Naoaaie a?aoee iicaieyao auaeaeeoue ec anaai
eiiieaena ?aaio iae-

aieaa aaaeiua, eaaeauea ia e?eoe/aneii iooe, e nin?aaeioi/eoue
ia ieo iniiaiua ?ano?nu no?ieoaeueii-iiioaaeiuo i?aaiecaoeee,
onoaiaaeeaaoue acaeiinaycue iaaeaeo ?acee/iuie niaoeeaeece?iaaiiuie
i?aaiecaoeeyie e eii?aeeie?iaaoue eo ?aaioo. ?aaiou, eaaeauea ia
e?eoe/aneii iooe, o?aaotho iaeaieaa i?iaeieaeeoaeueiiai iaeeaeaiey
iinooieaiey i/a?aaeiiai niauoey. Ia noaaeee iia?aoeaiiai aiaeeca
e oi?aaeaiey naoaaie a?aoee aeaao aiciiaeiinoue inouanoaeyoue
aeaenoaaiiue eiio?ieue ca oiaeii no?ieoaeuenoaa, naiaa?aiaiii
i?eieiaoue ia?u ii ono?aiaieth aiciiaeiuo caaea?aeae a ?aaioa.

I?eiaiaiea naoaauo a?aoeeia aiaeeca, ieaie?iaaiey
e oi?aaeaiey iaania/eaaao, eae iieacuaatho iiiaea ia?aiao?u,
nie?auaiea n?ieia no?ieoaeuenoaa ia 20-30% , iiauoaiea
i?iecaiaeeoaeueiinoe o?oaea ia 15-20%.

I?e aiaeeca, inouanoaeyaiii iaiin?aaenoaaiii ia
no?ieeao, eniieueciaaiea iaoa?eaeia naoaaiai ieaie?iaaiey e
oi?aaeaiey niinianoaoao i?aaeeueiiio ii?aaeaeaieth i?e/ei,
aeeythueo ia oiae no?ieoaeuenoaa, e auyaeaieth i?aaei?eyoee, ia
iaania/eaathueo auiieiaiea ii?o/aiiuo ei ?aaio eee iinoaaeo
iai?oaeiaaiey a n?iee, onoaiiaeaiiua a?aoeeii.

?ac?aaioea naoaaiai a?aoeea a no?ieoaeuenoaa
inouanoaeyaony i?e iaee/ee: ii?i i?iaeieaeeoaeueiinoe
no?ieoaeuenoaa e n?iea aaiaea a aeaenoaea iauaeoa eee eiiieaenia
iauaeoia, i?iaeoii-niaoiie aeieoiaioaoeee, i?iaeoa i?aaiecaoeee
no?ieoaeuenoaa e i?iecaiaenoaa ?aaio, oeiiauo oaoiieiae/aneeo
ea?o, aeaenoaothueo ii?i cao?ao o?oaea, iaoa?eaeia e ?aaiou
iaoei. E?iia oiai, i?e ninoaaeaiee a?aoeea eniieuecothony iiuo
auiieiaiey ioaeaeueiuo ?aaio, a oaeaea aeaiiua i
i?iecaiaenoaaiiie aaca no?ieoaeueiuo e iiioaaeiuo i?aaiecaoeee.

Ia iniiaa anao yoeo aeaiiuo ninoaaeyaony oaaeeoea
?aaio e ?ano?nia, aaea a oaoiieiae/aneie iineaaeiaaoaeueiinoe
i?iecaiaenoaa ?aaio oeacuaathony eo oa?aeoa?enoeea, iauai,
o?oaeiaieinoue a /aeiaaei-aeiyo, eniieieoaeue ( i?aa-

iecaoeey e a?eaaaea ), /eneaiiinoue ?aai/eo, niaiiinoue,
iio?aaiinoue a iaoaiec-

iao e iaoa?eaeao, enoi/ieee eo iinooieaiey, iauay
i?iaeieaeeoaeueiinoue auiieiaiey ?aaiou a aeiyo, a oaeaea
i?aaeoanoaothuaa caaeaiea, iinea ieii/a-

iey eioi?iai iiaeii ia/eiaoue aeaiioth ?aaioo. Enoiaey ec
iieacaoaeae oaeie oaaeeoeu, iiaeaioaaeeaatho naoaaie a?aoee
eioi?ue iiaeao eiaoue ?acee/ioth noaiaiue aeaoaeecaoeee a
caaeneiinoe io i?eiyoie noaiu i?iecaiaenoaa ?aaio e o?iaiy
?oeiaiaenoaa; e?iia iauaai a?aoeea auiieiyaiuo eie ?aaio.

Iniiaiua yeaiaiou naoaaiai a?aoeea: niauoea,
?aaioa, iaeeaeaiea, caaeneiinoue.

I?e aiaeeca oiaea no?ieoaeuenoaa iauaeoa neaaeoao
onoaiaaeeaaoue, i?aaeeueii ee ninoaaeai naoaaie a?aoee, ia
aeiiouaii ee i?e yoii caauoa-

iea e?eoe/aneiai iooe, o/oaiu ee i?e iioeiecaoeee a?aoeea ana
aiciiaeiin-

oe aai nie?auaiey, iaeuecy ee eaeea-eeai ?aaiou auiieiyoue
ia?aeeaeueii eee nie?aoeoue a?aiy, cao?a/eaaaiia ia ieo, iooai
oaaee/aiey n?aaenoa iaoaieca-

oeee e ae?. Yoi iniaaiii aaaeii a oao neo/ayo, eiaaea
i?iaeieaeeoaeueiinoue ?aaio ii a?aoeeo ia iaania/eaaao ieii/aiea
no?ieoaeuenoaa e n?ie.

Iniiaiui iaoa?eaeii naoaaiai ieaie?iaaiey,
eniieuecoaiiai i?e aiaeeca, yaeyaony eioi?iaoeey i oiaea ?aaio
ii a?aoeeo, eioi?ue iau/ii ninoaaeyaony ia ?aaea iaeiiai ?aca a
aeaeaaeo. A ea/anoaa i?eia?a i?eaiaeeony ea?oa caaeaiey e
eioi?iaoeee i oiaea ?aaiou ii iauaeoo no?ieoaeuenoaa,
inouanoaeyaiiio ii naoaaiio a?aoeeo . Ii aeaiiui ea?ou,
e?eoe/aneea ?aaiou auiieiyeenue a ia/aea ianyoea n iia?aaeaieai
a?aoeea, iaeiaei caoai auei aeiiouaii ionoaaaiea iiioaaea
iiaee?aiiauo aaeie ii ?yaeo A— , a iineaaeothuay ?aaioa — iiioaae
iiaee?aiiauo

aaeie ii ?yaeo A — caeii/aia n ionoaaaieai ia iaeei aeaiue.

Iioeiecaoeey naoaauo a?aoeeia inouanoaeyaony ia
noaaeee ieaie?iaaiey iin?aaenoaii nie?auaiey e?eoe/aneiai iooe,
o.a. ieieiecaoeey n?ieia auiieiaiey no?ieoaeueiuo ?aaio i?e
caaeaiiuo o?iaiyo ?ano?nia, ieieiecaoeey o?iaiy iio?aaeaiey
iaoa?eaeueiuo, o?oaeiauo e oeiainiauo ?ano?nia i?e oeene?iaaiiuo
n?ieao auiieiaiey no?ieoaeueiuo ?aaio. Aiciiaeai e niaoaiiue
iiaeoiae: aeey iaeiie /anoe ?aaio ( aieaa aei?iainoiy-

ueo ) — ieieiece?iaaoue n?iee i?e oeene?iaaiiii o?iaia ?ano?nia.

?aoaiea iioeiecaoeeiiiuo caaea/ nouanoaaiii
iaeaa/aaony iaee/eai iaeaoia i?eeeaaeiuo i?ia?aii (III),
i?eniiniaeaiiuo e ninoaa-

eaieth iioeiaeueiuo naoaauo a?aoeeia ia YAI.

A ca?oaaaeiie i?aeoeea nenoaiiiai aiaeeca
?ani?ino?aiai a?aoi-iaoaiaoe/aneee iaoiae, iieo/eaoee iacaaiea “
aea?aai ?aoaiee “. Nooue yoiai iaoiaea caeeth/aaony a
neaaeothuai.

Iooai i?aaeaa?eoaeueiie ioeaiee iio?aaiinoae,
i?aaeaa?eoaeueiiai aiaeeca aiciiaeiuo i?aaiecaoeeiiiuo, oaoie/aneeo
eee oaoiieiae/aneeo oneiaee iaia/athony ana i?aaeiieaaaaiua
aa?eaiou ?aoaiey aeaiiie caaea/e. Aia/aea ?ac?aaaouaathony
oe?oiiaiiua aa?eaiou. Caoai ii ia?a aaaaeaiey aeiiieieoaeueiuo
oneiaee eaaeaeue ec ieo ?an/eaiyaony ia ?yae aa?eaioia.
A?aoe/aneia ecia?aaeaiea yoeo aa?eaioia iicaieyao eneeth/eoue
iaiaa auaiae-

iua ec ieo e eca?aoue iaeaieaa i?eaieaiue.

Yoio iaoiae iiaeao iaeoe o ian i?eiaiaiea
i?e ii?aaeaeaiee ii?yaeea ia?aaioee oao eee eiuo aeaoaeae ia
ianeieueeeo noaieao a oeaeyo ieieiecaoeee iauaai a?aiaie
ia?aaioee; i?e onoaiiaeaiee ?acia?ia ?ano?-

nia aeey ieieiecaoeee iaueo i?iecaiaenoaaiiuo ecaea?aeae; i?e
?ani?aaeaeaiee eaieoaeiaeiaeaiee e ae?oaeo ?ano?nia ii
i?iiuoeaiiui iauaeoai; i?e ?a-

oaiee o?ainii?oiuo e ae?oaeo caaea/.

IAOIAe EI??AEssOeEIIII-?AA?ANNEIIIIAI AIAEECA

Iaoiae ei??aeyoeeiiiiai e ?aa?anneiiiai aiaeeca oe?iei
eniieuecoaony

aeey ii?aaeaeaiey oaniiou nayce iaaeaeo iieacaoaeyie, ia
iaoiaeyueieny a ooi-

eoeeiiaeueiie caaeneiinoe. Oaniioa nayce iaaeaeo eco/aaiuie
yaeaieyie ecia?yaony ei??aeyoeeiiiui ioiioaieai ( aeey
e?eaieeiaeiie caaeneiinoe ).

Aeey i?yiieeiaeiie caaeneiinoe en/eneyaony eiyooeoeeaio
ei??aeyoeee.

Iaeiie ec ?ani?ino?aiaiiuo aiaeeoe/aneeo caaea/,
?aoaaiuo n i?eia-

iaieai ei??aeyoeeiiii-?aa?anneiiiiai iaoiaea, yaeyaony caaea/a ia
caione — auione. Aeiionoei, /oi eiathony oaeoe/aneea aeaiiua i
caionea e auionea i?iiuoeaiiuo ecaeaeee.

Oaeoe/aneea aeaiiua i caionea — auionea

i?iiuoeaiiuo ecaeaeee, oun. oo.

Caione xi 18

22

13

20

15

14

xi=102

i

Auione yi

17,9

20,9

11,6

18,7

14,1

12,9

yi=95,4

i

O?aaoaony ii?aaeaeeoue caaeneiinoue auionea ecaeaeee a
n?aaeiai io eo caionea, ninoaaea niioaaonoaothuaa o?aaiaiea
?aa?annee.

Cia/aiey x e y ii?aaeaeythony ii oi?ioeai:

x= ; y=
; n=6, i=1, ….. , 6;

102 95,4

x= 6 = 17 ;
y = 6 = 15,9.

Aeaeueiaeoei au/eneaieyi i?eaeaaony oaaee/iay oi?ia,
/oi iiauoaao

eo iaaeyaeiinoue.

( x i – x )

2

( xi yi – xi yi )

( yi – y ) 2

( yi – y )

(xi – xi ) ( yi – y )

1 1
1,3 1,69 1,3

5 25
5 25 25

— 4 16 — 4,3
18,49 17,2

3 9
2,8 7,84 8,4

— 2 4 — 1,8
3,24 3,6

— 3 9 — 3
9 9

( xi – x ) = 64 ( yi – y
) = 65,26 ( xi – x ) ( yi – y )=64 , 5

i
i i

Oaniioa nayce iaaeaeo iieacaoaeyie caionea e auionea
ecia?yaony eiyooe-

oeeaioii ei??aeyoeee, eioi?ue en/eneyaony ii oi?ioea

V=

Iiaenoaaeyy niioaaonoaothuea cia/aiey, iieo/ei:

.

.

10,75 10,75

V= 3,27 * 3,30 = 10,79 = 0,996.

N/eoay oi?ioeo nayce eeiaeiie ( y=a0 + a1 x ),
ii?aaeaeei caaeneiinoue

auionea i?iiuoeaiiuo ecaeaeee io eo caionea. Aeey yoiai ?aoaaony
nenoaia

ii?iaeueiuo o?aaiaiee:

na + a1 xi = yi

i i

a0 xi + a1 xi = xi yi

Aaee/eiu x2 e xi yi i?aaenoaaeaiu a
neaaeothuae oaaeeoea

2

xi

324

484

169

400

225

196

xi=1798

xi yi

309,6

459,8

150,8

374,0

211,5

180,6

xi yi =1686,3

Cia/aiea a0 ii?aaeaeyai ec ia?aiai o?aaiaiey:

6a0+ 102a1 =95,4;

102a0+1798a1 =1686,3;

95,4 — 102a1

a0 = 6 , eee a0 =
15,9 — 17a1.

Iiaenoaaeyy iaeaeaiiia au?aaeaiea a0 ai aoi?ia
o?aaiaiea, iaoiaeei

cia/aiea a1:

102 (15,9 — 17a1)+1798a1 = 1683,3;

1621,8 — 1734a1 + 1798a1 =1686,3;

95,4 — 102a1

a0= 6 , eee a0=15,9 — 17a1.

Iiaenoaaeyy iaeaeaiiia au?aaeaiea a0 ai aoi?ia
o?aaiaiea, iaoiaeei cia/aiea a1:

102 ( 15,9 — 17a1)+1798a1=1686,3;

1621,8 — 1734a1+1798a1=1686,3;

64a1=1686,3 — 1621,8;

64a1=64,5; a1=1,01;

a0=15,9 — 17 * 1,01; a0=15,9 — 17,17;

a0= — 1;

Eoae, o?aaiaiea ?aa?annee a ieii/aoaeueiii aeaea
iieo/eei neaaeo-

thuee aeae:

y= — 1,27+1,01x

I?iaa?ea:

y= — 1,27+1,01 * 17= — 1,27+17,17;

y=15,9.

IAOIAeU EEIAEIIAI I?IA?AIIE?IAAIEss

Iaoiaeu eeiaeiiai i?ia?aiie?iaaiey i?eiaiythony
aeey ?aoaiey

iiiaeo yeno?aiaeueiuo caaea/, n eioi?uie aeiaieueii /anoi
i?eoiaeeony eiaoue

aeaei a yeiiiieea. ?aoaiea oaeeo caaea/ naiaeeony e iaoiaeaeaieth
e?aeieo cia/aiee ( iaeneioia e ieieioia ) iaeioi?uo ooieoeee
ia?aiaiiuo aaee/ei.

Eeiaeiia i?ia?aiie?iaaiea iniiaaii ia ?aoaiee
nenoaiu eeiae-

iuo o?aaiaiee ( n i?aia?aciaaieai a o?aaiaiey e ia?aaainoaa ),
eiaaea caae-

neiinoue iaaeaeo eco/aaiuie yaeaieyie no?iai ooieoeeiiaeueia. Aeey
iaai oa-

?aeoa?iu iaoaiaoe/aneia au?aaeaiea ia?aiaiiuo aaee/ei,
ii?aaeaeaiiue ii-

?yaeie, iineaaeiaaoaeueiinoue ?an/aoia ( aeai?eoi ), eiae/aneee
aiaeec. I?eia-

iyoue aai iiaeii oieueei a oao neo/ayo, eiaaea eco/aaiua
ia?aiaiiua aaee/e-

iu e oaeoi?u eiatho iaoaiaoe/aneoth ii?aaeaeaiiinoue, eiaaea a
?acoeueoaoa ecaanoiie iineaaeiaaoaeueiinoe ?an/aoia i?ienoiaeeo
acaeiicaiaiyaiinoue oae-

oi?ia, eiaaea eiaeea a ?an/aoao, iaoaiaoe/aneay eiaeea
niaiauathony n eiae-

/anee iainiiaaiiui iiieiaieai nouiinoe eco/aaiiai yaeaiey.

N iiiiuueth yoiai iaoiaea a i?iiuoeaiiii
i?iecaiaenoaa, iai?eia?,

en/eneyaony iioeiaeueiay iauay i?iecaiaeeoaeueiinoue iaoei,
aa?aaaoia, iioi/-

iuo eeiee ( i?e caaeaiiii anni?oeiaioa i?iaeoeoeee e eiuo
caaeaiiuo aaee/ei)

?aoaaony caaea/a ?aoeeiiaeueiiai ?ane?iy iaoa?eaeia ( n
iioeiaeueiui auoi-

aeii caaioiaie ). A naeueneii oicyenoaa ii eniieuecoaony aeey
ii?aaeaeaiey ie-

ieiaeueiie noieiinoe ei?iiauo ?aoeeiiia i?e caaeaiiii eiee/anoaa
ei?iia ( ii aeaeai e niaea?aeaueiny a ieo ieoaoaeueiui
aauanoaai ). Caaea/a i nianyo

iiaeao iaeoe i?eiaiaiea e a eeoaeiii i?iecaiaenoaa ( ninoaa
iaoaeeo?ae/an-

eie oeoou ). Yoei aea iaoiaeii ?aoathony o?ainii?oiay caaea/a,
caaea/a ?aoee-

iiaeueiiai i?ee?aieaiey i?aaei?eyoee-iio?aaeoaeae e
i?aaei?eyoeyi-i?iecai-

aeeoaeyi.

Ana yeiiiie/aneea caaea/e, ?aoaaiua n i?eiaiaieai
eeiaeiiai i?i-

a?aiie?iaaiey, ioee/athony aeueoa?iaoeaiinoueth ?aoaiey e
ii?aaeaeaiiuie ia?aie/eaathueie oneiaeyie. ?aoeoue oaeoth caaea/o
— cia/eo ec anao aeiion-

oeii aiciiaeiuo ( aeueoa?iaoeaiuo ) aa?eaioia eo/oee, iioeiaeueiue.
Aaaeii- noue e oeaiiinoue eniieueciaaiey a yeiiiieea iaoiaea
eeiaeiiai i?ia?aiie?i-

aaiey ninoiyo a oii, /oi iioeiaeueiue aa?eaio auae?aaony ec
aanueia cia/e-

oaeueiiai eiee/anoaa aeueoa?iaoeaiuo aa?eaioia. I?e iiiiue ae?oaeo
niini-

aia ?aoaoue oaeea caaea/e i?aeoe/anee iaaiciiaeii.

A ea/anoaa i?eia?a ?anniio?ei ?aoaiea caaea/e
?aoeeiiaeueiinoe en-

iieueciaaiey a?aiaie ?aaiou i?iecaiaenoaaiiiai iai?oaeiaaiey.

A niioaaonoaee n iia?aoeaiui ieaiii o/anoie
oeeoiaee ca ia?aoth iaaeaeth aeaeaa?y auionoee 500 eieaoe
iiaeoeiieeia oeia A, 300 eieaoe oeia A e 450 eieaoe aeey
iiaeoeiieeia oeia A. Ana eieueoea oeeoiaaeenue ia aeaoo aca-

eiicaiaiyaiuo noaieao ?aciie i?iecaiaeeoaeueiinoe. Iaoeiiia a?aiy
eaaeaei-

ai noaiea ninoaaeyao 5000 iei. O?oaeiaieinoue iia?aoeee ( a
ieiooao ia iaeii

eieueoei ) i?e ecaioiaeaiee ?acee/iuo eieaoe oa?aeoa?ecoaony
neaaeothueie aeaiiuie:

Cao?aou a?aiaie ia
iaeii eieueoei

Noaiee oeiia, iei

A A
A

1 4
10 10

2 6
8 20

Neaaeoao ii?aaeaeeoue iioeiaeueiue aa?eaio
?ani?aaeaeaiey iia?aoeee

ii noaieai e a?aiy, eioi?ia auei cao?a/aii i?e yoii
iioeiaeueiii aa?eaioa. Caaea/o auiieiei neiieaeniui iaoiaeii.

Aeey ninoaaeaiey iaoaiaoe/aneie iiaeaee aeaiiie
caaea/e aaaaeai neaaeothuea oneiaiua iaicia/aiey:

x1, x2, x3 — ciioaaonaaiii eiee/anoai eieaoe aeey iiaeoeiieeia
oeiia A, A, A,

i?iecaiaeeiuo ia noaiea 1;

x4, x5, x6 —- niioaaonoaaiii eiee/anoai eieaoe iiaeoeiieeia
oeiia A, A, A, i?iecaiaeeiuo ia noaiea 2.

Eeiaeiay oi?ia, io?aaeathuay e?eoa?ee
iioeiaeueiinoe, aoaeao eiaoue aeae:

min a ( x ) = 4×1+10×2+10×3+6×4+8×5+20×6

i?e ia?aie/aieyo

4×1+10×2+10×3
< =50006x4+8x5+20x6 < =5000x1 +x4 = 500x2 +x5 = 300x3 +x6 = 450xi >=0, j = 1, . . . . , 6

I?aia?acoai oneiaea caaea/e aaaaeaieai
aeiiieieoaeueiuo ( aniiiiaa-

oaeueiuo ) e oeeoeaiuo ia?aiaiiuo. Oneiaea caieoai oae :

min a( x ) =
4×1+10×2+10×3+6×4+8×5+20×6+Mx9+Mx10+Mx11.

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