optimization theory

3
o;rclr N o ct.pr0*o,= ruil' TicrpslcPa'olv eluprriuatoll' (otci$eco o-r.i' upLeoo rooto';) Eivetur orro r"1l o7,6o11 2t oe Lrio ;repio6o. T'o suvor"r.ro Kooro( iiopcTr-';Yl1g t rit or"txo xoo;o: = o-/-r] \: - I 0' 3acus (a) ro cptur:o pave0o9;iopaYclrrlq, nl' tr)r'ir't 6-' zse ,. ,4 , -^6 a: iB) to payeOoq rapo'lcrplq ?rcx ofioqtpci io liriroto xep6og' rur \ioo Lzolrs ' o:!3!-i = -- I -)Lttp\Jlu lrlq,ruu urLu\ycyoi LU l-.c/Lv ,'-,' - v ;- a { ,,)},o rte-iedo:;rapG-/,u-.rrl;;ou cn'Tloror7-el oro ii.cytoro ilero {ooro: d'nrtt ,0)L- 4aG l)'2- aLi j \11c. etcipiu ;rerpai-ciou ,r r.,:pi(at 6rt rccto. ;r1 otivor(1 Tecotpiloeclr' ';ra dr''tirlori zerpe)'aic-u oe ptu dedoLLr:,'1 ouoigol ebuoouq. ri c;io6oor-i a1; reooJ'1g tor') Jtoltpl;il{1\/ou' oe Baeo; 7etbtptl61-1g. eiap'catot azo -.i. :i.,^-^, ^-^ -- -^'t- \,' ro Zllolo lptiotuo;roi:1ol'; qe ;<al divarot G,7ro rI G^/.t's1 I a/.// - / ' Ct l- a ',/tt ) -/-; c,NL ,o6r\-1 B = 100 T':'.i B : ro clOgotorrxo BaSo; 7e6rplcr1g (petpal rctL T : o 'Lpovog yer.'ttprloriq (r1pap'eq). To creUepo KooIoc rqq iecl-rO1o1q aiYo.L 8i0 000 6pc1ue5 uYcr qpLepa To rooroq n1g xeour-l1g eiYcrL 2.i00 COO 5pc71tig KCn o o.;Eorrouue\o; /povLr; t)"i-r:Ln1; ti-ig rceooi"1q 18 cboe; I 0,75 IP€p{ H,verbtp1ot1 liverar ca 24op1 l3uori. o,iL-.1C6 lS'r' < or t-= l!- aNs/ola'7- o.rt- / / ozou (r-l) Epeita ro Beitroro Ipol'o i:."'ttrorooro,o1l; qq xeoeilg 6oie "'c' icpoirur;ct ro G.1,' rc sTrolrof;,re-r'o puOog i E.tripl1olg eivut 2000 ptrpo ro tllvo ({,1) Bpeire 19. B6i"il.oto Ipo\/o ,;r't-txctcto;Gon; nlg reoaLlq r':ote l'a irDoK1)fir€r ro eloXtoro url','tsio xooroc e)"ay1oro utlr'tcio Kosro: o.v rc uxoircupn'o pri0og ;'euiplolq 5ii's1 -i000 irerpo ro 1,tllvo'' (7) Bpreira to peirroro 7po.\ o uvrtxctootctolq qg raoa,,.r1,, roote !o EiLL'c1)'{XCL\!ttct ro FeYrcto paOoq Teurrillol,; aYo p$'o 7.CIPi; '''c a(etu'ietai tc rlootoc. iii) Ai' 1 a;a'r*s 61at a;io$ocrr 12.000 6pu;4ro'',' ova pirpo Bd0oug 7ecu1tp1o1-c. fipewe ro Bei"troto lpovo m,'rtKfi?ocraolg nlq rego.?-iq cbota vcl irpon{;rret ro Pt7toro rep6oq' I 6 \'ire Oeioual peiagopaq r;vp'r1i>1, rcoptiov eler rctrln'6pLrri 8ratoprq 6rou6lpou X xctt rc8e ai<po tou r.riildpcir rt)-eir,.ai !i€ ai,o, 1;iroolipr-c (Srauitl-.ou ETrioIq X) To x6oro; rou r.titl'Sprxou rolruatlou aivat i50 UOtr -\ : ip.s7116i fi.\'c uei;ro $11(o1): KCrr ro Kooroc rui3e rluiopatpicu eilo,r 2 "q 0. 000 X''* Jp-,u7p6q. C e.aLroilpLs,,cg oTKo! rn; 6aqeuer,"t1; ur'-rio;oi71o t(ooro(" eivar .i0 ri;. Bpelte n,, Bii,norec 6tso;soaiq r,1q 6e(o.pa'1c xrt io Q'Eya; riLcirric <ctr€.iaeva rLirlpa "p1; oyjlp-aro; op0o,vcrviot' tptYoivou pe ruOeteg zie-up6g'{0 rur 30 p' xcti u,-tor€i1,c.,loa 50 u. O r6L,r:r1: a;rthirei va y,rioei pta tepaTol'r1 rcu,roLrciu p6oc oto oir<o;ra8o !i-a rn Lrt'i'toEl 6r-Lr unl e;!loat'etc{. Bpeita ;qr' ;i-eopa rlg KctrciKlo,; i:pTlot,uoirorrbr"tsc (cr) aurriOq 6uroor:rx1 ovui,i-ic,1- i<ct (B) 11 ue0o6o ror'' iro)-iuzui"clslaotrbv Lagran-a:. i'i ;: i1

Upload: yiannis-hadjiloizou

Post on 12-Aug-2015

77 views

Category:

Documents


0 download

TRANSCRIPT

Page 1: optimization theory

o;rclr N o ct.pr0*o,= ruil' TicrpslcPa'olv eluprriuatoll'

(otci$eco o-r.i' upLeoo rooto';) Eivetur orro r"1l o7,6o11

2t

oe Lrio ;repio6o. T'o suvor"r.ro Kooro( iiopcTr-';Yl1g

t rit or"txo xoo;o: = o-/-r] \: - I 0'

3acus (a) ro cptur:o pave0o9;iopaYclrrlq, nl' tr)r'ir't 6-' zse ,. ,4 , -^6 a:

iB) to payeOoq rapo'lcrplq ?rcx ofioqtpci io liriroto xep6og' rur \ioo Lzolrs ' o:!3!-i = -- I

-)Lttp\Jlu lrlq,ruu urLu\ycyoi LU l-.c/Lv ,'-,' - v ;-

a { ,,)},o rte-iedo:;rapG-/,u-.rrl;;ou cn'Tloror7-el oro ii.cytoro ilero {ooro: d'nrtt ,0)L- 4aG l)'2-aLi

j \11c. etcipiu ;rerpai-ciou ,r r.,:pi(at 6rt rccto. ;r1 otivor(1 Tecotpiloeclr' ';ra dr''tirlori zerpe)'aic-u oe ptu

dedoLLr:,'1 ouoigol ebuoouq. ri c;io6oor-i a1; reooJ'1g tor') Jtoltpl;il{1\/ou' oe Baeo; 7etbtptl61-1g. eiap'catot azo-.i.:i.,^-^, ^-^ -- -^'t- \,'

ro Zllolo lptiotuo;roi:1ol'; qe ;<al divarot G,7ro rI G^/.t's1I a/.// - / 'Ct l- a ',/tt )

-/-;c,NL

,o6r\-1B = 100 T':'.i

B : ro clOgotorrxo BaSo; 7e6rplcr1g (petpal rctL

T : o 'Lpovog yer.'ttprloriq (r1pap'eq).

To creUepo KooIoc rqq iecl-rO1o1q aiYo.L 8i0 000 6pc1ue5 uYcr qpLepa To rooroq n1g xeour-l1g eiYcrL

2.i00 COO 5pc71tig KCn o o.;Eorrouue\o; /povLr; t)"i-r:Ln1; ti-ig rceooi"1q 18 cboe; I 0,75 IP€p{ H,verbtp1ot1

liverar ca 24op1 l3uori.

o,iL-.1C6 lS'r' < or t-= l!- aNs/ola'7-o.rt- / /

ozou

(r-l) Epeita ro Beitroro Ipol'o i:."'ttrorooro,o1l; qq xeoeilg 6oie "'c'

icpoirur;ct ro

G.1,' rc sTrolrof;,re-r'o puOog i E.tripl1olg eivut 2000 ptrpo ro tllvo

({,1) Bpeire 19. B6i"il.oto Ipo\/o ,;r't-txctcto;Gon; nlg reoaLlq r':ote l'a irDoK1)fir€r ro

eloXtoro url','tsio xooroc

e)"ay1oro utlr'tcio Kosro:

o.v rc uxoircupn'o pri0og ;'euiplolq 5ii's1 -i000 irerpo ro 1,tllvo''

(7) Bpreira to peirroro 7po.\ o uvrtxctootctolq qg raoa,,.r1,, roote !o EiLL'c1)'{XCL\!ttct ro FeYrcto paOoq

Teurrillol,; aYo p$'o 7.CIPi; '''c a(etu'ietai tc rlootoc.

iii) Ai' 1 a;a'r*s 61at a;io$ocrr 12.000 6pu;4ro'',' ova pirpo Bd0oug 7ecu1tp1o1-c. fipewe ro Bei"troto lpovo

m,'rtKfi?ocraolg nlq rego.?-iq cbota vcl irpon{;rret ro Pt7toro rep6oq'

I

6 \'ire Oeioual peiagopaq r;vp'r1i>1, rcoptiov eler rctrln'6pLrri 8ratoprq 6rou6lpou X xctt rc8e ai<po tou

r.riildpcir rt)-eir,.ai !i€ ai,o, 1;iroolipr-c (Srauitl-.ou ETrioIq X) To x6oro; rou r.titl'Sprxou rolruatlou aivat

i50 UOtr -\ : ip.s7116i fi.\'c uei;ro $11(o1):

KCrr ro Kooroc rui3e rluiopatpicu eilo,r

2 "q

0. 000 X''* Jp-,u7p6q.

C e.aLroilpLs,,cg oTKo! rn; 6aqeuer,"t1;

ur'-rio;oi71o t(ooro("

eivar .i0 ri;. Bpelte n,, Bii,norec 6tso;soaiq r,1q 6e(o.pa'1c xrt io

Q'Eya; riLcirric <ctr€.iaeva rLirlpa "p1; oyjlp-aro; op0o,vcrviot' tptYoivou pe ruOeteg zie-up6g'{0 rur 30 p' xcti

u,-tor€i1,c.,loa 50 u. O r6L,r:r1: a;rthirei va y,rioei pta tepaTol'r1 rcu,roLrciu p6oc oto oir<o;ra8o !i-a rn Lrt'i'toEl

6r-Lr unl e;!loat'etc{. Bpeita ;qr' ;i-eopa rlg KctrciKlo,; i:pTlot,uoirorrbr"tsc

(cr) aurriOq 6uroor:rx1 ovui,i-ic,1- i<ct

(B) 11 ue0o6o ror'' iro)-iuzui"clslaotrbv Lagran-a:.

i'i;:i1

Page 2: optimization theory

560 006

' OXuo=

V - n >*s ..,- n)A

o - I-r>&s

leo 2--46o ooo X

nxz

0 000 xo'5 ( o.

ive 7nr )(plor

(- J€,r^f,.*L

6s 2XIlxz 3 Fx) 3

It -F\344ooo X'-' - oI

- L.3o1q 14oo

Page 3: optimization theory

1n- ;$J

-o-5 4 ooo Xb4

*: -L nx3Lr(x - 36o ooo

6:J sr.o

6o _ 2^ )-r- IZ++ ooo}

tY- a'3\tc

l?!n= -ro. """r"'u r FtI) - . (,)

Y = 8- 06< I l3 Z 8- o05..^