صفحه 1:
ی
V1 ملاسما مه ر() توم موم لته سول( ود ساس م11
Oxotra ond Dusievakne Ovosatarnrannnt .با Dane روا ,مت 24
resection: W. Guarper
0
Copyright (c) 2003 Brooks/Cole, a division of Thomson
صفحه 2:
اه مه مس 1 21-10 3
و را و و موه توا رت لهج ورین تروق
raised ork ars. موكلا
we z= Oxy + Oxo وه اس
Ce Pe ORT Oxy te SDD (Prichin rocetctd)
OO (Gapeuy mwtrcd) 5 ولا ود
mS PO (deword sowie)
eX ZO — (ees revretva)
Okere:
aq = cucvber oP subdiers produced wack weels
امه < ود oP tras produced each weeh.
Copyright (c) 2003 Brooks/Cole, a division of Thomson
صفحه 3:
DDN 0-0 ۵ 0 © Cowan Pooks
“her opted ack Pow ty
LO wae 2 = 100, x=
BO, xo = OO (port O ms
the صمي to the right) ocd it
baw ma, 20, orl 56 (fe shark
تج امه لین
اد هت مت
ew would chooges to the
probles's vbievtive Pucmtioa
تام or right-hoerd
side vohues chorge this
vpttcral svhutica?
Copyright (c) 2003 Brooks/Cole, a division of Thomson
صفحه 4:
اه مه سس 10 21-10 3
(Graphic ocralysis oP the ePPet of مس( مشاه مه و من و
vite Por the Biapetto LP skews:
Oy tepevion, we cod see thot wokiag the slope oP the isoproP it lice
wore aegaive thac the Poishte coastratat (slope = -O) will couse the
vpticodl potat to switchs Prose poiat to نمی C.
Likewise, wohiog the slope oP the tsvproPit hoe bess oeyative tho the:
perpediry ovestratat (slope = -() wil couse the optical pote to switchs
Prow poict @ te port @.
Cleury, the slope oP the isoproPit hoe west be betwees -O ocd -0 Por
the curred busis to اون تحص
Copyright (c) 2003 Brooks/Cole, a division of Thomson
صفحه 5:
اه سم ۹ 10۱ 10-10 BED
Dke vdhuer oP he cootibutica to proPit Por svlders Por whick tke cuncect optical
basis (xq,%0,59) wil rewrote optcodl coo be deterciced os Polis!
Let ma be the coairbutios ($9 per solder) to the proPt. (Por what ches oP cy doer
مس متا امه با opal?
ممصم 2 رو + زورك مه له 0 - زد بو ۵
ed 0
ا ولتت = رس weg
>©- :ل > وراد > مه
© > وح > © ١. :صاصر يه سا وام
و
Copyright (c) 2003 Brooks/Cole, a division of Thomson
صفحه 6:
اه مه مس 1 21-10 3
(Graphicd @odbsis of the @PPect oP oa Okoage ic RWG a the
L's Opticodl Gotutiva (usiag the Giapetio problew).
© qropkicd ccdpsis coc ds be used to deterxvice whether ذا جات و
the rhe oP a poestroict wil wake the punedt basis uv brogyer optical. (Por
mop, bet ba = currber oP ما رجا الم
he curred opteal svtutiva (pot B) ts where the corpeury ced Pietshtargy
باه تسه IP the vale oP by is cbooged, theo os bray os
وی رن امه ری سا مور ane biedicy, the optical
از
Copyright (c) 2003 Brooks/Cole, a division of Thomson
صفحه 7:
اه مه سس 10 21-10 3
0
4a tke Btapetio problew to ke
right, we see that P ba >
(20, xa wil be مج قصب
PO ced wil viokte the لحم
powirad. ,مدا & by < OO,
رید Wil be bese tort CD oerd ther
اوه شوه Por x
wail be vickted.
DherePore: OO S$ وط > 00
on x
Rotoking cocstratal, bd = CdtD
OAD = 2 سا ول
وه
ایس مسا
Rothiag eoastratal, bd = AD
وه
هه
Dhe curred baste rewaier
دمج Por OD Shu S120, -g
bat the devisiva vorble uve
رت سره لو
و مه وه وم eo
Copyright (c) 2003 Brooks/Cole, a division of Thomson
صفحه 8:
اه وه سور( سدس 0-0 BOM
Ohad Prives (veka he Brapetiy problew)
is ote koportedd io detec how o choy io cousin's rhs chores the
ساره مرن جرا Or :متا
Dhe shadow price Por the tis cocstcatat oP oa LP is the ارت روا مج
و و او و مان و و و او مود لوف
pevblese) او بطم و خأ bay mar. (Dist ebsites op tre
Pei و ا eaves the ون مه
۳ ره بت ما ما۳ ۵ + 100 رم بط (ase cris fe
ع وج موه ام را با رن عم ما مه 90 + A ocd
x0 = OO - ۵ حطس = Oni + Oxo = (CO + A) + 60606 - ۸۵( ۶ 6۵ + ۸
hve, oe bag oF he cunt boasts ی بط و و او و ره مر
و و مج the سرد اوه by $0. Go, he shadow price Por
the Prat (Proshioy hours) cocmtrctct is $0.
و
Copyright (c) 2003 Brooks/Cole, a division of Thomson
صفحه 9:
اه وه سور( سدس 0-0 BOM
عصراهه<) روهظ oP جججواءصوو |"
Por severd recs! مروت وراه و6
۰ و ۳ سوه تن من راو ون cheer,
جراوه وا موی ج ۱ موه وراه رورطووو the problecr orci.
0
chaps to $9.60, sevstviy omer shows he curred schtiod recrcics
paced.
٠١ بف ص9 obo LP parnveters. athe Bipot problew Por رام
Pike weehy deword Por sober of lest OO, the opted schar
ewan OO sokters ord OO trace. Phus, evra P dewond Por
ری ها ماو the poepaay con be Rady ooaPidet frat it ott
و من produce OD sokters ard OO wats.
Copyright (c) 2003 Brooks/Cole, a division of Thomson
صفحه 10:
سه ما لت 105 2-11 5
AP aa LD kos wore thao two decisive varubles, the rocge oF
valves Por a rhe (or objective Puortioa ooePPictet) Por
whick the basis newvuies opticcd! cocant be detercviced
دی مد
hoe but this is oPtec روا مه سا مت مرجم لك
deterxviced by a puckoged دیص they are و رصح
powpuier progrca. LIDOO wil be used aed the
interpretaiiva oP its secsiiviy osdsis discussed.
0
Copyright (c) 2003 Brooks/Cole, a division of Thomson
صفحه 11:
عبت رم لسن 2-1 3
Oovsider the Polowieg soxvizaiog probes. Oteov sels Pour types
oP produsts. The resvurves ueeded ty produce vor voit oP eal
we!
شمه | یی | Prot | Prk | عمج
موم 9 8 Rav word
Ss 9 5000 م« 9 Lows oP bor
se 56 5 so عم 5
Do weet nse dew, exardy OSO total vite wast be produced.
بسا هلجم مومس POO units of product @ be produced.
Pore oa LP ty مرو proba.
Detox = xeober oP units oF product i produced by Diary.
00
Copyright (c) 2003 Brooks/Cole, a division of Thomson
صفحه 12:
3 ۰-1 هه مر لسن
ل موز ول(
wor z= Pxq بعرم ۲+ م9 + ©
ود را + xe + x9 + xp = 0
xe 2 FOO
Ox + Oxe + Ps + Pap S FOOO
Ox + Px + Gag + Oxe S SOOO
7,7۵, 2 0
©
Copyright (c) 2003 Brooks/Cole, a division of Thomson
صفحه 13:
0 — Vke Ovwputer ced Grusiivipy Poabsis
1۷۸ 411 + 610 + 723 + 06
SUBJECT TO
2( 1 +۵ +3 + 4 2 0
3( ۱4 <- 0
4 21 + 322 + 413 + 7 14 >< 0
5( 3۱1 + 42 + 513 + 6164 >< 0
END
LP OPTIMUM FOUND AT STEP 4
ای فجفی LAIDOO
و
FUNCTION VALUE
.6650 )1 مخ هو وا
VARIABLE VALUE REDUCED cost سارت
x1 0.000000 1.000000 ات لبون
0.000000 4400.000000 2
x3 150,000000 0,000000 اس سا نم
clea x4 490.000000, 0.000000, 0
Row SLACK OR SURPLUS DUAL PRICES الحم سره سل
3.000000 0.000000 )2
sek in. 3) 0.000000, 2.000000
1.000000 0.000000 )4
0.000000 250.000000 )5
NO.ITERATIONS=_4
9
Copyright (c) 2003 Brooks/Cole, a division of Thomson
صفحه 14:
له هه له 0 20-7 7
۱00۵۵۵ WW OVO MC OGOAG ۵ 000۵۵۵
Od COOPMOAGOT KOOL
CORMOLO — CORROOP.— OLOOHOLD
PUOOOOLD
مموهومهد 2 مومه
01
Xd F.OOOHOD همهم
x8 B.M0ODOD 0666668
©S00000
PMOOOOD — d.DOOOO
B.H00O0D =~ E.-MDODD
ROUVMLOOO O18 OOH
ROM CORREO OUOMOOLD
OULOOOOLD
100۵۵۵۵۵ مد
ae
IGaryriabtd@k2003 Brooks/Cole, a division of Thomson
صفحه 15:
اه مه له 0 20-1 7
MAX 4 )1 + 6 3ع 7 + 2ك + 4
SUBJECT TO
2) XL4+X24X34X4= 0
3) X4>= 0
4) 2 )1 + 3 2 + 43 + 7 4 >- 0
5( 301+ 4 (2 + 513 + 614 > 0
END
OPTIMUM FOUND AT STEP 4
REDUCED COST
1.000000
0.000000
1150.000000 0.000000
x4 400.000000 0.000000
Row SLACK OR SURPLUS DUAL PRICES.
2) 0.000000 3.000000
3) 0.000000 -2.000000
4) 0.000000 1.000000
0.000000 250.000000 كك
NO. ITERATIONS= 4
ط77###ح##7بب 77_77 22 ۰ زر
Copyright (c) 2003 Brooks/Cole, a division of Thomson
صفحه 16:
5-1 Oowputer ord Grusiviy Poabsis
eterpretaiva oP shadow prives Por the Diao LP
ROO CLOCK OR GCORELOG OOGL PRICES
سم 5000000 0.000000 (
اد
9) 0.000000 ©.000OOO —(praxhes
© decreed)
(raw watered ۱۵۵۵۵۵۵ 0.000000 م
chard, steht (Died) prise whine’ $O وو ع سم eins rece oF جد قيمع
عو تاج سس تن opi RD ۲ مس(
0.7۳ SOR رت 0ب rot pack al korewer fr he requirewed Fi
proche wil deorewse revenue by $2. Phe $0 shadow price Por ovceirctat © trophies
له من uot of ra arent (al 07 cost) eoreases td even by $11. 6۳
ای 4 مین coy orklioad kibor (oto pet) wil wt koprove tokd reve.
©
Copyright (c) 2003 Brooks/Cole, a division of Thomson
صفحه 17:
3 2-1 عبت رم لسن
Gkhadow price sigue
0 مرو < لب موی wil duvays have موی
shadow prives.
Corcstrotts with < wil dvds hove woreysive shadow
prices.
9. Equality coostrots way have o posiive, a ceqaive, oro
zero shadow price.
ae
Copyright (c) 2003 Brooks/Cole, a division of Thomson
صفحه 18:
سه و ای 105 2-171 5
Geusiivipy Podpsis ont Glack/Bxcess Ourubles
(Por ony equity comminddt, fhe product of the volves oP the coats
sholexcess varble oad the poosirad's shadow price cvet equ 267.
Dhis kophes thot oay ورن موه stack or excess vartble > D wal ave
zeny shadow price. Orolo), وله موه و موه زو price
swust be bray (have stuck or excess equals er). Por cocsirakts wth
xwwery stack or excess, rehiicuships ore detaled in ihe toble below
Dye oP Clune Iarewe lund Orrewe
اون Por rhe ۳ وا
s م = othe oP shaky
2 = ude oP excess bod
06
Copyright (c) 2003 Brooks/Cole, a division of Thomson
صفحه 19:
له هه اه 0 20-17 0
وب ز()]
or basic بسا همم تا م) مور سا مشاه ون بط میا
ta the opiard schiios eqs (D), coniog cet be used usec ter prety نون
te LIDOO rips.
Por aa LP watts oo
sree Fler eters 00 ۰ 10+ ۱۵ + 9 +
۱۱۵۵۵ له نت
fess نانوی جه نو are GOBIECT TO
-> 0 + ۱۵+ 6۵ +0( ره ec bein اد
بويا وود ا ماو
he LADO LE | PO سین
to te 9) +۱8 + 9 29 +۱۵6 <= 060 سای مج(
vutput 0006۵ را عطا لجت یت
> 6 .0 + ۱+ + 0< © ( ات مج wrt tke
6) ۱+۱۵ +۱ > 0
0©
Copyright (c) 2003 Brooks/Cole, a division of Thomson
صفحه 20:
LP OPMOOD 60۵00 6 و هه
6090001۳16۵ 0۳000۵0/۵۵ ۵ 8
0( ۵
60100 0) ۲۵۵۵۵۵0
0 .0۵۵00 9000007079
o.ooodkh 100000000080
Sboooow 0 000000
مه
ROD GLECK OR GORPLOG ۵86 ۵0۵
0 00000
0 000000
0 00000
0 000000
صفحه 21:
O@d COEPPICIEDT ۹۵۵
a. ۱ ۵ OI ور nee بارا RO ie
COG 08
06008
xa 0000۳00 90000000
9.000000
xe 0000 9000000
000000
xo 90000۳00 9.000000
9809
xe 500000000 9000000
۹
RIGLTPLOOD GIDE ROOEES
ROO CORREDT او
@LLODCOLE
RUG 08
06006
e 000000 222220000
6000000000
9 19000000 00000۳00
۲ سح 60
Copyright (c) 2003 Brooks/Cole, a division of Thomson] ووومومووه
صفحه 22:
۲۳۱۸۵۶ ۵
004۵ © 9 x
BONE, 0 Oana كك Bd oe
اه وس و یی
e xe 0.000 ۰ O00 ۵
0900 ۰ 00
9 X98 0/060 ۰ ۰0۵۵0 0۵۵0 ۵
8
€ GK F DOOD ۵۵۵۵ 0۵۵ 0
000
5 x 1۵۵8۵ DOOD 0.0۵۵۵ 6
0.06
ROO CKD )ارا 6: ۵9
0 990 0000 0
20۵000
e 0960 0.000 0
000
9 0969 0000 9
8 سس
Fe eer Copyright (c) 2003 Brooks/Cole, a division of Thomson]
صفحه 23:
اه مه له 0 20-1 7
by لح شاوی اون چا یحو وه ما تللن
ure: هجو < ۱۱۵۵۵
4 19۲ ۹۵۵60۵ 10۵ OWICW MLE C€EIG 16 OOCLOOGEDO
thew ar coastal wil have a DB or BO. Phir wets that Por ot
با منهج یا DDL PRICE can tel ur abou he ew رت
و سوه و و وی بر ia the rhe, but at bots.
©. ماو و و۳ vartble i becowe postive, «azabasir vortoble's vbjevive
و بو لو سا و جوا رو اوه مخ tras
000۵0000
9. Teoreasien 3 vartcble's objective Puccio oebPictet by core trax ts B41 or
deoreasteny by soore then ts (BO way feave the opal sokicg the sore.
oo
Copyright (c) 2003 Brooks/Cole, a division of Thomson
صفحه 24:
5 2 - اب10 2 Oke Prices
ke ای MAX 4۱ + 612 + 78 + 04
SUBJECT TO 55
ور + ۵+ ۵ )2 ما و و + 4 - a ad rw
Prices ts tho hey oot 3) Xa >=" 400
be 4) 2X14+3x244x347x4 سير ter
Pec be vse to detercice 5) 3X144X2+5X346X4 << 5000
هس سا a ENP a
لاس با له بو LP OPTIMUM FOUND AT STEP 4
ی لاله مت ۳2 روم و OBJECTIVE FUNCTION VALUE
oP موی و 1( 6650.000
2 ص مص( ددا VARIABLE VALUE REDUCED
rich. cost
x1 0.000000 1.000000
x2 400.000000 0.000000
Okt te the worst Oia 13 ۰ 0 0.000000
be onan x4 400.000000 0.000000
cuckliicod unis oP raw Row SLACK OR SURPLUS DUAL PRICES.
2) ‘0.000000 3.000000
لس or bebo? 3) 6.000000 -2.000000
4) 0.000000 1.000000
5) 250.000000 0.000000
NO. ITERATIONS= 4
Copyright (c) 2003 Brooks/Cole, a division of Thomson
50
صفحه 25:
و
۰ MAX 401+ 62 + 744
he shed prive Por raw مس
wwotertd powstratdl (row @) 2( 4لا+ ويا 2+ 1ك - 950
X4>= 400 )3
> 4لا 7 + 43 + 2ع 3 + 261 (4
)5
shows oa extra it oF rows
وه ات اون
Diary could pay .50 عمج
wp te $0 Por os extra uri oP
OBJECTI
re cote urd be oy well ea
4600
3X1+4X24+5X34+6X4 <= 5000
IM FOUND AT STEP 4
UNCTION VALUE
0
OPP oe tis ww.
VARIABLE VALUE REDUCED
; 7 cost
ده را (mu 9(
0.000000 1.000000
‘000000 6.000000,
محم اعم 100000 0000۵
that ca extra ها اه سح will 400.000000 0.000000
wt norrase revenue. Gv, ROW DUAL PRICES
3 2) 3.000000,
۳ عا 9 3) -2:000000
سوت موه سوریو رم 2 0 9
5) 250.0000 0.000000
oP اه
NO.ITERATIONS= 4
6
8
Copyright (c) 2003 Brooks/Cole, a division of Thomson
صفحه 26:
11 8. — Oat لا له لمع سل وا عم وبا
Qurredt Basis Is De booger Optical?
41a Gevion 8.6 shebw prices were weed ip detente the caw opted ude
the rhe oP a postnatal wer choaged but reczotaed wait the range Where the
Dunne buses rewake موه و هب بط پم اون ty volves where
مه تا مه بط racer opera cant be addressed by 00اط) اس
POROOETRICG Petre, Phe Prone cat be used to detercoiae how the
shadow price of a سارت امن کج اوه oho.
Dhe wer of te LIDOO PORCOEMCG Pecture ty thstrated by varie he
exont oP raw woterid ia he Diao eeaope. Guppose we usm و و
how the opierd z-vokie oad shadow price cham oF the او تج ۴و ام
vanes bewera O ond (DOOD vite. Dik O raw crater, we thea obra
Fraow te ROOGE axed GEOSIMOTPY CBOCLY CAG revs kat show
Row & ber ot PLLOOBOLE IWMORECECE cf SOOO, ‘Phes treater ot
feet 9900 rite oF raw watertdl ane required to woke the problew Prasble.
Copyright (c) 2003 Brooks/Cole, a division of Thomson
صفحه 27:
8. — Oke koppeas tz the Opttaral 2-Odhie P the Ourredt Basis Is De
05
] 6۳/9900 فلس | RANGES IN WHICH THE BASIS 1S UNCHANGED
OBJECTIVE FUNCTION VALUE OB) COEFFICIENT RANGES
PAIMESTABLEAU 8۳5 INCREASE
0.0086 — (BASIS) x1 202 x3 4 BLK 9581800600 0.000000
3 SLK # 0.000000 183.333328 0.000 5.400.000
6.000600 ART 0.000 0.000 1.0 0.0003 400.000000 55000000000
6.000 4.000 0.000000 137.500000 0.000 400.000
2.000800 x1 1.000 0.000 -1.000 0.000 - 39000000009 0
4.000 00 22000 1.000 950.000
0.000600 4 0.000 0.000 0.000 1.006 5000.000000 ‘ONFOWITY
00
eos 5 0.000
0.008 op}x9GAt (@}02903 Brooks/Cole, a division of Thomson
صفحه 28:
9۵ - 0 koppeve to the Opterral 2-Ockee the Ourrect Beasts Ir
111 De bower Opel?
Choreretery Row €'s rhs to SOOO, resvltay the LO, oad selevtay he REPORTS
20 20008 كم RLG MOOBL PRICE
O®d
۳ 10 ROO OL ®EPORE PIOOT OWL
9900.00 8.00000
SFOO.0O
xd 8 8
9600.00
GLa 6 6 9 S ۳990000 00000
9800.00
8 CM & 6 9660.000 0999000200
9900.00
re be te coord oF catkble ran wooterid. ۱۳9۹900, کی
Bw te Pare cove, Prow GOGO <r. < PPOO, te shabw prior
(OOGL) & $6, swrcher v $0 Prow PPPS <r, < POPO, ond Pay &
30.00 8.00000
9
9 Copyright (c) 2003 Brooks/Cole, a division of Thomson
صفحه 29:
— Oke koppecs to the Opticval 2-Ockue P the Ourreat Basis Is
ok
111 1ك
RHS Parametries for Row: 4
Righthand Side (<=)
Copyright (c) 2003 Brooks/Cole, a division of Thomson
يبلل :ابي |
‘Objective (MAX)
صفحه 30:
111 .P — Oke koppeve ما the Opterd 2-Ocke: P the Ournect Dost ‘I
Oo boxmger Opteral?
Cor oy LO, the qraph of the vpicodl objevive Puortiog value os
و و a rhe will be .مصاعصخا جوا مرجم و he
نصخ ۶ مره ع متسه اي ۲و رواد the د وه
shadow prive.
4 Por < poostronts ino worxivizeiod LO, the slope oP eu
the slopes oP successive له مرمع امه مهو
foe sexpveds wil ۰ص و
or و < powstrant, igo wordtvizeiod problew, the yrapk oP
جوا روصم و وی نوتم موه با
The slope of euck tae اجه توح لاب موجه the
slopes oP survessive sexes wil be actor easing
eo
Copyright (c) 2003 Brooks/Cole, a division of Thomson
صفحه 31:
CP=dhakees ele Od Ode PR Osa Oae'G ا
Do boxer Optra?
(BPRent oF chore it Obecive Puccioa OoePRriccl oa Optra 2-uchie
Oxia oP المح عا wax z= Oxi + Oxo
vbecive و جه دادس مس
Pocntoa oP a vartable's 9 بل 400 5 ود * ود vowwirctcd)
objective Puacton coe Pica
تفت 00۵ paw be oreded, Onvetder th
(مسه لس 60۵ ک .ود را مرا با وی
shown the rh.
(squresirvios) — 0 2 ورد
objevive ovePPrteat oP a. Ourredly, cy = © oad we wae to deter > رت اسر
ci عدي how the opted vce depecdd
Copyright (c) 2003 Brooks/Cole, a division of Thomson
صفحه 32:
9۵ - 0 koppeve to the Opterral 2-Ockee the Ourrect Beasts Ir
111 De bower Opel?
وه با مج سا تست بط Proc the Bropetiy problew, م6
و[
بط ما سا بح موه رو با ما مه و سا ارت
سرت بط Piri, Port O(PO,2O) t opal ۵ the slope oP نویه
رده تا و thre ctype oP tbe Bashy بو مه سا بط
hae i con + Oxo = by we hon the slope oP the toproPt hee i het 9[
تا ۲۰ .0ب
0. Port @ te opted F/O 2 “lor O Sm SO (lie he vapeur
vorwirict shoe).
Porat © is vpicod P -C ارم ک S$ -dor © Sm S @ (between the slopes
oP ke carpeury oad Prisha coamircd siopes).
رو Port C te opted P/O > 46 بات 46) 6 2 وه Prishtoy او
sbyr).
Dh piecewise اه با من موه هم PO.
oo
Copyright (c) 2003 Brooks/Cole, a division of Thomson
صفحه 33:
9S. — Oket koppeas tv the Optard 2-Odke P the Ourred Bass Ie
Optimal 2¥alue vs el
— evalue
Copyright (c) 2003 Brooks/Cole, a division of Thomson
LA Oo boxmger Opteral?
dcy):=|160if 0<cy <2 4950
120+ 2@1 if 2<c, <4
40+ 40c1 if e124 ae
doa ratio LAP, the stop oP
ان ای سا the optical zuko ۵
اه ی aa pbjevive موی
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