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HIF ITS HARD THEN oo IT HARDH YY _ { 4 eee _ Ear DR SI) LE C Chemecert Engr 2erincy) ENG BOs: 01 [08.019 LinEAR PRAGR Apart AL Ge | An €Pimizaien Problem Is one reabuiring te determination OF the OptioneMaxionum & Puamum) valite Sop a. given. Function, Kroon as fae CRIEWE FLNCHON COR) sublet £0 “a Set DR Skates Consbeiiats Or. VBC OR, ao » flaad 80 Vewiaties Qrtevaee. | iagaw Praganm “AQ Special Gee OF Opiimintion in wave. boty the Ogpeive Function» -ard Consbeuiatng _ W@sbrickOn owe Lingew With vespeck tO tho. _ Iedependent. vowialles. In general, the LP _ WOkLem 93 Povmuvated Meteneets Calbey bey te. Follesing OXPYESS 91” Ye Genie - ar ® = ‘Sued i the 1m rettbone tat a Se Bax 2 Gy i md ea MP DD poe ay te & hand ba. Hsretne: Os fy bahia ® FO eke” Constants Baationsi ana | | re ae ELEMENTS ces LP pReeEM — Heve ar@ 4100: Clements: .Op aq LP ee ~ {peoeLenn ~~ Bo at wit ik: > bie. Okie Functiog ATT he” Grbbaing eahteagon. . 1 7 ee - . “ TRO Bhection Punatinn fs te: nelor : Alomint CPL. P bequae ante is te LP poe POlom tip, ley bes tobe: Pyaurated | pate n eG ally And the eqjuatien muse Jost [he cbs aca: : vpn i 10 IPt Example = Poo ee he Ye EKO KS wy ! Pe xX bOge at oe ris at | | Nowraluy, Baty One: Obsentive Funcbon : Cast PY a given problem but tue, doce ii ables “Gin be -AS _MMeny AS.“ Possible | | depending En See ia “2 problem Tundey * Conpidevation, | \ | Also, the, O-F G@n_ te teed pinata | (2 prololem, For. Cxample. 46 emariny 22. Bee.) | 2S, Ieduetion prot Driminmizeriea problem [ Rt Compre tou munimite the) Cos OF PrOQduchon. “tfThe: Ineqwaritg Corsbeines the Specipication OF the |} ee uthe Crsheunk - Buabon. The Oey! ereny business Cancora awe! ay ; by Crtain CH Cm Stancas Put keting age, te Business. This LinutabOns. ave Gig, Daseounts. The Constyaints jin Or. gi : ‘Prottem must be distinetty ond “Clee o lident Red; Quantified and oRbeneecally Petonutated Ime -Lintar Povda. The Coniy BOP twee tyres “sca Sp the Inecunbite “Constraints HiThe: Entnlity Constraints : The NE-nepbvity Corebaires \ “h The Umitesion Of an Cnty Prise — cye nevey' Cxag; they We. ANonys expesse, § lan _lnestatsty Porm oo OTOL tneaivalitey «Constraint XibXe peg 25 ob SATE acy brhe 7 IMeVLEW ery Consheul ae Xi to tha MO ZA: 4 ° ok The. Belek ay Contre ae : \ a) |eapnicas “prethad’ SOLU ‘pee mothe! OF Spludier 1 Gra Price Pethdd AOludoa “This method is cpncvaules Limited to 00 Gréesian Go0ideme trae ts, ao. 'Oepedive With» Qrdecision Sis a. | Meninaize Poartoy Subeth to ye 3 \ | Y Jevarcen) aes 45° ms94 42, KUO, 470 ae Rae Y MARE Qn be used #9 seve al the | A Moxinuzaion oY minimisation OF OF | 4 baieins po Bivadiaizadon Or milaidnSsation OF OF SORA. Mata ~ Gorsireu rts: THE Seiflex METHOD | | THe qvaphicat approach Shaga COC | feesibucz for Only boo decision. Variable, dra Fad no of varabes tbat Gar Ory be vediCed LO 400. Whan. tie. 10 4 © cbaSOn Variabics Kean tND lenge, tne. GOial Men rediude. Tuo. ndtuod OF BOR UWCh ut atommeree as naing VOwNAbLes; 0S FOSS ible wOhICh rite tof Sane time ceted the | xeem@' POim~E 25] (SOL os Compare thom js Thee. Slaptex peau It was > developed by Burt ziag inj Vavious types. OE LP Rreblens. ff The veins Types CF LP Pelton With 2 Corsbaint eaqhagion AOIth TA Censteunt. eva ae a inimisation Cf OF oun Movenu sation en Pt jst 2 (Odfiation or Tams bite We Climinaled from be Systenr oF ViExbene Points These are the, pias fuabions. : SOR NabeSeABOn OR tte. _CoadyauntS, 6 foretty Puncvipa “This 'S the Conese: wm t ~ olSacw. Vomiebles Tose are. variates | OF Which venlts Prom tue addition oF Oddes ¥D- Ao. -bePishard Side OP < . OWticia, Variables, tp the Corftyaint CVA. ~ Cecstio\ine GVA ep Coewets he: fato IS aim_i'% Crewe tab mo. sum OF cooly. ! arbhidal veriakes is Zero. When this _ 3 Guplus’ variable? These axe Vevialles “ Condi#iOn 1S. aCh'ieved' they Ae USO! CLminte Surpoicted fren the -Leftt hand Side, : Wem tue System «yA. (DES the 7% Corctalné. can 4D Convert | oe ie falp coywality Ceyudeien Franfle 06 Moximizaion ep OB with Be Storidard oy Canta catl Foren Tai is | £ Corsbant Gauation. (The. Star ef the Pollaps” ase step |" Pub i& in tee_Stardans tr Kesuubing': eeyunbhony When ad “Jecoduaiee : ewn 1S Converted AD! an CMuaLity ty Ls ean ether \ addition OF abadid Porm, Hae i is, Nowialacs OY Snbbraction 6 Surplus os CBeveve ae teveonacite, reo equality \etakles. Weis. tue. réaulvemenk For 3. 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Missouri : 7 = Cobspiend a - ; webb ena “Rouse a Tho. sdericintses wer totale Ce: OF the + it (POLE Cu? fete _ of = =n fa C5, tne Fa B08 © 40 Leu denbte = Coston - i t nai aed?) tbe Sy gag Le daheee, Bits xeny lmmcdiake Gest cle _ Stage nt Main fuene| age Oba So Witenisthe, ISycaL ~pOvEION DR | “the problem _and Find cpa solution 7 __ Ter. tuls Smaker Prodbem. - Gradual frlaige the _Problen by Fl edie Cuywonk —OPpiinet— Soludion Fram the_ : —| __Prreredi ng Me _untit tho _ Orightal Probten ls Saeed Cate by wale Kee décision v Vaviables 7 N= StaesS The. wOULE 7 X= PS eT ‘nee eee. _ Pic Stn) = Tébal Cesk Op tho best Peuley, fev the wemniale. stages S= State. OT = Any volne cf Xn that mninvies. | FalSXn) oe | Re = Comesponsing Minimum Cost “Hieat = Mem 1225 £rCS xn) ae Cee ab Step nti eutard) ) en cemrenr gt mare ncn aad! 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