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B.S. GREWAL “or (auare Cor Sema TT ay Consfder the Qeneyat tfnear programming | involving Nn varfables and ™m tons bebo id, an: Determine the values Of Vorkttbles %,)%5,+.42%q Which prMmaxinixe X= Cpls Xa -b «s ln Fr > < Ohjectve 4 Subject te Qyy Hy FA +e +O nH ZO, y Oa, Xt Ago ey te st Aon Wh | ANA Lb A AA Zeb v i =%\=49% £ b ) (Vor tel Zu) ot Jo nity’ onroda 3d yf Mawinnivepoy ko at A wits : Oa a7 AX ABM, Sob i v Nish; is abi? sy i9 Laat HA %p nAa%o 4 ~b- par ons UE 5.80 dary we pave .aldumed tre dlecigioy yarabes Ly» Xa peer nq tO) be iol non-negatings ft is poe fn ackuo) preckte , thik 0 varsabe may tbe-Uin consheal ved =) Cunreshscted fy Sonn, Meee) TEx mou be positive, zero _ ry on negatives Shan warfabie te untiiichrafned Te fs expressed ol tre Aiphone between wo > yon-neuive \orsabial. forex tf! €e unconsbeived’ Naviabe, fon ‘tt Gn sa, = be extracted at — me xi-odl 5 where | 0¢'20 X x"o — Nalur of xf s+ve,zerp or -ve depending upon sobetiey _. x & Lover, equal fo. ov, Cyraley than ov _ _____— ee es | ee _ —" | } r VP wy, , | RTE | ral —— Standard form- 4 The General Unear Progemnen vg Brollen | Car) abucats 4 be pid tM _ the! folowing “form, ‘lied the standard por: q Maximize (or minimize) v2 D7 Cit La) Subject to T3 Oer ea= be fe 2,..m, i) anna, x) J ee \4l HHO, yet, 2. and be % Oy. €e1,2,....m, Theamoin chivaderckia of tnexGhandesd orn anc. Je AW varfoubles Are non -neg alfve. 2. The RHS' of each congbaint fs non nective 3. A Congbaink are expremed as equator. \, Obredive » of" may be of montiri za” oY ini Zod" ‘ype. Any Linear Programmi vy pwobiew Qn be pu m_ Cand forrn ud th the hele of” come elementary har oration. Lidald.”) Subjeck fo %tU%, Qs BHA SQ* 5) Wit %aieI 1%,%7O >| Standard form. ‘ ; ee: & Monin xe SKE 5r +O TOL tOLgo) == Sublet too CtUApt OS) HOEY = 2xjd%e the 2) WtPo $a aI 49% Xo Si p6a, 5,70, G92 oP Oo ©. Bs oe * Cas Bv 2 % = Kee Sw S._Sin bv raho: ellos oo fy 1 so gg. ay) sek fF orvs, 93 (1 Ol at CO Ot 2) Gog TOUS O\e/o mee A q ~~ | Zp OOD OY “OV 0 2 4 Gy 2 5 O = 0 O Crinut » ey CRC Cy 2) fe) Oo oO = Ceo Bv.2 Mo Se Ss S$. Se b ratio So Xe Va \ \ ba Ov a 6 Qu ors] Yay } fe) My \ QO Ats” 6o/) 0284 C34) eo yo OO NN BD iy) <— tl7 Shy Sh Syo 200.'0 230 - Gy Me fe) “Hy OO YS @nknue t G as Ly ) © ie) () en (ee a ee eee = 5 Xe, 8) yy fe) “Va 5S oS O Q. + j ote 4 sx 0% bo @ oF Mee 4 ) Zi 2 yd O 1 33 Gy Oo oO =| 0 9 =|)" Sep Maximizes Ze UY, 43% +X, — GES 2H TBAT £UYO F UNAS AU FOS 2%IB% LUO. Ry Xo, %a %O Standard form Maximize %- U%t8%a+ 6% + OSH OF, tox Subject to 24 43% 40%, +S UO S UNAS 825 UF. QUNFSAU tS. = NBO» Hy pHo %a, $1)$9 5.50 —— G 4 3 G (v) 020 0 Co By ®% MR, —% SS, S&> $,° 6b rahko L oO Ss) 2 3 9 \ O_o Wo 229 | os CG oO [8 O10 Yio) “me — Os, 2 S of oO oT 430 co Zz 2) io) 0 O On-0 “= O G-z MN SB. 6 . O02 OF 8© Coninur = 7 Ceo ¥ oS zs Oz 0.0 "D Cs mi Ry HG ce Me 2 Spek Se Soh. vat (0) wax 3 oO. . 11 ~4@ 0 Bey B86/q< 6 ma 2) | Loa= oo TR Oo tee os, \a/ sho. 0 oye wy = 3 O05 6 O20 \ bentimse qn Seg ath ; ) O° =2 DO “buku C Yo 3 6 oO: Oc O5 6 3% | -% | 2) Va “70. 3H 0 ve 0 Yi, “= "Yq Nt \ oO Zi ie RA 2 6 Wen | 3200/2 (e) ~\ -Ye 0° Stop MEP | Yee 20, ya2 WHOS He 2200 sd q 2 2 \ LLIJt ) 5-|Maramize Le UY, +O%e St. Yaar, 2 2N0s arta, . vp - CG y 6 ec. 9 6 re) Oo . Ce BV Ln XR S, H Sosc Sy b ) 6% Ls rm tho ew fer of (5) 0 =i, Vo 0) 30 € (9) $3 5/4) ae) “Vy ‘ oO x 1002 60 4 a ig 2N o oo NBO © ei i. ©_=2 ce. O- Grdnne lp By x x 8 g a By Mt, $8, % |__W% "Ye 6 to Yo Xo YF, O ~% %e oO. Bon (3) Ss O oO \ -| 1 Bo 2 qe 7 6__“/e Yeo sub Y C % -%e 0 stop X, =30, VT = FO, Zway = SUO. ] ) Y 6 Moximi ze -Z= Sat 5tot ur, Got = DNA B%o = B45 WPot Ss 410+ Byt2VatUYwsie, XoXo %AgwO. ma : —ySbondard. for: Mantimize ve SP t6% +U X24 05,1084 0% ——_— > Subject to 2+ 3xstS a8 5 QX%y+6%_ tSerlOs BHA WX tUA%atSe 1S Hyp %a Ha $19 $2) a7. = C; 3 5 y (e) (6) O 20 : {— Cpa BN X, Heasicaine Kong S$; Sie Sate bb yoo o 8 C2 (3 & bev Oy Ox BD BE im os o [2] 5 Oo. 1= 0 10. 5 ia Oo SS 3 2 f U e) ) \ i IH ia Za fe) fe) O O Ome On, 0 Ge Z; 3 Ss 4 © fo) O Gnhuud sao t G 3 5 4 oO o- 0-0 Cy, By % Xe x Si SS, b eto 5 % % 1 [oe Ma, Cage O PH, HO Oo So Crary 2) [5 72/3 \ o Ma) %e< 0S % o \Yf -% oO 1 2% % Z \W%, oS ) Sf Oo. 0 WR 1 Cuz 7’, 0 4 2567 of 0 * aninue, a T G93 Bs py OOOO CO g C. By % = HS OGG HO si 5% 2IN jl o \/q ome F, | 4 |= YX — hg | o \ =H Ve 9 MWe ~% a 0 & Og 68 0 He mye MEY hy © at ee MWe y Whe We 9 2%fe | On Wie 0 oO SHe We 0 buku ~ 4) re) : q x 4 |e y of | IY{ J a = x mi is 1 | |B] 2] fol) — Bs r S 3] 3) 4 | \3 IN g if a 4 iS 3] S) | 4 00] py od “| | A a 9} 90] aj =|0/ 2 | | lol|-}—| a] 8 NI T= leq] rt NI ar ta 3 g|-Joxo! | 3 | @|—[1>) ol] C 2] Fei 7|7/91° re ay ey a Ji 0|o | Y } =| 0 } \ e | xl di Noe \ do 4 6| At 49/9/54] 9] 9) 9 | gO] Of -]]0] 9/9 Naa] T]-IN “Tas | No “ yaa Jol|-|ofo}9/© “1 9} 7] O}}9] SP9 o| Ax |ole a fas - on yy f - | 4|& ors St | | 9/2 | lol Ooi ao ON Olofalad + 0] A gy uw] =| 9 ‘ y fi NU eo nN] t | 9) x 4 a dle Sy si Ol St} dal-]-}e]o]- lal -P)3] 6 | [x92] a ld al EL] oS) RP | pap \ oe § BLE] >| 9 Ales [ | dole|-Ma a7 Sg} 7 2AC-|-[9| Ie #2} O[9}—| ao aro UYx|R red thba | Fiza ao | | = S| - ) at -% 7 NI ’ 2] yy] of! Awe 42164 also] al = hi | Rl+ ¥ &| a] A) of] ofl pal | 4) of of] op OF el oa] A) REPRINT 7 21" |% HO] Ol alo QO) Oo] a ololol—la tt t | = WA LL \ a re = ol Yodo % Vv Sacer ry lft LN loo] +] eer rtp yy" aBe Gh _|ole] 90 o| 9} 9} 0 © o| —|o| —| 0 lajaj7 2 di. 4-4 A) &) &) NPS o| lA GC S, Sy 2 & Yo © Sop Tyo Ly Vio ‘2. Pfs Ve. TY No O Xerag =O, x=4y 8 %=2, a ——= r ms —=—- | Mawimnize Ze Sx tow, +595 3 Sti MH te tHe £45 WitB +S ¥s £305 2%) ~A%q~%_ LB Hy Hy %aZO => Standard fovn: Manimize Ze BU t2% FS gt OS, 4 05,405, St HAM t+%gt $295 Wyrswgr Sgt S530- 2% ~ Aa Ag tSa,> By Ky %,%a Si) $2)Sa70. Sc 2 2 5 0 o oOo oO C By % *% % SS Ss, $3 b rato oS 1 \ oO Oo 9 os @ 2 [5s] o 1 0 30) Ce Oo f& 2 -1 va fo) o A eg -g ZO Oo oO 2) o Oo O G-z 3 2 o 5 fo) O © § Continue ) G8" 28 | oO On 8. oO Co By = ONES, S$, S$ b&b ‘eHo O 1S CA % a6 Wetk 3 > F< 5 oi 8% [, 2 | Oe | o- A o 6 Ww OSs \%/ -% 6 O vw | hy 3% Zp 2 BV 05 & ORG =z i “lO OS _fontinse G 3 2 S (a) (0) fa) oO @ bv % % % Ss SS. 4 3% | % 0 % y oF 5% O “Me, \ -% Yao & OS O “2 *@ -4o “Ml 1 > 43% 5 fy %% 6 35 G3 0 "8% 0 -% -% 0 chop are Yo tol Minimize = He 3%, 43% y : = 2 BY, T%2t2%q Stondard Rory. j , SY ; Minimize X= % + 37, +3 %q FOS, + OL, 40S, GE BA Met BAe tL OH) RMR Hoge, TUM 43% ot F%atSe 210 4 1, Ua, 82270, Gt 2 8 1% O. © vD Oo Ca BY x _ Xo . Lan at Sui S$ bh YoHO OS SRS ite ae brio oO. F -# in Os -2
