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GCo/i.[nSA>v cDVNO< ފlOS$;Y}6*pZt  آ˟^%xQBI6̀&q?6>NumӚM**θgr$"՛t7kvCm$q^"=K5'5oeΘ*ɾ %)T:Y6Jx2Lmlfb14㕙*8}Ls*3~qFrV6qv^o0T&: ^N*lC '⥵V(wح g ^Rۨ#}-jr^&ҧVK:q&)O3?z96|0,Ξ&Do?PK!ݲ+drs/downrev.xmlDN0 @HCd$n,!ʲ2*p3Vk* [8zֳb5^ȇY6 >73!;K N`X`іtb#XbC TPd0L@yGHr˻$y;Z襥z_~ۛ1b^׹RWc",+௪r?ӷt!W}\ PK-!Zf[Content_Types].xmlPK-!1_a /_rels/.relsPK-!$ir>*drs/shapexml.xmlPK-!ݲ+drs/downrev.xmlPK `}  S eProblem Formulation  e     xS0e0e?Rectangle 3" PK!Zf[Content_Types].xmlMO &2WR=cJ`F0iK`#̼vLw 9uSq:w`G ^i ½KI)c/ $oVjTMRc|}042ҥCƔM̏P~*ka/8^DkHbL8e i"K\XN\6rco4y@_;oPK!1_a _rels/.relsj0 ѽqCNo^K [ILcX&m߾0XFo;>0xM e`|X}đ I`߽N4aG2$RKIZ)4(M9`ctB{m:f@`3n|O,ܗr޾jxR0T ,0@}WBLǬ5vPK! ydrs/shapexml.xmlWn6?Y;78$@ˆcAK"Ur|}ߐ=,!}9rf̓|e_*F!gR'&-fο=ܝ\pЩPF9?Hǿ\e5svjs`\}2eƖCAe J5 gR_([UKKniY"xh좋@ l]`R+86[r;m䵵1"u{!6VP)*gP!ʵI|2Ng/\]Y-ե,ctsT>iL=K,x2b$!Z5Dޔh5} S +9Sjyz: 4 gY5.o 9孇DY~WUBKebjլrQ` v mcБ,I76|JahJCEP;T N1s~Z+R=ꩁG)nC3upY Gau M jYb+a4Pɞō^ۢ;Slq׶푰kVaJq=q#UMͺ^=u1;$< &;$tUO;Q 4B:Gqp8v:6K/ˢ4BvΥ>%qu5|ט&!¶Qj +ζf iP9h U$"=֘,]o SiP*wQEJSu< 8V2@( KGV)R@àG N|HP>*u4Owv XS:4xJ}|DQW )"q#F+|v݉db=р}lm7E+(4TA/kVǧN3cS'ΑcB#}N$@DS4 NHPp -$?H-Z>3"yVЪK1>/6v']ɵmPK!udrs/downrev.xmlDN@EM͘&[J, F`V397g4M+|cY A\Zpx@L a2a7t܆JD !tɠ؎8uC<]%SV%ɣ4p\YM~{0 r2}ȊYae=J~ "P״?ZrO vo/ @NA싵PK-!Zf[Content_Types].xmlPK-!1_a /_rels/.relsPK-! y*drs/shapexml.xmlPK-!udrs/downrev.xmlPK `S  S Problem formulation or modeling is the process of translating a verbal statement of a problem into a mathematical statement. Formulating models is an art that can only be mastered with practice and experience. Every LP problems has some unique features, but most problems also have common features. General guidelines for LP model formulation are illustrated on the slides that follow.H     D   H  0޽h ? 3" 0N0 <4 (      xS0e0e?Rectangle 2"PK!Zf[Content_Types].xmlMO &2WR=cJ`F0iK`#̼vLw 9uSq:w`G ^i ½KI)c/ $oVjTMRc|}042ҥCƔM̏P~*ka/8^DkHbL8e i"K\XN\6rco4y@_;oPK!1_a _rels/.relsj0 ѽqCNo^K [ILcX&m߾0XFo;>0xM e`|X}đ I`߽N4aG2$RKIZ)4(M9`ctB{m:f@`3n|O,ܗr޾jxR0T ,0@}WBLǬ5vPK! sBdrs/shapexml.xmlUKo7 x-ɊlǂW-@mz,fv#.ɒ\YGr9Ej7}>v0LjaV iy3Hפ?I?μeP~f ބ`g0Vjm(uuK(QFzQk)xX;ֈ3Mn@;%لBce v !K4jw<7j(F1*۰p7AI<Nn7۫A1K=OyラO;UjT^8{v?=9r:ECbW70:}0*ACZjEpefC_RXҊ(·_,$hʆLtX=Ml"Q>&IP^~J2 uV)mD $|%j}|x,/i>5:'|&GP]^ZNMD#X+5_<x& ?ʾA6Z 垎 ت/_%xcBH*Wf@cz?>Nd}vkAEKзJhe.rcM(ȋ8TlO\鸦T"Hl[q٥3fh߅86Vܹ2vb(;1bc ]ϬRP]PH6qaAi~4[+=tjֶ$ʃ1{vC5™mhԵBB4LMJ-L녤?̈́A ߯_Xb`82p PK!̜drs/downrev.xmlDN0HHܨCuD9$o(٦MyzV\z\j>r=AȇY6 !88K N`Xbt(c#XbC LPd0HyOHr34I`győ[(x|zMmΕ6 x~Nj{w-w;]`p2PK-!Zf[Content_Types].xmlPK-!1_a /_rels/.relsPK-! sB*drs/shapexml.xmlPK-!̜drs/downrev.xmlPK `}  S r Guidelines for Model Formulation ! !e!     xS0e0e?Rectangle 3" PK!Zf[Content_Types].xmlMO &2WR=cJ`F0iK`#̼vLw 9uSq:w`G ^i ½KI)c/ $oVjTMRc|}042ҥCƔM̏P~*ka/8^DkHbL8e i"K\XN\6rco4y@_;oPK!1_a _rels/.relsj0 ѽqCNo^K [ILcX&m߾0XFo;>0xM e`|X}đ I`߽N4aG2$RKIZ)4(M9`ctB{m:f@`3n|O,ܗr޾jxR0T ,0@}WBLǬ5vPK!]#drs/shapexml.xmlXMo8/uڱe#JHQq J,)RKR_78AEz+Br7f&d?nk6Һ脟~r&ufJ3΅2Z&|'x_5 6 /oJY 4RCV[ ] +^x`4^ jQi~f,,/eU,1gZ0 3X)|-8&[0O' WNaJX֚R2=V )5@|~lrq9w2xt[w\) F/]v}1Tn= &X,(HZ3;D70j ٓVr |O8ǒXzfTL &s3yiF^6)/uqM؆/fYF;O|i _27Cٗһ?󄏑~0f!j(a90'{ V{Y.G.; k}#\ura [R4ԳBUZ:lE'xgA '"yq'H*xѸ-[i;SR$1JUuࠓ˽]${C"C#gM^ԕrB: Gp8Vru\" &vFDLdۺUM'_hiXvYR6q`vz ̋] oJ6˻d7av"'%hկK0NVx#^_nXT``,ǚ~3h7)RgevM3iT[R~ruv2αSߩT.%8~̿ӌcU fHON(M4dqvRQV)4^V%Ci{4;gLl߅h#:gѪ=(5J68KL;3tPS_Zy"vtT#%4Oc5*eBҩ)?pN1^)ÉYF or@7ᇪ]8,#}qHFt#"sD%4XeN_@(|lvH&*uǢvLsс5m6M> b k$7"I<@uq y-ܩSDIc!LKZplףC)++V7z56X*rx=ߏ.yezP,.PK!IRdrs/downrev.xmlDJ@Fa;?nK5f'? kz9|f48 6 >n "D{gIlW+̴;=,!CmC&eZ2&n ˬv`7R{<>I`gyŁv-U_o`XOٲܕ.-ߔ "kL?z2K)rcp2PK-!Zf[Content_Types].xmlPK-!1_a /_rels/.relsPK-!]#*drs/shapexml.xmlPK-!IR{drs/downrev.xmlPK  `V  S /Understand the problem thoroughly. Describe the objective. Describe each constraint. Define the decision variables. Write the objective in terms of the decision variables. Write the constraints in terms of the decision variables.   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Standard form is attained by adding slack variables to "less than or equal to" constraints, and by subtracting surplus variables from "greater than or equal to" constraints. Slack and surplus variables represent the difference between the left and right sides of the constraints. 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3\F{ F~%7I@\Z9 C+G2ݿ5.@?Ā`DsxϑVo$ !10nVa6ni;Hd>OsWÉџPK! 1drs/downrev.xmlDAK@ah1 RFڔ4fgڤŃ7|}h:q$[ ' k*2)8lo 9*hBs)}ՐA?=q t7ITl964Ӻsm~uNc6W./@c_/Y+YN􁜂m)PK-!Zf[Content_Types].xmlPK-!1_a /_rels/.relsPK-!wnL7*drs/shapexml.xmlPK-! 1 drs/downrev.xmlPK `@E   Interpretation of Computer Output We see from the previous slide that: Objective Function Value = 46 Decision Variable #1 (x1) = 5 Decision Variable #2 (x2) = 3 Slack in Constraint #1 = 6  5 = 1 Slack in Constraint #2 = 19  19 = 0 Slack in Constraint #3 = 8  8 = 0"  %    "$f&f% ">     ( %     (   R H l 0޽h ? 3"[% 0N0 $$ps$(  p" p C d6/Gf21?Rectangle 2"   T      p  x80e0e?Rectangle 3"PK!Zf[Content_Types].xmlMO &2WR=cJ`F0iK`#̼vLw 9uSq:w`G ^i ½KI)c/ $oVjTMRc|}042ҥCƔM̏P~*ka/8^DkHbL8e i"K\XN\6rco4y@_;oPK!1_a _rels/.relsj0 ѽqCNo^K [ILcX&m߾0XFo;>0xM e`|X}đ I`߽N4aG2$RKIZ)4(M9`ctB{m:f@`3n|O,ܗr޾jxR0T ,0@}WBLǬ5vPK!#}Bdrs/shapexml.xmlUKo8/uqܦ6".`bň,%)ίGJIVz7}:~7LjaF2iu3H?I?-~νeP~n3^`磑lɿ3VjUƵ:UxaR!)x8֔nfijv+)nhUq!`JG"͟\çٚ0P~s湖TxF)ר5QٚE Jrqt2>Nf^~+LyZѼ/!YH6gGHۑCpolf)3};_ݵK4f\Y,x Z k[Ec6teBM^Ik"粉큈Fy8 ~_B-uJ6CK|"I0_ RVOT/KZOVFT*+Nԩ x$؁bK$dW?ע[*tL]FD}i4cѼ?k|mzPqƥc%=-(ZHq qcf1&Og{?EA*'t\Sy%6⭚S%ڷa$%;1NͪQՔ2v1VP 1YUXq%.H3+TTb~D!9+8;o mrT&lٺpۭP.F?ЩZHc^k3Qm y>Zҙ+I1 Ã0o`_džo` &n  R.PK!0]drs/downrev.xmlDMo0DV8-RER * ^zK%#{ [FӋ#:a [9Z~"0ZLV3Ncɵ2T0j`l}-S^>&ɓ4@/ U]knߛqz-9/>\q i] t8| L^APK-!Zf[Content_Types].xmlPK-!1_a /_rels/.relsPK-!#}B*drs/shapexml.xmlPK-!0]drs/downrev.xmlPK `}   {)Example 2: A Simple Minimization Problem * *e* X  p  x;0e0e?Rectangle 4"PK!Zf[Content_Types].xmlMO &2WR=cJ`F0iK`#̼vLw 9uSq:w`G ^i ½KI)c/ $oVjTMRc|}042ҥCƔM̏P~*ka/8^DkHbL8e i"K\XN\6rco4y@_;oPK!1_a _rels/.relsj0 ѽqCNo^K [ILcX&m߾0XFo;>0xM e`|X}đ I`߽N4aG2$RKIZ)4(M9`ctB{m:f@`3n|O,ܗr޾jxR0T ,0@}WBLǬ5vPK!{ drs/shapexml.xmlUn6?Y;FEbmcaYI"Ur|>cTV 9oޛ>vZ_r&TZmRequϙu ZgNmpXiʹv:ؼ O Rf3hB9rA2 ՊpڭەneX]f2aE)؈zxcSzE8rz^!x4FV w*@XڊC .)%d|LnsjC4ݗYd )Op8i*0 -rx&uE !}V$j捳WC`בɿ\.,Fw ܒ[T̵ jqkgq:wX$uӒ[u{GKk{#2?!PE+jEp:oXF%Һ; ͱ~ؐi,0 s A6jUR~u AK QP~%xFR=m`=#Y/:YfZu*GH{xWc;(cYs'Q~#qr*W¯f\?_%EDPZmCW>Y~;a; $= Yr."cObr픫(FS2}qۮo%)1t1eQ0vٿզ0l+ t{-hY+ rp0xM e`|X}đ I`߽N4aG2$RKIZ)4(M9`ctB{m:f@`3n|O,ܗr޾jxR0T ,0@}WBLǬ5vPK!Rowdrs/shapexml.xml]O8?+'-+@I쪢3rձsSZ4Ij *Ӈ4=ǿyJ6&O 8QA,`*R+1">_ۧg Vy?Sk~GS΄{cmRnLZP[(nDДRu>4,y0SND@D vV#,_GxL)!.яS{k9* :YE@+/ؤR-`@ڝN c9I}, cEX;H'f& 7Y Ž*wS&r1p/)վͰGi( d6~" bWD2 Tncx{x}a]\xʯZێuw +wvd$5_1/F p r.Dŀ/L,{;L,3V]>^GBI)`1,TGRe,F94)1ɦƕo|UM˱ݮ[ k p IEǏ7YJXJOOJxofpVH,Kl4i"NUGX|Z_C~YLެHTyaB}) db(%If@#W LW0@ EIG&Oow*_P]zyjДGKl({e#AG)'a /%`6]Č# eax h}, llëL k(vH_붸U 7C*;L3vl_⦜gHՑ!r$V`aOy^?( C#\ 'pQ*!A7*$@yB"*^IiQHB|kewN[괍QRHS0{24{E;=Hp$ASIrN ;8CAZ2> \WnՅ.Tek d˒-}/gjV:6JQ<齣(I<WNH!C#PH3;lՄZ';,#baZ,~,<PPJNW[U@R[}j2(FB<宾F2PbWqhvԶT֬T5!!Eѻ+puvJPB7 ng?5% Ē#Jl n:rtʗEn"d-2~%㗌_R r5zQb1=LPTivFTxwaGIōK̼ SlXW őc Kh86Joy@mVPEW}a.x $VKy-+yWҐo1u/^h>H4~/U+V1& _ͦ 7?PK-!Zf[Content_Types].xmlPK-!1_a /_rels/.relsPK-!Row*drs/shapexml.xmlPK-!pϕ drs/downrev.xmlPK  i  ,Min 5x1 + 2x2 s.t. 2x1 + 5x2 > 10 4x1 - x2 > 12 x1 + x2 > 4 x1, x2 > 0T~ Kf cckcckcc cckcckcccckcccckcccckcckcccc cckcckccc  H p 0޽h ? 3" 0N0  t5(  t/  t  xN0e0e?Rectangle 2"PK!Zf[Content_Types].xmlMO &2WR=cJ`F0iK`#̼vLw 9uSq:w`G ^i ½KI)c/ $oVjTMRc|}042ҥCƔM̏P~*ka/8^DkHbL8e i"K\XN\6rco4y@_;oPK!1_a _rels/.relsj0 ѽqCNo^K [ILcX&m߾0XFo;>0xM e`|X}đ I`߽N4aG2$RKIZ)4(M9`ctB{m:f@`3n|O,ܗr޾jxR0T ,0@}WBLǬ5vPK!"yydrs/shapexml.xmlUMo8/unĀw0Jǀ(K5EjIʱ8TŢՁrfșfwf|m͜> 9SFڢ69򴺺a Qs~R^];-vΫ`e?VJuAW&=׃FԆ/p9dEI>6ŜO1gF4xv$i|%8V}?N wq0ctHe7ֆ^ZVxW;g_*% BA1b"P88"t2O?7)}1;Dwbf˒ŧ?hNsq8LPߎ먗0&b,Sd,lq9~QFʺW^N86y:LZ %™5K3a$nsgi <eQu@fhڇ-mCN_V? -֔6- Cm "BU'g=s!+6nOք{rʅlMKl֦3ZGr#;\nA?R݂iv6= ؼ^ i7mdD3ݸb _*2sed@u rB+tsnDc>^9{[#秮__x:Nam%ɾ K&ƮjS[]ps$2j/TYbc\V/,םۊsDrVԱw&RM߿zQ绩=ۭMOUe*<=7ᬭVump^QJ\|R"MGPHR{їg֟>Q`6@!v PK!k`drs/downrev.xmlDMk@ERDS~E{fI03f}.^̗nřoA% ؔV5B?MA@FQk #\r1S|.B%"TJ_֬ɏl&vG4]%KVd"55&>T|koW*+Bo vدAs_ԫBxHf1_ ?PK-!Zf[Content_Types].xmlPK-!1_a /_rels/.relsPK-!"yy*drs/shapexml.xmlPK-!k`drs/downrev.xmlPK `   pExample 2: Graphical Solution  e  t  xR0e0e?Rectangle 3", & PK!Zf[Content_Types].xmlMO &2WR=cJ`F0iK`#̼vLw 9uSq:w`G ^i ½KI)c/ $oVjTMRc|}042ҥCƔM̏P~*ka/8^DkHbL8e i"K\XN\6rco4y@_;oPK!1_a _rels/.relsj0 ѽqCNo^K [ILcX&m߾0XFo;>0xM e`|X}đ I`߽N4aG2$RKIZ)4(M9`ctB{m:f@`3n|O,ܗr޾jxR0T ,0@}WBLǬ5vPK!а{adrs/shapexml.xml]QO8~?RJjˊE$*jWn](6EnoIL8?\*cRD(L_/Wg;NKFɽɧ_X m%PYa5JUNǦ UHF޼4tHNeUIvBf:9ƣJ/nFdQ ef/U "s%N,Hq^76#wBtem N)J,FO#-B TN}Ww?cPx}@Ӄ.xvrVN?(~ow ^Ҫ[}F6 y&c9H43/Q`nҜOzH͜f^ee&upyꐢ^E%ݹT)TƺWi*A\/ oϭ#yozHncD%^6ӌ݂| iG .=[p 72=2牘N.Q\67R_e*- c6@K8O*NJX>qmbO%NyG\̝.Osh)'lRH yo"2aMc3tk\%aMDtq&,:0Xo99 L˱cDy,+ "oG;_&diI4/Pd7 Se gOIb)yI,>olrmNs%s\ӷ.ϲ<wlg3nkgDoS9 L:)3Y4_K9Cg1d0J3RubBV. l7[%9G^]뫕W%Qo]2 }kd7|K+J}FЇҦꯕpcM n+`&rlZm5$| '^51yTV=[=Mځ,emkU>Y^_|= 7#/~zXhêP }ZԝѾQѾ:hVɳm?lpkcKŠMx~m GY8~J+Pl@w=FGh?G76Ը*~LM?}nB4 Q}4jA]DvElozU*z;7ʸ`> >[͝l7j03곍?Dy|@'ղˠϠ_n>Eo??tl?9Ÿej~'F"S`O]zؚl8bTtMT(u1u/c˟-crj3ڷU,a4~!ߌ9!xb~gC|(pM@^@> 嗁Fak íx;b /1__XMo +T56mViڡjIHJ 3&֝@m>?Tº>N7LF/0Qu3Z)ҐO&3 1KuYm/l[X;u /,CkV4j$2p e(m?YkjԄjiȮkD?,&\W#˨Ҋ*B7/Y{jKT)m&ő``KhzUzij7`~RZiנZ+ٖ[ n?cpu RμyrÇA( 5?҉baOl5|L==t#_o]~/e//!\ p1ЦnͿPK!8ZVDdrs/downrev.xmlDMO0DV:P (R.ܖxud6X8զ38eqR[0ZYcca0:e>EUm*/*2Ƕ%:!FWJᦑWI2kʾvΖ.}Rn{ "PY13_z p>DhMAPK-!Zf[Content_Types].xmlPK-!1_a /_rels/.relsPK-!а{a*drs/shapexml.xmlPK-!8ZVD drs/downrev.xmlPK `l5  JGraph the Constraints Constraint 1: When x1 = 0, then x2 = 2; when x2 = 0, then x1 = 5. Connect (5,0) and (0,2). The ">" side is above this line. Constraint 2: When x2 = 0, then x1 = 3. But setting x1 to 0 will yield x2 = -12, which is not on the graph. Thus, to get a second point on this line, set x1 to any number larger than 3 and solve for x2: when x1 = 5, then x2 = 8. Connect (3,0) and (5,8). The ">" side is to the right. Constraint 3: When x1 = 0, then x2 = 4; when x2 = 0, then x1 = 4. Connect (4,0) and (0,4). 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B_ÝR$!XRa|(KOX9kܒdk4̖ډ>hI񢙪`8yx凌\H 6TF)!OTMi KIj`Wժ <{<ǺC~7 >Z\P/TLsbk%^,6C;NRιTx21cx 1"ZRlnsQq'Ee"D:kܸr6]x2 (T4I$Gި _3ankӀE% ,V NLDuIlzv6tgW-8bŀ ^+i*jTf҂sQG8?ݑPK!Y_ drs/downrev.xmlDj1!B7R3QE RK)޺trf I7B?o]+.iT (0xM e`|X}đ I`߽N4aG2$RKIZ)4(M9`ctB{m:f@`3n|O,ܗr޾jxR0T ,0@}WBLǬ5vPK!W|W4drs/shapexml.xmlUMo0 t8X`vȊ`3-˱Y2$9#%'ivŇ(|qj+kr>~q&2p 52[ׯ>t1lyB7hd ںŨsK AgٻQ [ eVE7wd1U2@ΔjGOr0b /@*k3E|vxdXL&ڵ'F(kKζh/.M`s_]<$r=ʹDX@㌝*O"ͩa:WMEjU:ݢ|Ў@|"9rs7UDH> vZԵ)93}h5>~ۢRK|3gO9}`ܒ txltjoՖ-F'nuà r#TiSbL7Vʚ7#6 fTmLUXY?AY< \Hf-8քX0xM e`|X}đ I`߽N4aG2$RKIZ)4(M9`ctB{m:f@`3n|O,ܗr޾jxR0T ,0@}WBLǬ5vPK!}rdrs/shapexml.xmlXo"7~k6@͉DDO(t\#}glNJQ `73|6ӦRl%F͙й)b PFon~c=t5 /BXilvުpB{QZIoU 5jVO-ϫeHyt9P"Gs%X/᭝adbۡF_a-p1֬ ZFC,[n  7 7NEE똲dH;]1C۔'*  Ƴ :Y>v/,k/œB))&SP[vڌR ˰5F(+eJV)J YăT*^=}*.Z4a(֬uñc1@1Ps[ά__P#Gγ;e >sbJW {\'5ŖdljZ[@aШ4R2 PO|/{}1 Wrǭ3E=8f^,!"N(Ը dp&u1 +fO{hh.`o2ؗFQH}$Y(eFa=|H1%ԑŭ( %Twu~h 6!Y3{znэgŮ0pGe ]62=N_fx8a|w3W^ʷY)XD?b-ٿ7 PK!idrs/downrev.xmlDN1E&CLIGRd5AfBD=iqmm\ޜ3[ cG x'vT#xe\+uyS ;p +OnMMjYXR_qMrb1\0xM e`|X}đ I`߽N4aG2$RKIZ)4(M9`ctB{m:f@`3n|O,ܗr޾jxR0T ,0@}WBLǬ5vPK!D&Qdrs/shapexml.xml\mO8~_OlKJ(+*TQVCsu¯gvW'HD~yf&هE\ߵ9:-'OW]άz"Te?J?Yճ`m{UOzM]YI4pVe JNxRz=OsEiod &dǼЅ!| tffafbVK9Ĝ cʇK͘\*RM{帜9N:(uѓ RwY '}/.pWXznkѴ6 j扳# ow-L!ã#|ů33^uqY*)玳Pt*ˢnGUJXw,LŨAu9Jz1XGxj=DY7rc4g /  *ԏF A!%4z#%P{Dfb4KNI \M>g3i3S,MܴʟJB8,3_TRJ]WRaŖ*P\jA& .B1eM'ljs#&.TZ*ÄNy+ Z=ۛƴ@.9}S*o>P.(V#[mVmᢛ5DHT˶@$w ;ܡ=Hѫx \+~^uɦw+s_w9F7K7 w ?%^F~l :ީ 971v/UD俊<ۉ#/S/Nڼ"zav/z=0x0R߹6]L9#|N110a xpt{s1J$~{^vp?O`ts!%!3qۿC11)揙^ cCJϓSMO0 +hZBL&g:U¶_ONӺ;`~/?bb3UJ0WvDI}*mai9xM +>rH ||;Yg% gݓ&:^V(U7 h!ktWtƛxلrL^uṅ MGokb.6ޅ ٬blIKlϬV& zNfNp}4O e u_,O%اUtFɭjy ~{5?"aۙ?TPK!Udrs/downrev.xmlDN1M|fL.*Y)F N7mm˓s|yoZq" qauÕ.2)jgi*!3TPeR&~`;ؕ 1Jj7O4p|eMqmtb>äno@}og/j0xM e`|X}đ I`߽N4aG2$RKIZ)4(M9`ctB{m:f@`3n|O,ܗr޾jxR0T ,0@}WBLǬ5vPK!jnDdrs/shapexml.xmlUKo8/uNbD.] +EY)KR_ߏ:=,Vz7~:0LjaF2quq͙KRFˌvk2(k?CȋZ?+5*Z `ndR pԪdv"%ǚ2zƙnR lG\BcmЏS:zF`%| W9gkI׈`B}Z#Y8Y$GG$2̮&7^~+MyZҼ/!P[Rٳ#$!8F67)3x5_ݵK4f\Y,x Z k[Ec6xeBL^Ik"粉큈Fy8 ~_B-uJ6CK|"I0_ RVT/KZ{OVFT*+Nԩ x$؁bK$eUע[*xL]FD}i4cѼ?k|izPqƥc%=-(ZHq qcf1&Og{?EA*'t\Sy'6⭚S%ڷa$%;1NͪQՔ2v1VPwbJ1].gVm($gegMÂJ{=k7i޹z(UxiU$ʽ1{vC5™mW6BBLMJ-L˅?ͅA׷AXn\80{p+PK! fddrs/downrev.xmlDMK@Eax;;Q$R%~@+{ͼ&03wp˽˙G݋#;Yp;I@LYd | a>Rɔ|B#"\J_O&v{4]#S^%I*5u&>4sOuEѨUrYWD1U+Q >Ms*v/FSPK-!Zf[Content_Types].xmlPK-!1_a /_rels/.relsPK-!jnD*drs/shapexml.xmlPK-! fddrs/downrev.xmlPK `}   pExample 2: Graphical Solution  e v   fxCxaxa1?Rectangle 7"1 + PK!Zf[Content_Types].xmlMO &2WR=cJ`F0iK`#̼vLw 9uSq:w`G ^i ½KI)c/ $oVjTMRc|}042ҥCƔM̏P~*ka/8^DkHbL8e i"K\XN\6rco4y@_;oPK!1_a _rels/.relsj0 ѽqCNo^K [ILcX&m߾0XFo;>0xM e`|X}đ I`߽N4aG2$RKIZ)4(M9`ctB{m:f@`3n|O,ܗr޾jxR0T ,0@}WBLǬ5vPK!eĹN drs/shapexml.xmlX]o6}@uHQv*,0y$LI9v~}%ua, 6I]{xy!֕b+i]it;oڜI~rйPF˄on~}=r5dFuףVe Y R]al%XE V%FV"?(:ovIuz0D8H=~FRa{~DBuiFQ-v%T&SR!(6R ,Rsݰ'd;@Ђ2UVBzbZ?)߯oM)Xbjߵ{ &Mz&&ߠ⛗A zwT =$ R94&W; 5Y.GΞNGs[ 8LI ҇$i3DRzVg4l% 5(`q+(ڽ)|,ƅi ۾M;ID'"XR/տIzTkp7,D hguŽJiBa:tc Fpu" FHCͰ7`eS'\3;جnت4nnl'J\6l)-aH( J[: 35F|.00fj)BUNIW&Q˨Xw *s~;Olb&wAsL-'>|`kI:p~h`ǐ$l3яP ߶Տ(pk̒/l t${!q4J_Iic[ d$D;nxp7 [ 5HN屠K{I1N8o('@`_ TXEj^pъ ԊWw)9u᜼IwݯIN%+;y g:W\8VQK0+!2MQ` 0>˵M4I~ԕUE& iJr]%w a*N!L #0%I0 !k|lcsoFuK]  er": {q#*d[ $Ə()]HUX%>^*]1&HJe5]^@_![%b3:$9+Bh"v7JCNjeK`6 Tez$~4דcrl'q4bĬ̌'1>+X;_c˓]+UJ*n| %{nC$R!,^%x.C%G(#JNr)B+O[:%}96)POty+l*PK!B"drs/downrev.xmlDN0DHHܨӪ(ԭR8ějl|=8fFol/F8V0e k >ޟo !"k3ج//VXjw}lEp(QAPJ,S8o1[=reh8=t8ж >Mۂ+{?~t]s+Q/Z2ϊ;鍮0D _M ?PK-!Zf[Content_Types].xmlPK-!1_a /_rels/.relsPK-!eĹN *drs/shapexml.xmlPK-!B"drs/downrev.xmlPK  y mSolve for the Optimal Value of the Objective Function 5x1 + 2x2 = 5(16/5) + 2(4/5) = 88/56 nK8~ Kf6gfg fgcckcckcn H  0޽h ? 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C$ %d rPK-!Zf[Content_Types].xmlPK-!1_a /_rels/.relsPK-!M*drs/shapexml.xmlPK-!drs/downrev.xmlPK\  Optimal Solution. nKgf 2 "  #  L L 111??AutoShape 48"k e PK!Zf[Content_Types].xmlMO &2WR=cJ`F0iK`#̼vLw 9uSq:w`G ^i ½KI)c/ $oVjTMRc|}042ҥCƔM̏P~*ka/8^DkHbL8e i"K\XN\6rco4y@_;oPK!1_a _rels/.relsj0 ѽqCNo^K [ILcX&m߾0XFo;>0xM e`|X}đ I`߽N4aG2$RKIZ)4(M9`ctB{m:f@`3n|O,ܗr޾jxR0T ,0@}WBLǬ5vPK!^EHw.drs/shapexml.xmlYn6}/ Zd}cmwaY1$֚"U%_R[lXוlRgng\&S2wMJUyH?=od„<[n臻{_ MA`4" kaaϙy .a.U:gnQhnƒrh7A#gw\͊Qq5$KBzmJ$ᱣҪقtQ 5 LT4O$A Ds>Z%,Ok8\; 'WX`A-6ܤ:?ҔlBA< icC$mg : VPPٰnRJ<:}jb,>eT~cgJ\SVLV Q%8`•R3!5nC`vt%!Nу ]^'b> ӏ2qc2ǠOS"\̸*-׳E&I^jo 1E sjJev, %JG]``vͽJ%o Mllz`$N'SєsT1,Xz88!٭BsQDD!9t@ L&n]'<}b] Xzq&^/|9wGpJːJxV?-ե%KV%1W [)n" OjJAp[D pgbgWΞNp}’H%P>Kd_ O} ذ[%f5vG)(J-HQRd6^Y `i]X:sv\pĆ9Az.@@Y{GȳvguZ&]{i 5NkW'i|Yӆו\H Xr„7U'kAu :tIcW!oB)P,ګ~$XZQ{K_(}#*ɔi ¡n/UMCv^Z]kmy߆?C!>¯0էU7"/Ϩ7x唂7EU_k0*^XcRlAكEqf&]n_S?y7%Vcx _62K16zf?H 鸏j-׫m4^< c}R;夹 :ʄVHf /1 LDZ"F|;Z>XEm+2\1dzܧZ8J0͙cuVg6oLEM\>Vug[.M@*ɝjQH kAHɱ96yȗJH߂FIHwBo*Jkj;#(BW-olDg1D}<#jadkj3z)W sűA)[WdP1Z-?P&*A4MPK!^drs/downrev.xmlDQk0|9録 Cߤp>^k$%m {f4-4FvRFg"Z$F6 KrbrC`l.)KCϳl jvUTW#i8|ű?BLƷW`?vREew;{- l)PK-!Zf[Content_Types].xmlPK-!1_a /_rels/.relsPK-!^EHw.*drs/shapexml.xmlPK-!^Tdrs/downrev.xmlPKZ  l   ? Optimal Solution: x1 = 16/5, x2 = 4/5, 5x1 + 2x2 = 17.6t@ggo ggoggggoggogo ? Z2  X1?Oval 49# R = T    H 2 0޽h ? 3"  0N0  (  <   lxaxa1?Rectangle 2"PK!Zf[Content_Types].xmlMO &2WR=cJ`F0iK`#̼vLw 9uSq:w`G ^i ½KI)c/ $oVjTMRc|}042ҥCƔM̏P~*ka/8^DkHbL8e i"K\XN\6rco4y@_;oPK!1_a _rels/.relsj0 ѽqCNo^K [ILcX&m߾0XFo;>0xM e`|X}đ I`߽N4aG2$RKIZ)4(M9`ctB{m:f@`3n|O,ܗr޾jxR0T ,0@}WBLǬ5vPK!U'{drs/shapexml.xmlUMo8/HmǎU 'X 炒(kԒ?WzX,j8yyiWk+k2{L–,3ez3aJK?=fƏBhƝ/Vm\e]-ni֝nwة2[͢;ocw7̈aeK--3[?`J' f 19]IQzB:=˷_m Yrh[Ul~3aM.ӣw?sVaG> Yګ11(gD93v6nö8 -n] Ӫ&IeFDҫ #kqmJі{ ㋚J 56B ;T/g)Ve.q}X=zJ4̣hvN[-,s4Fǯ2%&B/!k +e"+ b#G *k$.ʅi9O@@8)b͢)M1/l;Rǣ~%7?N~ټ}eɜ"PyT1I" ]?*3.nIYri3n. 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 :Eݪ<éwxmg ocYCPdb̆1-pfU)4J >xLyIA!p _NLtsa٥Ľ-s6mWW{[p2;H[p4(},F:`]Њ5^NJz K&JpPeݫ6d\^W Qbٶs(:gYp_H:A խU3Y [,Q /I4VGh[G.W(D[\f8q[ 8K|6)y"oqaEsAD$qnYa4.y;X˖abt9 %$R6^ C%ҿw2Mt25r|XCw]0xM e`|X}đ I`߽N4aG2$RKIZ)4(M9`ctB{m:f@`3n|O,ܗr޾jxR0T ,0@}WBLǬ5vPK!] z{drs/shapexml.xmlUMo6 x-c;FEbm#0,z\PeiM,I9v~>J(v}`f437|j%9 2:4D(F3i}5yJ&= G?/,!Vna2Z{ohPUڶC CeK\ ֒hkNpKAtҲgdQOTFxSUwŽt3 "W *S6/ENƷl|{&o𞶋ũ&c ]UO$!&y@ y>^a4D%$,2]CtQӍǵ/<[ݿ`M@h24l ^ZKڕfLqܚQ-%IYy!O7*7gt/:V?MmL jĴ! <4,F=?rUK}'6"V>̅jaUoFHֶS"EkK6ۧu+HdLA.PK-!Zf[Content_Types].xmlPK-!1_a /_rels/.relsPK-!] z{*drs/shapexml.xmlPK-!Iqdrs/downrev.xmlPK }   r Example 2: Spreadsheet Solution ! !e!     xe0e0e?Rectangle 3"PK!Zf[Content_Types].xmlMO &2WR=cJ`F0iK`#̼vLw 9uSq:w`G ^i ½KI)c/ $oVjTMRc|}042ҥCƔM̏P~*ka/8^DkHbL8e i"K\XN\6rco4y@_;oPK!1_a _rels/.relsj0 ѽqCNo^K [ILcX&m߾0XFo;>0xM e`|X}đ I`߽N4aG2$RKIZ)4(M9`ctB{m:f@`3n|O,ܗr޾jxR0T ,0@}WBLǬ5vPK!Q\-drs/shapexml.xmlTMo6 x-v'eǂ(K5E$}C^;Erߛ}N:OcΤ.MMƿ.>sЕPFˌ_hg2k?oBȗdԐu"6#뤗:@MQ'Zpw];ڕ_wk*7kδEHb$A/2ɈL*ȃiC),DOΙF5b\5R\l"TNw.)Z=jń3,bFPBp07'PNr(z:!ܹ8[׌vpui:+J$E:^߅0䍰2*B\7 DxIHQ~Kt~:VcԎKA.Z]3~ujRU~E>P@d#J?mD6:4A:98QS|qۯ>rS>uJģR$A?J?Tat8/ jvv|v/PK!~vdrs/downrev.xmlDQO0M%MA&dRA Uvi+o<:ݰ9`dJ+슗10Hl!0L0l6tچE9 Chs}YF߷-bt>HQPcKЎOl\, ;\V_ί>uG`pt7) rpJnr_PK-!Zf[Content_Types].xmlPK-!1_a /_rels/.relsPK-!Q\-*drs/shapexml.xmlPK-!~vdrs/downrev.xmlPK `  v(Partial Spreadsheet Showing Problem Data) )$f)   pA?1?Picture 4  H  0޽h ? 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3"$ 0N0 `((  4    x{0e0e?Rectangle 2"PK!Zf[Content_Types].xmlMO &2WR=cJ`F0iK`#̼vLw 9uSq:w`G ^i ½KI)c/ $oVjTMRc|}042ҥCƔM̏P~*ka/8^DkHbL8e i"K\XN\6rco4y@_;oPK!1_a _rels/.relsj0 ѽqCNo^K [ILcX&m߾0XFo;>0xM e`|X}đ I`߽N4aG2$RKIZ)4(M9`ctB{m:f@`3n|O,ܗr޾jxR0T ,0@}WBLǬ5vPK!Ym|{drs/shapexml.xmlUKo8/uQ;Eb acAQ"$Hb@pf83<|IrֵZtaLP\W癪J,;9C`\frxoFt}F(jm;XQ'GzԱV%RlmqkI[t>.\nw#dJG^2ac Le32|QOT&wԪ_qo~n\FQARPql-o`[.ϲSm_Mdy2]'lsq<Y&Npoo?Ca2E&$YLO:QÍƍ/<[ݿ=@Mb2!4f ^JK껕fLqS-%Yy!O70/E=kYHwO/ } %d rPK-!Zf[Content_Types].xmlPK-!1_a /_rels/.relsPK-!Ym|{*drs/shapexml.xmlPK-!2drs/downrev.xmlPK`   r Example 2: Spreadsheet Solution ! !e!     x0e0e?Rectangle 3"PK!Zf[Content_Types].xmlMO &2WR=cJ`F0iK`#̼vLw 9uSq:w`G ^i ½KI)c/ $oVjTMRc|}042ҥCƔM̏P~*ka/8^DkHbL8e i"K\XN\6rco4y@_;oPK!1_a _rels/.relsj0 ѽqCNo^K [ILcX&m߾0XFo;>0xM e`|X}đ I`߽N4aG2$RKIZ)4(M9`ctB{m:f@`3n|O,ܗr޾jxR0T ,0@}WBLǬ5vPK!uv3])drs/shapexml.xmlTo:~A)mjZ$IhBM=NNbH.k;;v`OWwyplw>[v_~r&uiFo2iq32Zf =<{Ne0~j3^`/k X![׊ ^ j0oh4vhW~߭k__&δhQHb$^/4ɈL3*|C)i5{s-Eq1cR.f`eaGGv42գXL?rv''\) 4^8{vU;$gF1Lx_ߎpp\vnTDF^38Ky ֥iKے|x2Hwʨ vKsxL0C/!AD[/ i[f $Q;NJhtVQC KqV(=$)m#k}4)'05Äzݻt lESzޖ2 †grVyR?Vz HRjOSt)c\4@q֢ByGl1.^g\ `b QԊiZ@k$ mƥOW"һ-&;ζҁg4sM4=y_㑘803f s%ECy*M6F4,TtIb6 WjrC PtAY:(* -.mh\OL(QJ<:;R?#gecQ*$x#" JFPj83+~?D'AQoPK!sr/drs/downrev.xmlDN0HHܨӢ6ԭJU ěבm8q4o-Vđo-+ĥ- ދ5vI< ̴=yEPABIˆ cWYg0j"tr$w`6 _QOtVl {?߿)u}5A|\_ԋVD|p>DhMA.PK-!Zf[Content_Types].xmlPK-!1_a /_rels/.relsPK-!uv3])*drs/shapexml.xmlPK-!sr/drs/downrev.xmlPK `  r$Partial Spreadsheet Showing Solution% %$f%   pA?1?Picture 4eH  0޽h ? 3"% 0N0 >6(  "  C X/Gf21?Rectangle 2" @` T       lxaxa1?Rectangle 3"PK!Zf[Content_Types].xmlMO &2WR=cJ`F0iK`#̼vLw 9uSq:w`G ^i ½KI)c/ $oVjTMRc|}042ҥCƔM̏P~*ka/8^DkHbL8e i"K\XN\6rco4y@_;oPK!1_a _rels/.relsj0 ѽqCNo^K [ILcX&m߾0XFo;>0xM e`|X}đ I`߽N4aG2$RKIZ)4(M9`ctB{m:f@`3n|O,ܗr޾jxR0T ,0@}WBLǬ5vPK!Y͙tgdrs/shapexml.xmlUMo8/HmNU 'X.-8=D\S_7E473>kͶyeMISRUƿnƜ L)52L|ðIuͤZ¿4EЭz^ պwj Vflv*3~w?rfDϲl{_Z"cnS:Cop0cֈ!Z҃֋ gYǖ*`+W_Urw;|}ML>#dƃp<lJ{5&FeLbb;(9pΔsm~?ghqZV5HӓXÔ% WG"ڨR- 5kZmP# q0P%r&X["ąa+D29;np#[ʔPh Q&Ջȗc0Bbn&. Ӹ(^r!Xד9C(wWyT1I" ݴ*3.%nIYri3n. 6P@cl#]+I.α).^_qHkE ؅Ó[MM:ؖjUD*=0xM e`|X}đ I`߽N4aG2$RKIZ)4(M9`ctB{m:f@`3n|O,ܗr޾jxR0T ,0@}WBLǬ5vPK!ĜHHdrs/shapexml.xmlZ]o6}@uHQ'q*E,ۀ$:,E%N~%mʀ5fͨqyyxxxEn2"{LD!g*V2C9JªZ[:*BTt)M)ŭFVRYaPwAǨJݎKCaYgJhJ&0&l;|:U cSIC[v0ϦhCRBuYK  WVWwt [Em5z%F)ѓ G`?b|#w( ;H-K~؅S!AA8Z&V1(z*n/*KNY5A)}.pնհ; g^[.2+ ˳\Hw+!W,VdOr^L{t{[m4{C뱏U⵷AN`K bCANl`&]CO=G#L=H"a8I, a8 xP+&u'(AP4;VP^*u/j%@S-΂6 ڔ>z]qAЦF>>f r.XbނpY2IaUB:˳:_玼_J7͞" V~&[(qAK{q'kV? `f?,o!Y/KOBKoJ :V6͆0<0(ɛPd{JE`l uB%Nfgy- %;f0^ %9_*SG5>HKRRem$`\fB) cP-XChQ,Y-3x'  Gqi~@>:lpq;v ʹJUş@VOJ\:J4wv tw ƲaW}?U^Hrp͈o?BYD=.2Ї#})=TFÆ-F?Tܜ6!t&r)M6nqY~VI:qMTxǻ::?Dѕ%ZʎNq§HnP3fPK!drs/downrev.xmlDQK0Co.mʨˆLD}Pks׆57%ɺ_oAfXA>@7Nn|?,AwL `Xa݉kw ¡B]C%eh:fn Ny1EJ඗EҢ@ێhƹY,}ŔkRWHSǣ_ԳV(o9]c$dLAPK-!Zf[Content_Types].xmlPK-!1_a /_rels/.relsPK-!ĜHH*drs/shapexml.xmlPK-!Q drs/downrev.xmlPKW plY M[Interpretation of Computer Output We see from the previous slide that: Objective Function Value = 17.6 Decision Variable #1 (x1) = 3.2 Decision Variable #2 (x2) = 0.8 Surplus in Constraint #1 = 10.4 - 10 = 0.4 Surplus in Constraint #2 = 12.0 - 12 = 0.0 Surplus in Constraint #3 = 4.0 - 4 = 0.0" nK~ Kf%l }f~ Kfl }f"gfg f%cc @ c  c  k ' c  c  k 5 c  c 1 c  c 3 c  c   c \ H  0޽h ? 3"& 0N0 (    lxaxa1?Rectangle 2"PK!Zf[Content_Types].xmlMO &2WR=cJ`F0iK`#̼vLw 9uSq:w`G ^i ½KI)c/ $oVjTMRc|}042ҥCƔM̏P~*ka/8^DkHbL8e i"K\XN\6rco4y@_;oPK!1_a _rels/.relsj0 ѽqCNo^K [ILcX&m߾0XFo;>0xM e`|X}đ I`߽N4aG2$RKIZ)4(M9`ctB{m:f@`3n|O,ܗr޾jxR0T ,0@}WBLǬ5vPK!9p0oSdrs/shapexml.xmlUn8}_`"%NU 'X  Jl)RKR{-}(399qWk+k2{L–,3ez3aJK?>LJfƏBhƝ/Vmni֝~{ߩ2[͢;c7̈ieK-Ywqi-F ҉-*|B9qnWRPNuDh0yF큞/VxWZT*!Q]v4"hb,wv4 l2p$L@SP:cJk5js6lZܺVA:U ҺKmFDҫ գkqm4Iі{J㍖J-1h1 %ғ_z)Ve.q}X=FJ4̣fvMM[-,s4FǷ2%&B/jT +e"+ ⠸⥘G *k$.ʅi9I1fdmz)9QV?ƖC֟*$'^vؼ])8}|p9O*`9XdRA~VO%RQqƥEw9I#K!m R=h"Z[b]'M77t?h*?O\+enY[EIK!LCtKo*Iu"untS&LGjX[= \C#%G>0&,5YQZep<N%; FV)֮+8kT(VSQ+ ap^ƶ-ڿjs#E_8&N bF B7X|Kgg3>VTPK!,drs/downrev.xmlDKK1!\MJdlZDEur硓i:Bsj F򡷬`1/@V*8nAqL N`>?[a푷4b+2C ]%e;2箱`ѷR{0xM e`|X}đ I`߽N4aG2$RKIZ)4(M9`ctB{m:f@`3n|O,ܗr޾jxR0T ,0@}WBLǬ5vPK!/"drs/shapexml.xmln6EƗ؉c2p-)8.(USJRd5G')r08@QHyxG]!Ȇk+޻.%\&*2W#Je2eBI=7?/Ǧ$,͸rd fީKeJ̢Rsåevo:%Pr(ڕ7sM47aoHd} D,'״Sۅ. :f*YZ 1f[Dq9Dk]q8 %GIRheUX2]ʍp!; lw$h\0H`1#/?(q6VE@RrM'4\E y0d oᵣ4?t[ȋ¿[],SobY.B+{=˰z,\]m.B݃JnoDUHojDu#d`D[VKp G)v 7/9X,׃Ԟ"e D`X<{f g3׾.13Wl+`HB.3e2O,0 kgmA0GIf_vuk\= ]z9*AJr]gcWF q5‰ݗ 0a2%λ_/77Sj5\U|ZVN}] d"mW^@$i"pVߟ yYĴ&:gHp(9ޓ?Z?jkټ1JnS(iP *(iGI,$k1u>]vv' G.4d@ ~5+5(Ҙ}eI..޼E›& r$K r Cf. : Wn0 AסYg9Mwh[NȒ'mӾe/E9NR)zhYyʓ]]d~~':-hlU.oo$qV4>Vh6qj7IeYMqNdeYv:MS!$TǜI] Q^Ƿ`jsD5_G77Ae=ɵ~F[ pނ`hNEKu[ 3"TsQ[h1shk^Q&('>Iѭ_dE{L/8 0P,'{Xx6&"`)c }}͙CuAh\:oNٚ$vbFa[~DW!CJjڬ15ɮJJpf!w+(YEB9QޙkQz%l1vY:Uίo1Xla} 8| YFU,H(!oΎ햺[eT_ZQC̍ٱWҗ4R og+ JwY '9!j.p ?|X~@Z~YB&B]D6 =]5" \aPpwdhO#{$i3{?PK! rodrs/downrev.xmlDN0DHH\*j*ԭPxXבmҔь護H> yqpxxyXYc\)vs{J 4c+C Jtd1@c%m/YVJC:j/<.MwywSN AD87\yzF"y/&SPK-!Zf[Content_Types].xmlPK-!1_a /_rels/.relsPK-!/"*drs/shapexml.xmlPK-! ro drs/downrev.xmlPK& <5 Infeasibility No solution to the LP problem satisfies all the constraints, including the non-negativity conditions. Graphically, this means a feasible region does not exist. Causes include: A formulation error has been made. Management s expectations are too high. Too many restrictions have been placed on the problem (i.e. the problem is over-constrained).x nKm }f% fgfccg H  0޽h ? 3".$' 0N0 ##F#(  "  C h/Gf21?Rectangle 2"   T        ~xaxa?Rectangle 3"PK!Zf[Content_Types].xmlMO &2WR=cJ`F0iK`#̼vLw 9uSq:w`G ^i ½KI)c/ $oVjTMRc|}042ҥCƔM̏P~*ka/8^DkHbL8e i"K\XN\6rco4y@_;oPK!1_a _rels/.relsj0 ѽqCNo^K [ILcX&m߾0XFo;>0xM e`|X}đ I`߽N4aG2$RKIZ)4(M9`ctB{m:f@`3n|O,ܗr޾jxR0T ,0@}WBLǬ5vPK!$K1drs/shapexml.xmlTKo6 x-vǛq1hKkdIʱ#$E=yr$ Zr~i̙P[5gΓIj%r~ۭɜa0V.39o7hFt>i#dm;`vdpByx<u*>+/zد,kOWKuJ.hK&<ڹ!djKO]L?-J9GL~ ;kS#v32T_VH:deKQ!瓋`l˧LE+GKI%&{]gk( i}0sdQ[c#3L0TTRJT͵h5畷%fþҝ!TjX5,].2"*~|T7 D:_#ꃠ |KtudlH= E$Fjyx8퓾F+Jr[XF5aKU?3ժlOS O4g5ؿI6?iϥ}]+􁜂m)PK-!Zf[Content_Types].xmlPK-!1_a /_rels/.relsPK-!$K1*drs/shapexml.xmlPK-!jdrs/downrev.xmlPK `}   nExample: Infeasible Problem  e     ~L!xaxa?Rectangle 4"1+PK!Zf[Content_Types].xmlMO &2WR=cJ`F0iK`#̼vLw 9uSq:w`G ^i ½KI)c/ $oVjTMRc|}042ҥCƔM̏P~*ka/8^DkHbL8e i"K\XN\6rco4y@_;oPK!1_a _rels/.relsj0 ѽqCNo^K [ILcX&m߾0XFo;>0xM e`|X}đ I`߽N4aG2$RKIZ)4(M9`ctB{m:f@`3n|O,ܗr޾jxR0T ,0@}WBLǬ5vPK!m drs/shapexml.xmlUn8/ x-R;$F"1ˆSI5EjIʱ}$eiܪDrf8o͌ɶZ_~r&TZ23H$ ˿N?qNl`ڹv2b-_t+d6 9ljar਑p*] Wŷ°x^ g}@` zфcSzAg8r z7qo~Y *?Axci[ux2MnUoq[6L]eDW󮯮]~ 4; $阳Iz3Tbb8th敳C`בɿ&7(^6I\!%TJT̴ *pkgq9sMKnm},yLF7\S+mLmLDZt{SX>4/'6~2QȾ{ I[d *8h\aHJQ=S|I⍍6lB+}0z0T/?tSdKy϶ŢplK>x{]QwiWJҼI;)'ֲVQ'G(yQQQik9kkW%sz[br㌫x(FiaZ&27]S7:Rf\K w4"w~zJ/Ê0z-8R~UY$A0ZWam7=TN X-ϢvʏIOG<}DUgx9a3OT" zܠG&b%;؞z<+xwh3\=B;v}%~BF]HyN ( NP>j9vSO| AwBqޏnh9#oXoo_,m; PK!drs/downrev.xmlDMK1ECxf'شHAFʹuC'ɘ팿B{9X c'rF<F5iv4 ;kHHVˋ3eϦ&,BPBBqˆ4ĮNc\9\ 􁜄m)PK-!Zf[Content_Types].xmlPK-!1_a /_rels/.relsPK-!m *drs/shapexml.xmlPK-!drs/downrev.xmlPK    |"Consider the following LP problem.(# "$f # I  f&xaxa1?Rectangle 5"Y S PK!Zf[Content_Types].xmlMO &2WR=cJ`F0iK`#̼vLw 9uSq:w`G ^i ½KI)c/ $oVjTMRc|}042ҥCƔM̏P~*ka/8^DkHbL8e i"K\XN\6rco4y@_;oPK!1_a _rels/.relsj0 ѽqCNo^K [ILcX&m߾0XFo;>0xM e`|X}đ I`߽N4aG2$RKIZ)4(M9`ctB{m:f@`3n|O,ܗr޾jxR0T ,0@}WBLǬ5vPK!< 5^drs/shapexml.xml\Qo8~?SRʢޝ]}āsJoƆ$Sa=:y(N33o/N>Y--3Ǽ3cdz6oNND(?ɒŨ,ܬQ1sQSs)kppjgRj'4NtETbb[N,˒1 giCw2%fJ3Y˅[qkEVFe+[z0mІ<ΥHJ0jm4Ԡ`gu ڳI@WQ9Uj}zL՘>w'(? Q;1+bg  CPE [?[-m*M؜67RwR}a9XQWgNZ|pb/DBzzBf[] *ׇKC :h~abW֕`M=m@ ˅sP wf:|EffD">C>내.xjD))\FPT:գ*JO eObǖヤ, g u4ەWZ\­vA1?HTMk7sOLE hglj+9+2oD)@o# _w PI->.yEo5 dԗ8[H 12Z3ʞ2_ rk%TP! [8.74*K˼1nx-%7 f:OY*{'@! h@ZX@z0vՖ&,꺽[V~=T벏㯌YK*.`FM{! ufF`O4`heyhrFa|p(AQJ?Qqz?)@9HP9y ez54;"u2Vz>5W;v#ID4> Q#M4@PEk=D18}`kӝ"^? oADyCS"OPE/Q/9̊'LPJ=Eȴw"’3.[Lk/*[vnխ XWb]u.b]P| :HP9H!ڕhW]e=!g(D+4''8 ]?.if3텧we] @3#<tEX]k0+!CƤ dnڦ5M$_CA\Pq{ m!J e5AImiavX; ?;x I^PܭBeLl=)1ۘn:ؽRRT*pj1R}i@YϗJ = \ j|v,RL}p!v1JuaXBw1' 2ةAG@*|~#1w)7պwW(Dì\[zW$굽VS1AGJd(-d5 :=18{U(,A7%ޭ@YP1Uy84 y'o'!+qP% ;; riK;,q:NkDcJCKJzҍr PK!3Ncdrs/downrev.xmlDN0DHH\P"JV)mMvMX8&vVlZ#8m+a7q ,R; 8 x1, x2 > 0q~ Kf cckcckcc cckcckcccckcckcccc cckcckcccq  H  0޽h ? 3"R( 0N0  RR)*Q(  5    ~1xaxa?Rectangle 2"PK!Zf[Content_Types].xmlMO &2WR=cJ`F0iK`#̼vLw 9uSq:w`G ^i ½KI)c/ $oVjTMRc|}042ҥCƔM̏P~*ka/8^DkHbL8e i"K\XN\6rco4y@_;oPK!1_a _rels/.relsj0 ѽqCNo^K [ILcX&m߾0XFo;>0xM e`|X}đ I`߽N4aG2$RKIZ)4(M9`ctB{m:f@`3n|O,ܗr޾jxR0T ,0@}WBLǬ5vPK!K|drs/shapexml.xmlTMo8@HQDZEbR$RM\r>PP3Ùy3n?[AFɔ>)Pe#w)Qb%J򔞸}Չ&:s: lQُJs ]Lf7І[.sԊx8ZHSRpҔ)\ϦH"Hb'8Ao]Xbod$S AǠbrjJ?#AH%k}V&kuS:'x~;FkZ X,nY7SJ>8KёxV%Y=dG̸hZޛ}RY-pKt{bS8r`S {^l2Uv6<y=8_ıO!Y X%SCr`1VeO#oxUQ&'lYO34s`7$Naۨ#p~;֛Z|/v rԞI׀F(э+kiDRX> ߿WE-O8nA ?_pN N>!ZPK!sdrs/downrev.xmlDQK0Co.Ui7!M6|]lnjuݿ_Ar4ymI$T[}A%pF\ʞa!s) 9uFbwkrIq#5ŇVj**>S/=Tq{3>? 8s_zSi:ˀӪ>m4PK-!Zf[Content_Types].xmlPK-!1_a /_rels/.relsPK-!K|*drs/shapexml.xmlPK-!sdrs/downrev.xmlPK `   nExample: Infeasible Problem  e     ~x6xaxa?Rectangle 3"'!PK!Zf[Content_Types].xmlMO &2WR=cJ`F0iK`#̼vLw 9uSq:w`G ^i ½KI)c/ $oVjTMRc|}042ҥCƔM̏P~*ka/8^DkHbL8e i"K\XN\6rco4y@_;oPK!1_a _rels/.relsj0 ѽqCNo^K [ILcX&m߾0XFo;>0xM e`|X}đ I`߽N4aG2$RKIZ)4(M9`ctB{m:f@`3n|O,ܗr޾jxR0T ,0@}WBLǬ5vPK!ƠVdrs/shapexml.xmlUn6}/@u%N|AEb mcaDYcAI"Ur|}ϐ PlDrsf&w_b{i]mtG_Iۄ~qЅPF˄_~ke8ݢMx} \^F/Fx,vZF K\id"ӛٔ3-<$s*ɮGpMs=V ßp0m~He7ͪkZRIQ8ƻU*ai+-Pf8r?$|2O?q[.,6E S O_F!t<tt B<៍sd9"fx8D cG!EbN,AX;.Ckc_9{ʹ:a%gO b2 c{.=kVFqk=g\y/Ӵ¯uHa[F&o&D+Cد'&.c2@(SDm)ؐi]PT+X=,a9W B"K_!h23RK}8 Ga2ލ#Ms<VES+4V $ qϋ,Xk&XuMݘ(!MWS wt b8ˢ{6i8I SQ4U*KRxm1e]WJpTq3.hG2eKV TgDOGiMF%-B*4x.ݡz[CƎv ?7J(RDG9rG% ?o?N{Fo= n @Mw] PK!Hzldrs/downrev.xmlDMK@Eax;;QHRb_nR3򡙙83i ]^\b5AYMmUoZח9(a#{X-T({07b|A]c!;gvd:M!FJz7IIM|qӶNc=lbx \_zTYsMy|wv/FSPK-!Zf[Content_Types].xmlPK-!1_a /_rels/.relsPK-!ƠV*drs/shapexml.xmlPK-!Hzldrs/downrev.xmlPK`0_  nThere are no points that satisfy both constraints, so there is no feasible region (and no feasible solution). o o o %   l;L L 1?Rectangle 4"PK!Zf[Content_Types].xmlMO &2WR=cJ`F0iK`#̼vLw 9uSq:w`G ^i ½KI)c/ $oVjTMRc|}042ҥCƔM̏P~*ka/8^DkHbL8e i"K\XN\6rco4y@_;oPK!1_a _rels/.relsj0 ѽqCNo^K [ILcX&m߾0XFo;>0xM e`|X}đ I`߽N4aG2$RKIZ)4(M9`ctB{m:f@`3n|O,ܗr޾jxR0T ,0@}WBLǬ5vPK!b! drs/shapexml.xmlUM"7G|f``=+fHdsvn>s!(Y)p2.^=iWk+k2p˙4-Yffę”B[#3z7 7_Ќ;_d-HʺZ,ݲ8 " P;aG\e6fU|SeƇQ#,b%㝃_:"cf?L^`>CNە!1Z`LQ{gW[hEVb\}-x*xo6]]`n~Y^7 Htl?I{5(/ʸãPb3!rr;UZ_͵װ-^wZVuGHєFU"mɖ /D*EuiP_LtoDh5Vn+b'hqC{T0c;d#Xp#+/d荦_eJ 2^iJY|fFHR̓[eMЙ\H&:9o΁2oMA;fb^{i$?;_vY񚷋9Eg kl,6xל+u{/Asخ/Em$? 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R9FS# N ;|0Mbԋ -[)'KW4[$dڻNM&&2gqP>je,Tr'dB׺\>tZq8| ?􁜂m)PK-!Zf[Content_Types].xmlPK-!1_a /_rels/.relsPK-!7'*drs/shapexml.xmlPK-!9Odrs/downrev.xmlPK >  *2x1 + x2 > 8ggoggoggg H{B @  t111??Line 8"PK!Zf[Content_Types].xmlMO &2WR=cJ`F0iK`#̼vLw 9uSq:w`G ^i ½KI)c/ $oVjTMRc|}042ҥCƔM̏P~*ka/8^DkHbL8e i"K\XN\6rco4y@_;oPK!1_a _rels/.relsj0 ѽqCNo^K [ILcX&m߾0XFo;>0xM e`|X}đ I`߽N4aG2$RKIZ)4(M9`ctB{m:f@`3n|O,ܗr޾jxR0T ,0@}WBLǬ5vPK!d/cnVdrs/shapexml.xmlUMo8/ur>U$Xw¨R<(kH!e;aQ98Cq8f}V:ya̙4Vʬsequϙ`*Ȝc7ϻ7!tȋF?Nܫk!ҭG^z4F-(0ʑ%lW*wل3-]*#= .Ҋpr 0c0kY4ɗC3J6 BKx=f_[|_bPV?"ںf_Lf1:sLC6dל N;^$aH᳴@9XKs JgBi})\퐡9xjUpY;E{loP=F:)l&-9keř8\d%~Hڥ`Mcd]qrNMz8Dp9Ć[ c '[Kq*8PU{p,1Q~+ݚ$6 vT~LUXY@Y|T%,͓ښ WG*4J٪7[wb%B,5OXw<} eC}z2x 5(j5rIV?MߪxKs 21cx jE8HGO@ûƓ-^%j/EIㆽoóNrw$9Ne联' EK3דX vl(85DjATZ  8/cŀޜ5WP fU asQG8?>{PK!qldrs/downrev.xmlDJ1঴ NشXm]NL!Bpy8|:qgwqVq3~3)PjgZG8VWRڐ8=q,C+uswE)Z{z2T~~}yM2uXst7#no#DCZA9OA4ϗ`c #e r PK-!Zf[Content_Types].xmlPK-!1_a /_rels/.relsPK-!d/cnV*drs/shapexml.xmlPK-!qldrs/downrev.xmlPK p zB  @  t111??Line 9"PK!Zf[Content_Types].xmlMO &2WR=cJ`F0iK`#̼vLw 9uSq:w`G ^i ½KI)c/ $oVjTMRc|}042ҥCƔM̏P~*ka/8^DkHbL8e i"K\XN\6rco4y@_;oPK!1_a _rels/.relsj0 ѽqCNo^K [ILcX&m߾0XFo;>0xM e`|X}đ I`߽N4aG2$RKIZ)4(M9`ctB{m:f@`3n|O,ܗr޾jxR0T ,0@}WBLǬ5vPK!ӕ.LmVdrs/shapexml.xmlUMo8/ur6IQ,)R )w$ŢÙ73ZvyeMγcΤRf˛OmQz>w 1lyBhd ںͨsK `V&tԂ2C]ѭYn혪r>o93bڕ2hpIހVVl3E|>v1d #nV>X<,kUkE@(kvd6HGw3,!0xz;q&c6'QD᫴@9Xv+K JgRi}-\푡 9!hjU6vl:xloP9F:)l&-9keř8\d%~Hڵ`Mgd4rNƇ3! 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For real problems, this is the result of improper formulation. (Quite likely, a constraint has been inadvertently omitted.)P n%  gfc$ H  0޽h ? 3"$$* 0N0 ## <#(  "  C /Gf21?Rectangle 2"  `  T        ~Txaxa?Rectangle 3"PK!Zf[Content_Types].xmlMO &2WR=cJ`F0iK`#̼vLw 9uSq:w`G ^i ½KI)c/ $oVjTMRc|}042ҥCƔM̏P~*ka/8^DkHbL8e i"K\XN\6rco4y@_;oPK!1_a _rels/.relsj0 ѽqCNo^K [ILcX&m߾0XFo;>0xM e`|X}đ I`߽N4aG2$RKIZ)4(M9`ctB{m:f@`3n|O,ܗr޾jxR0T ,0@}WBLǬ5vPK!rZK1drs/shapexml.xmlTKo8@HF"1F`X)z FeH-I9v~}?P}+Nh gBl&_g7YG$HAXyׇnj;ce]khdZd?N(*mZr`far$(>+˺T[֔)N.')jv- $}A/XbkdO) =7y01(1Z׈+ϵ`RB>f!_8)8ا||1O/&aԆײm(J/)[J/n얦9@7vq:6/=f _$ x{9 qdp !4t(ζ?~-?͋7od+uhۺ\fMe?ݠߝ#u fqœ dF=[oK5tp)+*ʽ[v\3Y׸^PCRdCZ- _?M 0&0AnPK!$(drs/downrev.xmlDQK0Co.UYպlԁ$>;|h:1eqeu˵#5vI<,3̴=rI&"Bg ϤUCı[g0j#t.IRi`O(Xl8KJ]_g?N?_wEkI:}O;} Eh r~PK-!Zf[Content_Types].xmlPK-!1_a /_rels/.relsPK-!rZK1*drs/shapexml.xmlPK-!$(drs/downrev.xmlPK `}   nExample: Unbounded Solution  e     ~xaxa?Rectangle 4"1+PK!Zf[Content_Types].xmlMO &2WR=cJ`F0iK`#̼vLw 9uSq:w`G ^i ½KI)c/ $oVjTMRc|}042ҥCƔM̏P~*ka/8^DkHbL8e i"K\XN\6rco4y@_;oPK!1_a _rels/.relsj0 ѽqCNo^K [ILcX&m߾0XFo;>0xM e`|X}đ I`߽N4aG2$RKIZ)4(M9`ctB{m:f@`3n|O,ܗr޾jxR0T ,0@}WBLǬ5vPK!Q drs/shapexml.xmlUMo8/@ZvŎEb q1([kԒc;Es?7͌kvJ_s&TJSy~uǙu Z_o&a8Iƹf|#j_t#Jmjru1 Q-{~ثR|n,vKê"p4j}9@` uvB[ہ0/p04>loTX Ul;4@~d0N`|۝Ƹ-Vbɾ4GOi˒y׷#:Mޱn0,E2'1J+)? )l&nv%hsB:h+g/%#8+6'wH^&I܂s喝i'֔;p0\ Z574ƺ2 CjC[X8 HDZr) * aA"7HdL=,aR9WG ktY!gV:IaA hR+ddh _er8dKϼg|;#/X?ţ(ۢNtmW®ڙDýr`#+lvz8:EsEI9zD黭嬩\S]I!cX )WqQ&ii\&1m]*JnS.;t "w j Jˆ0:+_XRU^Yaoi.n&{0xM e`|X}đ I`߽N4aG2$RKIZ)4(M9`ctB{m:f@`3n|O,ܗr޾jxR0T ,0@}WBLǬ5vPK!b:^drs/shapexml.xml\o6NU$Xias@I"5r#mY]p U}<ӲPl!m޻.gR'&4_oNUNT(eğd?]rT ը̹rTLzgJ^fl!\i v:5bR-/eyY3- N&TIv;+>nM2V̈a&fzcKkLh֚C p],~lRUhb_el=E?}@#t,A}OC`IK[?ٛ-E܂ZTr(867ROR}a9HmÚȝLEQk SODBfzabCo W&}b f|f`x h&}'n =ɀl  6<4|C-7)R݋x _uZ[}e<3]GbQIFP:#+JOU5dCq%]Z`g@ }l(.3K<ЭG4f~+oHzܰx~ژw\{*e&Fbc]Ydv#\!̄$`'@HXG_@w Iϩ"/y5R|@Loq C`Xf[ͥxbDa'5F??%U\5&pJ *Bp[kgS2/tr[(hS5>#GމzZbxiO6oְ_z +cRZ쨽}nD }"E0jݸ~ vq &^o,P c+>Vcy8O+95+ O Y ԟJ(zYJ2eLӬ{T^XDӱChc~Sn" v"j7/i%(/V"[Q"h$PPo'BЧDS"X]k0+!CƤ dnڦ5M$_CA\Pq{I![ h{pQbݔ,t9JhlL;ӆHϴYܸݡOzn"@.cdyNƴwDH*RIVjkLKܔX&~T7`W@T3T린cPg+Մ ]Q d 6]w>iXN :"UY,D!uOA ~B %f"Q=ضʧiX.BG8m|"G(6ˋ;Q>,C(TJBXq 37"U1Gr)B*CS#n;lOn=lS7Sݜj)),uW^{Q]K~6_PK-!Zf[Content_Types].xmlPK-!1_a /_rels/.relsPK-!b:^*drs/shapexml.xmlPK-!ܜ< drs/downrev.xmlPKB <  OmMax 4x1 + 5x2 s.t. x1 + x2 > 5 3x1 + x2 > 8 x1, x2 > 0n~ Kfcckcckcc cckcckcccckcckcccc cckcckcccn  H  0޽h ? 3"^+ 0N0 ^~^@./^(  4    ~xaxa?Rectangle 2"PK!Zf[Content_Types].xmlMO &2WR=cJ`F0iK`#̼vLw 9uSq:w`G ^i ½KI)c/ $oVjTMRc|}042ҥCƔM̏P~*ka/8^DkHbL8e i"K\XN\6rco4y@_;oPK!1_a _rels/.relsj0 ѽqCNo^K [ILcX&m߾0XFo;>0xM e`|X}đ I`߽N4aG2$RKIZ)4(M9`ctB{m:f@`3n|O,ܗr޾jxR0T ,0@}WBLǬ5vPK!C|drs/shapexml.xmlT]o: }pס61 ml";ǂ؋,Jr׏4ŰALR$sJ5Z|ișP.MŔ3A )? ǿpcg:+ޛd0pE-Zp u-xX1P+jBR̬-I~mYSzt5sŰQ`[)ؘzJ;'Li +|SRFSoEqŭP: B/Y+L25GKC'dvu=]_x-ۅ!9T}o!HtU1 }y@svLC"dz+R&xbdDb}&;]qi8ةZgΞ,`X^~Wجp22L.d{5kZ΃*Քr/ wLJe SX5D^g5 `r>j@#q Jhr5,P vFaGFAEXz<{FG ^J]u Ajt]w!IpX:s{\yfq'm__^w iؼ˞O8]!Qtf PK!ӎwdrs/downrev.xmlDQK0Co.:1RkbsS}4Ӧkw2 &/ۇPsno@c/aW޴i:8旃ku>Sm4PK-!Zf[Content_Types].xmlPK-!1_a /_rels/.relsPK-!C|*drs/shapexml.xmlPK-!ӎwdrs/downrev.xmlPK `   nExample: Unbounded Solution  e     ~xaxa?Rectangle 3")#PK!Zf[Content_Types].xmlMO &2WR=cJ`F0iK`#̼vLw 9uSq:w`G ^i ½KI)c/ $oVjTMRc|}042ҥCƔM̏P~*ka/8^DkHbL8e i"K\XN\6rco4y@_;oPK!1_a _rels/.relsj0 ѽqCNo^K [ILcX&m߾0XFo;>0xM e`|X}đ I`߽N4aG2$RKIZ)4(M9`ctB{m:f@`3n|O,ܗr޾jxR0T ,0@}WBLǬ5vPK!odrs/shapexml.xmlUn8 }_`A뢓K4 ] MXȶ{#K^IN~JΥ>,EaP"E}NZW>gRg&&ߟ&9/t.2530"0 ai@ngMQԕD:q7::y3ie^$f2m]*R&\klwtpF^÷E,|Z6 q<>h"piM,AAv_()©4}ډ gT.}J~,PzbZ/_YZ$r:AǠI+> ,A٫0nD㩁N4 .>LcK;9tJHRDE>(2G ,k)s WAI':]T.5 ;/4x֜$#;||Ͽ ]3 PK!Odrs/downrev.xmlDMO0DHkMAMnP*%-b;ئMXq47zՠ;g[k$G 6U%0xM e`|X}đ I`߽N4aG2$RKIZ)4(M9`ctB{m:f@`3n|O,ܗr޾jxR0T ,0@}WBLǬ5vPK! drs/shapexml.xmlUM"7G|fz=+fHdsvn>s59DɢH9qUOJt^Y{Τm2_ަwC|}Ǿf8lN*z|%+?ZU"`閝I/M*IJ(ßp,깋Vy3wL)=ΌUԒx1pb p0c_V!'JƒC Q{gW[hEVb+]u+x-KKy2z@{no@X {}r8Q;-X;~fP,^rGDfC"3vJQ[a[fJVU.>-Q?\P6yY"{}+H[Val} j+EuiP_Lt$@AwM8sW[V 4=U7n "Q7$䛓b!VRBJhU@"S%欐`?J3_Z&t&>Nf۱sĎYy_>\=itx};)_vE59Eg `1m#2c(4f|uSZNqʥ}I/6%rSkFcdq.D)7qrh.e\8nY[Um]6XYrV"v#-3Ӿǔ>!K7y,x6Uenܫz-{i@L#XreTr8>n|k5&e)rlMLP4Z|5Ҙ]TzK%g̝m)> B!HHx- -H!Oe%}z S;;O_PK!1drs/downrev.xmlDN0DHHܨIVP x`Mүь-Vđo-+Hg koWs> k,0xM e`|X}đ I`߽N4aG2$RKIZ)4(M9`ctB{m:f@`3n|O,ܗr޾jxR0T ,0@}WBLǬ5vPK!/B drs/shapexml.xmlUMo8@Z#F moayAI5EjI}$a[@AÙ73w$kn* %\jїՐ*Ԋgt-xۻfdʎ.kF-fnZM^͢nr!Q-;i;5#ZϛVu=3Dt%H XHNz[pLu{0쿀) g8ҏKccfYiA Ə'ICZq*6Vl3 NI:\:Rvxopx _4c'/E|\J8([O)|:'BK@\60dLIGh!t-7D:R"=>&ogn{t.1_<1 !_ @}D9Z}58;4보TovqW)ZX9w(i+V 9EKf, ٛkuYy}06<7PZ߂B4\{9Bδ4a]PK!^kdrs/downrev.xmlDQK0Co.neC'Ca[5uMM5|9|ocgt$ djZjnn|dg aXRفxB|)s_k4OluF]ÕCfYl)=hZc}N&8̶;]i* 8Ǘ_zVfy1;<U{:/&SPK-!Zf[Content_Types].xmlPK-!1_a /_rels/.relsPK-!/B *drs/shapexml.xmlPK-!^kdrs/downrev.xmlPK x18go    @AB4CdDEFQ>R"UVWX___1?44ad<@44ad<4dFreeform 6jrB @  t11??Line 7"PK!Zf[Content_Types].xmlMO &2WR=cJ`F0iK`#̼vLw 9uSq:w`G ^i ½KI)c/ $oVjTMRc|}042ҥCƔM̏P~*ka/8^DkHbL8e i"K\XN\6rco4y@_;oPK!1_a _rels/.relsj0 ѽqCNo^K [ILcX&m߾0XFo;>0xM e`|X}đ I`߽N4aG2$RKIZ)4(M9`ctB{m:f@`3n|O,ܗr޾jxR0T ,0@}WBLǬ5vPK!q fGdrs/shapexml.xmlUMo6 x-o5VY$A= cE#XS@Rȯ )X`!͛_f[鼲3iYfƙ`jȂ_s?=!ċVv?^\k [Oz'46'((-#K|ۮSug: TF>]7 ?vA`ƾ`ֲl#l>zͪݟ=0|߸jPVNM~f3Y>'>0l:Lcv1 c|*蠂k,Lۥ93v6vHCEjU:ݺzюmA|wnhZ @iY^ҒSN֜iEVGX" ifE!HWՊʒdYǙ/L:t^,P q ֺ=U߇26J<\?-M2GCo25]4S4gl^* )N [< M;k OpxBfqP#б){A|/V"./ z,ffy 7V>Z \`oXJ:sd{%^6C:JbGψ*1cx e8HGw^9CNCVoŖEIƵ‹GIcsCK_ FIY>+XK9 XhXicDi@ HTg Kh) Zp^J[gn$Pa.6͘չ(IݣoH?PK!^drs/downrev.xmlDn0w$H!J-Qu7KlGC%ƣour^Y#`HTP~|@#~7l1j aq!9jI_؞Lj4(]åk_%I5*Z饥rSVRKVi,-u>N} ' "E|PK-!Zf[Content_Types].xmlPK-!1_a /_rels/.relsPK-!q fG*drs/shapexml.xmlPK-!^drs/downrev.xmlPK   i   l_~~1?Rectangle 8" PK!Zf[Content_Types].xmlMO &2WR=cJ`F0iK`#̼vLw 9uSq:w`G ^i ½KI)c/ $oVjTMRc|}042ҥCƔM̏P~*ka/8^DkHbL8e i"K\XN\6rco4y@_;oPK!1_a _rels/.relsj0 ѽqCNo^K [ILcX&m߾0XFo;>0xM e`|X}đ I`߽N4aG2$RKIZ)4(M9`ctB{m:f@`3n|O,ܗr޾jxR0T ,0@}WBLǬ5vPK!h+drs/shapexml.xmlWMo6 x-,n #Ξ Jb? 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