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⛖ֽѯ'~#1aryr: `[GaUN'HG910M3ϣMCaUdOvW"l"n+Cixpn)6k1-Ԇ5f Zw(핂f:z ~XzJh҇[rϵ5 okL.r~A\el}k/(PK!bdrs/downrev.xmlDOO1G&~fLIwB ކ۰m7 ƃ'o~yEo[q;(AڸZv~#:w` jsk$ TRrՐE\bG,tZꀗ$gكh\ZhSm?۰̦|<.w_drno3H}v>tjOrpF#/& rPK-!Zf[Content_Types].xmlPK-!1_a /_rels/.relsPK-!0*drs/shapexml.xmlPK-!bpdrs/downrev.xmlPKv8B:2___PPT9  rDefine the ProblemZC     # aB/Gf21??Rectangle 6#" ÅPK!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!Tdrs/shapexml.xmlXMo6 t-v;uɢEgを(5E$e;}3fPμz#ueR&P6si2!JK㬚&O*$~}= e&4)c'^JUp~ޫ F2AޫL嬾$e^XgA"Ae17J'^{EǝaF0+Dc {*@"G^]QɺաȎ+ ez& 2ȉZGh8B~lkjC&eP.D{jc͂.c9+e <'{ v(Vsb) ~꟟ǭ* U{><\,jQA+-Q 1w^FUBlz]0UuMv6iay\s^fo3*Qv-q2  _H좩tmN=23 y,ihn Эu3Pd}o)#&ll{\Abh;lʉRëtF;ʩi]iyhbNݿ9rM}h#sTBfHÍs qmu[YiCYY)}P܇\T%;w쉒gsp4/PzJh_.ru&3=og'w"x_ ~PK!8drs/downrev.xmlDAO1F&fHI ])M`a;6lM[a68yiٙ|JF)mk *l% W nfX(w[:fIbCP5d0\G6c:}͕KBsڦ;Z5To#qK1]gt&_> ^6WRd<Ɂ׃j!Rm?PK-!Zf[Content_Types].xmlPK-!1_a /_rels/.relsPK-!T*drs/shapexml.xmlPK-!8sdrs/downrev.xmlPKz8PB:2___PPT9  yIdentify the AlternativesZC     # cB/Gf21??Rectangle 7#" ÁPK!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!Xdrs/shapexml.xmlXKo6 x-~Ɖu΢Egを(5E$G~}?PXÙoߌ6f+鼲f{ﺜILŔya2SW TS^PM:Yn])ݢS9 "Q;nw)2j^=(W X3#J})@,dWkื&sb_`~,CΜBD!X{=гd̀U"*1<Ucm|0]h;2B7ꍢB ^;it(Qr>|dX,rPbuCEtp"SZlCb^ υOYeQgGJhF]|Bd9WMY}ک h^.ŷ<59xy2~8=$C+S~9l2 -#E~94kX_SbG4 aGZ 1)nS"5A(ȈTh[9z p*hր0/5Tlxp`BÇ3ipn|l}0NtMc%΍8f%_̒f,[;l0ܤE$:S0[a18>K#H^EsLAb̟D2qo^GYB/ŽuK[fTDx$CcqXIAͼJ! ͠ DLxTkսOg9ɖ4A 5Q>Dd<6k!.ROf4_XH^VJ$}9I-o XX2CTt}ճc1h`c>8kx5,66n}V)S -J= ̽5pd3Q{OjToLSLjv25 J"En] ZpVwT:kgp^RRQh4R4N}`Я/KQpþ>wх񌾫x~/]-^{oj 3s;yϛ?l7)_!oPK!̈Gdrs/downrev.xmlDQO0FM5M102)4yd.e+V}97˙-zݲ 9`d*+g`>ZCna10jt)B͢4!t9jHڎLd'4xK(-%רL\h׆[ xo-:y?*>R! @}>6Y[8vZߎN-@N@싵PK-!Zf[Content_Types].xmlPK-!1_a /_rels/.relsPK-!X*drs/shapexml.xmlPK-!̈Gpdrs/downrev.xmlPKv8X B:2___PPT9  vDetermine the CriteriaZC     # /Gf21??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!Pdrs/shapexml.xmlXKo6 x-~'Y4ۃ0,z\PeHȯP4(և}pFp7Bؕmʚ)r&Mj3eVS3ɄFN^zW_1l"jl% ֕"[u*'4ApTN۽B~fY-J1`8̈>@d+pm odNl!8 !gm!EzB'гdd\Th9Mh8PGDL.z1D4@sht"T=CCS,}\ك,0g*BT.\yI^<,+* ?u.RP|!2χQ̢2O DXVeԅY|SP]!gdhet1Kt|*ā^>jsvi`sHՊ*Ɖ aw@Z 1)H8 2D ږy p.~4fk,-`48<84 > Lov`UI87 YlP \ǹl&-,D)ڇe酌cŨ>K8(<78) ULO"Y>O7$s!K17nMrkŒ*а 6)9@0,_4DS@ԁ'{V%VF ,'jl5I 򴣼&(>@LJPUR " %!Ac$v]Si,aCzgIL4}ׇ5ЭK8[Ko aɜ: V7zČav]8ks<@`qp*%M f('vxopK[?G;XUoNsԧƈ}%sB] ZpVT5gp^RRQh4WRN}`Я/CA1}l]hB< /K]ךX^2Io2qYb/7FpxWwPK!drs/downrev.xmlDAO1F&fHI])M`a;6lM[a68yiٙ|JF)mk *l% W nfX(w[:fIbCP5d0\G6c:}͕KM vj:Ftbv!ˏ/ҙ~,R'x_՛J-$ρ׃j!Rm?PK-!Zf[Content_Types].xmlPK-!1_a /_rels/.relsPK-!P*drs/shapexml.xmlPK-!mdrs/downrev.xmlPKt8 XB:2___PPT9  yIdentify the AlternativesZC      # dB/Gf21??Rectangle 9#" ÎPK!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!Z&drs/shapexml.xmlXKo7 x-^%DNj Xz \-+.%zwfڍ":"d8|YmZ:3i2+/OW L.5rwwa!Nggki`ݲS; 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RJxב6P[&Ӌ9ZV0% +[l_2> k-3yX-k;rIuEQAK髆 c`R;#>IRi@ Uh[QtY6۟R7#@SK*4KSεD)~6\PK-!Zf[Content_Types].xmlPK-!1_a /_rels/.relsPK-!0yv*drs/shapexml.xmlPK-!ldrs/downrev.xmlPK4   hExample: Project Scheduling E  @  xMxaxa?Rectangle 3"9 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.xmlYQO8~?iҖT qwR*j84WN)NCaB*ڞ=3ǜ}muS~˙ԉIs0Ɯ9/t*rʟ_?qVN\0YI9+I㒕,bJ!ˌ-G>tJ+^xlTNv k~fQ-ܲ3ҏRA0E8G; PTfwbxǃ?9R](gF0e)zֵSՠNI ȓyLgAuSgݾƥ^*Uq׺%WKՕBb{&N`r ht⹱q_]PHP%q}EPN=JX'~V7`bJL۹ShDL0\WE^B:R}[Ol ՔklADm5fZOj-* ibg?˿BEL0=֘,]ᯔaSi:W*:GQyJ$~m 2;bBSL]GT)|#Q9iA]8*`BɛfPV3} Td|B)@(H+AHbu/ ?z/dzC>~~}hEt$TiY YDKC ;VMgleK6U<3"оx 3):׍5ԭ!ګ)ï_MLJp|@ErѲC>An.u}'Aj֤rA-ERG "F% ZItЦrUQ0 +Q^'V`hۡ+qiMS&Q9IDNٱcM}+x5kA(xX҂]l0Ӱ*W+rr*)xeӇlO6ji9PRk埢I _Bj4i@1M^2QIUsm'n'l-T[%zm=Ka-MBLC¼V8'k`<1 _G5+h)sX,B$U }3 wumV/IjH(`F\MvOzz)~z9&"bKjBu 9R9̳,gmB]O8o" &t"9'J8#:<1G PK!drs/downrev.xmlDQK0C\:V!*߮][ܔ$oAv0eiZ~ deR0fWRZD 4!jȠڞ8vG ]-kN>$I* 驡TM<)bxYpNRa"߫_ԳV0O0~V9/FSPK-!Zf[Content_Types].xmlPK-!1_a /_rels/.relsPK-! /*drs/shapexml.xmlPK-!! drs/downrev.xmlPK( P   Consider the construction of a 250-unit apartment complex. 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U(2gG(ْCr7j&12Aq'nQ f\Yt X K[Mc5teQBM^ɀK"I퀈(p  [oIC e*: jCKP>U)7OT/=KZKnɩ 1\"+UEbj'oJةa%3 ?N7oӢ+tHmr(ZҙX?M@ WȒ'C̡(IbU&\4=N_PK!3drs/downrev.xmlDAO@&͘x TJ5ŋ; fwxMj08eqeu˵ ;ˤLVڞcj!STЄЧR!~d{3j"tr$`˱6 U(?vYʐUͰ~h|+ʵtSm4PK-!Zf[Content_Types].xmlPK-!1_a /_rels/.relsPK-!\*drs/shapexml.xmlPK-!3drs/downrev.xmlPK `}   eModel Solution ( E   \  xE0e0e?Rectangle 3"ðPK!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!I'GEdrs/shapexml.xmlXn6}/ Zd(qIg Zl{;آn/)j?ؼ 3sf(_Tu)?~L^g eLt.둫k7Sz.[JwsEIA%Ycl׳zj}XO-+pș@,d'%8&&[x ܊xi+8,q<, ^ŪKk&txv h }ug1VK12E9#@t12_$eHNdDI2BG~s h5f"_dC>q`~m5<<>=4:|wF7ՍQ33rYlxKSOȐ|O֌X|0e0m0&DF~cH7RO%$'H?bF0PE򣭅P Խ,ŽϞZ `k}\#D_Ura KigNc U j `+[ފTTNȷN$6HNc^c~7mQ*+K)DlS.$<*G^wҤض\6l%-xE\kE!M2'S5mW%E؇p*MܖJE3i a(cJ1%Ζމ^ c%UkA'%LD*ԯy4%Pwc߄jl|>R>(ŋ )D^Ld& '6Rnj}nn4 o{߰0hoN5/VsWZudqTX0xM e`|X}đ I`߽N4aG2$RKIZ)4(M9`ctB{m:f@`3n|O,ܗr޾jxR0T ,0@}WBLǬ5vPK!)wwdrs/shapexml.xmlUn6}/ Zd}syp[ ;>#H;_CR8P~̙>Һ茏> 9ZֻyY^s<邔2'<328k7k3^y'*ِdZ+mckwJ''5jJI<֖Eo'ijF )|%{׃?`no񽴨|ּV `~C:j+O-+1t2Oozdv1|Kl d;)=D@KZ'F蔓 BK^ .huElHO <kفBPlrSO6-wcîBٗc$6ogq0Λg̶h)O٦جm4K wMݘu"g\/[Jyd+tx"R[1F"@oG:OU?60nm)P=afY+H'Ψ7MJp\.q>K3Y %KWn\G"9+; m|Ry}|wl}cy[)O٣5gmEVa_LTdES-땤4N!\OMeoX\!A\>>!v/PK!D&{drs/downrev.xmlDN0EH5HëӪeMwC0xM e`|X}đ I`߽N4aG2$RKIZ)4(M9`ctB{m:f@`3n|O,ܗr޾jxR0T ,0@}WBLǬ5vPK!}qXdrs/shapexml.xmlVMo8/u#vq@v0 #NcAKT5EjIʱeC2Arf̃> Һ9|s&ub\痧)g etݕ3W2nVrd+ >Rj2c !^i 7B*_+K~eYxr=pEge ^d׼W#q,Msu0GIxC"4-^֚#5OjJ[%ܘaGdx;Eg\pՅW3e O_O>p<"At=B3y,}z3ߐC`KڏN1s~us8Ke"6*gXG UΌF8 k3`VNH,SxLVg{ACc_mG]*Wqxohu\ ں S q#ت\o|6qrz_=!0H0_%q}}E0NCVX'0.&\G`b?lk'b0BvΥ% D\Z41wSuq8?h"D*Eqp (!^uu M06 g~9i(z:R>(ŅAhH܅!qd@cg_ca ;Z %nn[;a->l3G3VE!V2N; 4-"%ZN:h/5ru4D IqI4t1K,5/yWF#Mmi ٥}ck UQ0 +U^'VUW DoMS&Q~NZ:@Djǟǟk,YLQ)ӀC'Fx=nKxToMԀdd6Mk >DF&$ded̟fb/3"HT t:Fqo4_)^Ka\p\f ٶ5YMESċkĒUX^B"JetXOa@m~]Nhxȝ4=KYihSFeXp'lgD!uPl "V~5])Bo6QyG"V7#L~$T2<AZ<@I$:TyHt`F<=4 [wg#[%#\Q mJ0q|BU5¥߱Jo8~bUŨÚx:f њ6Ǟ6 ;(XBSNf_ \{b޻9ȷcr+4r$\G#wj˙I~]2tBXwWU2|iSHN1.1SjS! ?iA0xM e`|X}đ I`߽N4aG2$RKIZ)4(M9`ctB{m:f@`3n|O,ܗr޾jxR0T ,0@}WBLǬ5vPK!e@drs/shapexml.xmlUQo8 ~ %u m  p-˱Y$9MIvtHtl;H3~n̙”e#g>.I-3~Z}sc28k?CȋZ+5*Z PndR Ԫd<0j|!%q8֔M9"V $SMh]y!dJGULJDL5a5[c-32TH:fekN&(Q1l:p=] 5nYGp3iqCWޢڸ'@#gjf)2@q'ڥQ f\Y,t Z k[Mc5peQBM^ɀk"I큈(p A?%]֩l$ .A$aVȟ#ޡwnୌɩ 1\"+MEbj'oFvةq|ŝ~}6*pZtK آ˟^xQBI6́6q?6>NwmӚoM**θ_r$"՛t7kCm$q^"=I5'OR#ު.m1U}JR't|kjF5epsWrh+3YUXq%.H#+TTfG4`&}Yϰ4Q(rwWaZ9/@3fnuhF8MFYՒ|j]H\_q= ‚}Οw&Do?PK!/3drs/downrev.xmlDN0DHVbGH[ Hʆ%uvdMX,`9z4;YYl㤶JXh%vΒ3X&K,lE:* 6(/8MKdSw`L+.= n:Ȳ;nPbOO-5hî3_T㽎e֔B\NHc+=lEJu~lrZV"y/&SPK-!Zf[Content_Types].xmlPK-!1_a /_rels/.relsPK-!e@*drs/shapexml.xmlPK-!/3drs/downrev.xmlPK `}   ]Report Generation E   d  xE0e0e?Rectangle 3"D > 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!E`drs/shapexml.xmlWn8}_`"= JFa)%֚"$!e P@f=̐<3gf@^ߗu r&ujBb™BgB-~j*ͪofK7.7STV:8T~{)E5һe4J?YGtę%})@disn]F| ̊'x W Wz8mp\16xl{__s/'N] frY x2CRXz b0 #eV>j Dƿ=H5} U +9Sky͇p4cbO5S;gB5ឳ8󘑗e!RY `Q` vs牷S0aMK@F~gH7RO)<1C!J:C&h!u8d(V k[ Q΍7aJ8" 5PՠNqH Nd#&^&{b+U 2IZPx?ULdB:^Lm{j~ul=׏P5o!OGx"*RF:RHfk3츬-m_Q-%ihKRBAsKOi4I4j%|-Bq1-#\^["o-hLwHS˥?9\ޗWxlgtSKo0 +CaEPX=`v,dYNȔ [_?@I}]%[r~V'(*>\@?zSnE %>L-,vlKsejǭx WT]Go"X;QR轊`y<$-!;ӿױPj:8)UͯFtOġh9X #`(M kRLFjTټ٪dN4yd ~kg\{gdx-zۊ8Rp;J@ 4T)(7n XW3w-v\k5sK#!nᶕwIr/n(>ԺUqmt2͊Uƛ0R~?)b4|lu` _ ?PK-!Zf[Content_Types].xmlPK-!1_a /_rels/.relsPK-!E`*drs/shapexml.xmlPK-!-+drs/downrev.xmlPK3 E  MA managerial report, based on the results of the model, should be prepared. The report should be easily understood by the decision maker. The report should include: the recommended decision other pertinent information about the results (for example, how sensitive the model solution is to the assumptions and data used in the model),   N 3y___PPT10Y+D=' = @B +"D h(  h h  xE0e0e?Rectangle 2"êPK!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!5u)>drs/shapexml.xmlUn:@p{qAz; PK!oHdrs/downrev.xmlDMK@EaxR4vZj. wk 36.tys9`:q"ZgL' ӭOw 9K F Z^^,0l :\!C sI AR{n;9ZoUհ~48ӛEjl8_& Eh rPK-!Zf[Content_Types].xmlPK-!1_a /_rels/.relsPK-!5u)>*drs/shapexml.xmlPK-!oHdrs/downrev.xmlPK `}   jImplementation and Follow-Up  G(   h  xaO0e0e?Rectangle 3"qkPK!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!kdrs/shapexml.xmlXMo6 x-vl'@E mcaY챠%VM*I9v~}ߐ Z`{[HArf̃컏R0:IЛ~ypЙPF˄rW\ŰYYլsV}0԰ƖC^e JRqޯUi~{= 9Ӣĵ2E%ِE Iw F|K086[r;{kV̑BX5BX- QMv`:ގӛf_t\]Y-4/-. Ԅ{C,MY Ы*%Gʥο[1ZbjɬAǒ}Cbё?Xi!-S HGCzEP{T Bg„_<`g_z@@eq `wʹ>lY Gaucղ).VTy U2l/>=M]z(٫0n-c@a^Cƚo֡/WGxg"Rΐ:2am_ QsGIjѕND|dv;. :.$D-](N =-[`t'IyBdRC:[wuGq"g5S(;PK!޹drs/downrev.xmlDMK@Eax;;m}-%* Bq̼&L;^6đoAl*ZS#7K>QYgY_^(Udr>b|JM}*GguB)u''I2Z9k*5B?Successful implementation of model results is of critical importance. Secure as much user involvement as possible throughout the modeling process. Continue to monitor the contribution of the model. It might be necessary to refine or expand the model.   3y___PPT10Y+D=' = @B +":F 91l(  l'  l  xExaxa?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!4zwdrs/shapexml.xmlTMo6 x-BEbm#0,z\PiM,I9v~>J(vu͛NժOcJjSA<.n(qIDAOϋ53妠&oD'mֶc[42V8 Vv魵wѩd.d 5\B6ⱃ"= 87ܓ o(7yfq/m_ ڲ_JxĖM\!F[4Lf9n,O ]om"T/;J+#[ɤ/av.J6C VTޯRW#HC߭^(mLny)0D %&SPK-!Zf[Content_Types].xmlPK-!1_a /_rels/.relsPK-!4zw*drs/shapexml.xmlPK-!Hdrs/downrev.xmlPK    iExample: Austin Auto Auction E   l  x@Exaxa?Rectangle 3"àPK!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!z!7drs/shapexml.xmlX[O8~_i V R*hGnl;k;;v,Q>O/R0:O}ΤNMV规};pЙPF˄Hǿ\}㲚YYլsZ}2ƖƒOJ'7ǽR_(]V KTz]XVd δ(qLē"ܤ#O0(͟Нv䵵y-EH{{!6VP)jK(W&{~p:?_4\]Yv-5K13ypp8=A#t1;R'cA `:LB1e r"o "c<:d+gVZXə[0ht8fuuykT)NM,eiJ^V)R.uqM؊ ',ע@lSm@(% iW BJa ?Q="-A3,aZ Lb|E 9[} U΍e%5 5\hkWZ$[Q)GmC.[2v :!FHᦗ7IILJzj>GO)e**l|\4qv_z ۻE b2}N9/FSPK-!Zf[Content_Types].xmlPK-!1_a /_rels/.relsPK-!z!7*drs/shapexml.xmlPK-!}=drs/downrev.xmlPKi  N An auctioneer has developed a simple mathematical model for deciding the starting bid he will require when auctioning a used automobile. Essentially, he sets the starting bid at seventy percent of what he predicts the final winning bid will (or should) be. He predicts the winning bid by starting with the car's original selling price and making two deductions, one based on the car's age and the other based on the car's mileage. The age deduction is $800 per year and the mileage deduction is $.025 per mile.    v [ m lC (Group 4"y l zA??tran0764Picture 5tran0764- m l zA??BS00330_Picture 6BS00330_[ #  3y___PPT10Y+D=' = @B +"#J "p(  p p  x`oOxaxa?Rectangle 2"îPK!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!Ddrs/shapexml.xmlTn: }z%Ү ml";qm9"K$I~Gۥ{LIH㡓l/k1gBj6_gW9O"Q8q͍9`dF#W6#NpWkۑnG ''GMQGsFAZ4+nՏʅcD0>Gt4 #CƧ`ҏyÝ E*O=ZBgO/ \Wt:MqzneTW3^zY,m[aŻպB 8 Vtlpqؤbb1㕚k8lt͛2 jCln,1M {~R!Aċcicʷ#֗͒VQ !D$},gB4+~ξǏ{@ +ȃ̞'DgPK!drs/downrev.xmlDAK1!fiAmff&iw 8{/ۊ38V0e Kgl>_f BD6:& \\_17Xᐣ:.25Y #lŘN_IOp,J ;z0xM e`|X}đ I`߽N4aG2$RKIZ)4(M9`ctB{m:f@`3n|O,ܗr޾jxR0T ,0@}WBLǬ5vPK!8<@drs/shapexml.xmlWo"7W`Ze!eJh+Xyf LSC }g@=0~si[*F'C33zϓΜ:htݏ?V#W1k7u:.[ReI텇RuzSB;қy573ˊӄ_.b)$Am%:G'b!ݥ8YW@pQF~>hݐ!B:lE'\26 tpF\ûBXMmaZZ zᢎaWKHmfY+XIJ[ITlx*r:$˴M`0dM.H ɘK;_/,U}9AɠJ jv@Uh#c[AGf~jY?R_(q E$d&j1w02:>3Fo7xh=MsfKqǯx~?΀;ùjp+:.KgԿbh0%cYQgy8ž']B U;o0+ *"Tu`@ŹŎl~}φҵ,HXu/KB9B6wbӷfUH4~_q*92/`Ib$T2Z ǗV9sgmd߆)!8N2q7Y Shn├*d؎{¦AfOrtu%*+(6[k~),.)V\X UuJ1)v,m?3o[ > 6":l@ܵf@!FPCc~7ORDM:7~#H2>q\___?P퓭wI] PK!drs/downrev.xmlDQK0Co.seC[xmbslk}tL'۫;!"k-lg+̵=qA26"A8䨠R%abq)Fj7β4qzhcKwy0+^e!;./{?v7mW|>[?_H^AKPK-!Zf[Content_Types].xmlPK-!1_a /_rels/.relsPK-!8<@*drs/shapexml.xmlPK-!drs/downrev.xmlPK `  hQuestion: Develop the mathematical model that will give the starting bid (B ) for a car in terms of the car's original price (P ), current age (A) and mileage (M ).    fB3 v [ m pC (Group 4"pi p zA??tran0764Picture 5tran0764- m p zA??BS00330_Picture 6BS00330_[ #  3y___PPT10Y+D=' = @B +"@ ?7 t(  t t C @"@/Gf21?Rectangle 2"  ` N    t C `#@/Gf21?Rectangle 3"    N    t  x$@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!ZXǧZWdrs/shapexml.xml\]O8}_iS(Њ2$vWPEMmbgm~iڢ1M4c_sU*Ȓ+J1G)"q*F%0L >O\v^ uAPYa1sca9ϙ$ .PH3W)\fQuNRA/ДXNv9Q$GzrCIv*9_ARFXGpG" C9BzRqYm68׺ ju)<r&' W#ziwpRh`3V̆D?9$!SX'(?lWD(?v}+Aw=􏝒^7JZ14+ֶc2fTϔ<*{J8%fzP͸7JvlDfLDhuD %>ymfG)󂙱c)6L&Q 9+`˱6mY`ɴ'xaқ |r#z ![JHE Ze}FI̓{6>W@V_R gD s̘Ϣ*FjRxcgV=]DȐ%OuW 8jiP#,Nvxo b|3ʷ 8'9ac$͖?輿 {sO~)vvMJw]7z{@_?0e7z|Qw|o.?_w#@5 4z|#ȿkVn0 ~ QaSE{Ҵ4H[2ܤJ x9)B3Fs9qm'IRgp2lӧ$,:Od캘ߒ2l,SyM-k,-ǎQ*N+-ZCGn2Ey@Jw(|!Br`ՋۮQR\9z ;E .m4r[YE -7lO.ml#I-tHJs:õYZc꨻ e'N:HmBgHU®`' nr'fDA}"P?1PCy8o8ȇ=~퇙CH]ˏ6SPK!")drs/downrev.xmlDAn0Ezk*uWRAAj b; cuA?z ;5^{ 02QvK4kHGUmι/+{%uC<%uI2k*li^Qyܞ6]~,gmi+!X.?jso)`8~uuܠDhMOnPK-!Zf[Content_Types].xmlPK-!1_a /_rels/.relsPK-!ZXǧZW*drs/shapexml.xmlPK-!")drs/downrev.xmlPK   `C  Answer: The expected winning bid can be expressed as: P - 800(A) - .025(M ) The entire model is: B = .7(expected winning bid) B = .7(P - 800(A) - .025(M )) B = .7(P )- 560(A) - .0175(M )p 1   f. /0   $  t  x`&@0e0e?Rectangle 5"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!n&cl칦8ר]jsǭR6K}S !c8ˬ!ADνkfD4`WQ""\" <SBZf1l((*ыQdrƏ\z`Es^HoNs![hiի- Xŝ~}Jjo+?v>#E?+l&)l6'>7i&3*ŷnADJ&]F6{(QÞByH)'%n߲ S86V*ʮK)X'*J)Siٔ0fwIW7f0{AJѝ6GRnYُJ&N7av_Ta^nro_=+coy[>U]@˱⼭)wZɭ %^a_:>Z3 tw=16_#z?=O`}YPK!Adrs/downrev.xmlDN0DHHܨ u r$iӿь5@>t\2ĵ7 ޷OW!"k4I,g3̵;rI*6"A8䨠ϥ uKĩ9o1=yecibO-*><~ ˢoU,ʗPbXރ4q2Ed b:}N"y/&SPK-!Zf[Content_Types].xmlPK-!1_a /_rels/.relsPK-!0xM e`|X}đ I`߽N4aG2$RKIZ)4(M9`ctB{m:f@`3n|O,ܗr޾jxR0T ,0@}WBLǬ5vPK!XOEdrs/shapexml.xmlTn8 x-R;F"1F`X)z,FeH.I9v:=,Ԑ̼y3b{|ct?9Zیy\p钔2G_n[cg6uv6yQ˖c]e\K[Y'ԁjt1_Zj4)EI<׎5eƯחWijv#*.hMq!?86;rfc -jwΙZR1"P_:Fek&(ɑ!㓋dzbz5xg駼ޔ- Eg"ڸgΞ!AoGLǓ8d2MqzvaTqo{ Z +[Uc6xJβ(!y&ʤ@Sݴ큈(p ?}%= V)m$= .A$ڢVȟd2x^_J߻]2:%|:G0ם xk؞bK'UE ?ozm-{<$`.~HuT}i46h/@v׵Mk7=8R}1^]Uk5;6y8I#7c Z8qLYoaΘ*ɾ %)T:,z'ި 7-M_x\,bQUPty]>BunCe/oPH&v/0T& ^NmC '⥱V(؝ g ^Rۨ# A"jr^&ҧRK:}~?\?z9>ooqR-K$V;{PK!6drs/downrev.xmlDQK0Co.buAk575|9|om'CXt iVy`(rq~6¸K:c-C BP5d1L\OcඓYK-{zlگV=)?ׯz_3oz)uy1>܃4qEi onAlW/ߚC$ %d rPK-!Zf[Content_Types].xmlPK-!1_a /_rels/.relsPK-!XOE*drs/shapexml.xmlPK-!6drs/downrev.xmlPK `}   iExample: Austin Auto Auction E   x  x*@xaxa?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!O ^drs/shapexml.xmlX[o"7~`BeJh+123Ⱨ@~}cT>u ۘ:D9?[$`Nl N~#{ IPkd Bg迄_$Zg̟| P5l}ԑb*d97pZY7lPàNa$&[Q=WԳ 4Uw(q/SYL(xH5y=RhP$,UW{y={x<4x.R4DIqV>]EY(SI߉mA Hb L ǩmjF\eQ!rp/>0%<5 `@Ӱ nj3 +VgȧsuH&*^aK"9P5&kW"C~*MomƅR1HqFCbOz7dHL9;B:Ζ > Q2҂uAwL`J*4;J8+hvh#D?mB;}%~oP>( CH #uM6bos|MOqMh ?-&O-{?ϚϞbEܰ;=;"P}n"U6GˎBN?V{gr+SΟTMk1+B54C(Kv֫Z+ iI\J{ daœi XFpX*4 zu{}<%wvބBS#Nțu4N^gN69ǧYt8FvԸI*!D9|X A6Ԣ|[K.Mzr?u#o0`D{}#E<6C+%5r6S;κMAR0TgWȺ0GRDuvo] 'dl^[kcj$:|BixRÀ'Ka3EgRxk:r?Mqfˉ%hvYynfeM۾hr'l=d UE. ՠASաJL+!s )TEyDEM ? FPK!Qt]drs/downrev.xmlDQK0Co.BݲP -67%I|÷N'r`H@Vw(=YcoaZc :>GmC.[2v :!FHᦗIJLJzm-GOy8 WU~f*+u{3=@eR>4KR:]DhMAnPK-!Zf[Content_Types].xmlPK-!1_a /_rels/.relsPK-!O ^*drs/shapexml.xmlPK-!Qt]drs/downrev.xmlPK @  Question: Suppose a four-year old car with 60,000 miles on the odometer is being auctioned. If its original price was $12,500, what starting bid should the auctioneer require? Answer: B = .7(12,500) - 560(4) - .0175(60,000) = $5,460   6  ff3 v [ m xC (Group 5"@9 x zA??tran0764Picture 6tran0764- m x zA??BS00330_Picture 7BS00330_[ #  3y___PPT10Y+D=' = @B +"I ~v`|^(  | |  x-@xaxa?Rectangle 2"ïPK!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!5f^Edrs/shapexml.xmlTMo8/@Zvn>Eb ac0(K5ErIʱH)âhu g͛rhK3~i̙”f3H?JϿ?qcg2k?CȋZ?+5*Z غ:Ux|1j|>k%q_;֔0xM e`|X}đ I`߽N4aG2$RKIZ)4(M9`ctB{m:f@`3n|O,ܗr޾jxR0T ,0@}WBLǬ5vPK!-drs/shapexml.xmlWn80@p;HR[R$<3q. Zl)RCR!)ˏ U{A>>JA\BɄ>t)2UY!W 2Qb,JME,M\%tmmw:&]\YSinP):nw)Y!=E5n>mYBo{рJ})X N?f*ݘ4{Eg~j5z]sGݎwૄΗjM쾂K)%4ꏣ?a\pYu߱X9ip{Ѡ:,;KRFqo"I!Q0'|*G]X(J(]fQ(y 6LsJwCE>,O9.'Jr1քZJvbqrQbv&U],6e銸-'X{J}*! aь?_}wb}XO,t0N> b,P Л+$ [.P^9emg37>˹,qE(ˆ 70y-S .=SԒ-sCWDO%y~) hEqQ!q% (H8(iVfY/ZovY!(<J¦)+ qLap9(Ph-Cy8,(.RS" h: J~aZ)(p:C>u3HI:]e{\+)Dpq~ V!@1J#ղMp8ůs;tTm^W~feХ 2: ?ԪcA~3X;oQaC9`p`Z{5CZ\7鸷{s.÷Nֈ08V/2ĭw >?v7+!"k4ILˋ5ڝS; JT8R'aF흷S nͲ8pzqC}餙sb~57?2š5/E+(y0D _M 7?PK-!Zf[Content_Types].xmlPK-!1_a /_rels/.relsPK-!-*drs/shapexml.xmlPK-!Fdrs/downrev.xmlPKK    Question: The model is based on what assumptions? Answer: The model assumes that the only factors influencing the value of a used car are the original price, age, and mileage (not condition, rarity, or other factors). Also, it is assumed that age and mileage devalue a car in a linear manner and without limit. (Note, the starting bid for a very old car might be negative! )d +  D  f+fD v [ m |C (Group 4"  | zA??tran0764Picture 5tran0764- m | zA??BS00330_Picture 6BS00330_[ #  3y___PPT10Y+D=' = @B +"M (     xZxaxa?Rectangle 2"îPK!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!ӛEdrs/shapexml.xmlTn8/@ZvIEb ac1(K5ErIʱ}aQ4:PCr3|9?8LjaFo3ayvřKRFˌ_qcg2k?CȋZ?+5*Z غ:UxyRO}n.J~v)3~yqyh4pAld>zB+#v~~%#2|/TlLE 9XK*}D`OuӶ">|$x'(p/}%= V)m$= .A$ڢVȟt:x^_J߹]2:&|:G0ם xk؞bK'wzU=E?KI*4XE4 ڦ5ߛTdqϾI@ǮHh*]5\ĉP0xM e`|X}đ I`߽N4aG2$RKIZ)4(M9`ctB{m:f@`3n|O,ܗr޾jxR0T ,0@}WBLǬ5vPK!Hbdrs/shapexml.xml\O8?˯'P(+@$*j4G NCӇӪJ:}HgEm83ҔB(i =JQ8e&*Ɍ7]ȯv\)@ΜFt/Y MC>5r mr(Mf󤑪 4e^FR({ZOuZR{DlB:n(Q?CĪWF0ٟC>zӗf3&%߆'pIDK>-l&Ab I}v\ X ?f_Lm-窟M]&`SzD^#EǝVuDJ(iy-0&jo>5e]W0ſse|B䜏tc ĮWs<3e":NvvrfGTƒ=,+ .T}r[8jY @$7HSn˶FTہ@H` p %TOVˏuV>Yf]*cUӠϦF5ЫD$LvB3Oy4xQİ&J[-qeUQQr.D2wU4;FIYH.ݨ4NNmLBcmj9}Щq+tm)b#<8pS:}Cq`Ҡ j?:|Hgm^HRH2IQb(}fԇ]'Zvd7q"K %RlEOd)sBUv4q2jBP 1)i^=s%^m 4Lܫj+qyXx̉2{(qZeh2b-#*((b݅x)F\\>  AҏkBA/ IV!g^j^/ J(x`cYmG ؕp~nbvu76 |P~ &` jÀ%@i-1_efOrl;$ז}m,׀&Dr}9`2f`ut`'o| ,aMȗJp壝lQlQȷs1o91N:}l?eUlQWOCx猰?Q >+qێD}Gv! vl)> > ڇOVMopԝ~W +]Bv'[+CH)S;o7-y^ATn0kmVQP*.\.vd;-=;J]9rgsiAO+/¾@(1n LŊP'%b5f]H4P2,HXL\eآ3I=Z c]%x$muNoY[7aF)O'8sFګ 68#' vg*kTa .[noQRޠ*$>,7!C 5o,LEݺodl80xM e`|X}đ I`߽N4aG2$RKIZ)4(M9`ctB{m:f@`3n|O,ܗr޾jxR0T ,0@}WBLǬ5vPK!͇HKDdrs/shapexml.xmlTn8/@HNĀRq1(K5E$}(:PCr3~<|7LjaF2quq͙KRFˌqk2k?CȋZ+5*Z غ:UxaROCn7.Jq)3>\S [)NI6A7!ı6b`W)=!7q0m>9r fk -kwΙZR1"P_:FekN&(ɑ1lrs5x{駼ޔ- E E*qϜ=9B[G5OsHtzFwҨ iW3.,:"l9ˢ1<&+>D`uӶ">| $MP^~*Ԓ[!l84HjJXz"8z}Ik} p Z=\$ tZ$&x"QVlD`/1iG5Oۢ[*xL]*#$*jhlccѼ_k|mzPqƥc$"իtp'khCm$qGn"=qRͳoa6Θ*ɾ K%)T:ڬz'ި 7+M_xZ.bQUPty]>BunKe_M m2 zɿzF׷SoqۭP.F?ȉxiU$ʽ1{vC1™mW6B`Ԓlj^H\.q= ‚>BZBfqL* KdV;]PK!Jdrs/downrev.xmlDN0EH5HS$HV zy4G$;:n68eUF&2)Xn{y\ۉK:W>Gmc.[2Wv$:!fIr/ vZ驥Xsk~iފc9eWj~|hYU~ QVޥix]]K􁜂m)PK-!Zf[Content_Types].xmlPK-!1_a /_rels/.relsPK-!͇HKD*drs/shapexml.xmlPK-!Jdrs/downrev.xmlPK `}   fExample: Iron Works, Inc. 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C+P>评U%'*`eӈw%m;$xk}2*jsx J0xkG[)Vj<x u_`7ޖJS싗7q46!I%P9T@c d}vk;s.՗# ؕ AϹ8\{@jS$t?r3#ǔj_iVmvn댩컰R;1NͺUj`pjxps ŘNj,;5Yq%ژ>HW43+UvT[AnaAn^P[=яr"^k5 `́bpf 5u:$!e"}* _Wb G`@dაY +.^'DoPK!5drs/downrev.xmlDMO0DHkQV yhlI=rz;^ֲ"A\Yr`rYcoaXcPa&!W  ;nov8FmK-LJzn:G_PiyꔺA8-+ktub6V9/FS_PK-!Zf[Content_Types].xmlPK-!1_a /_rels/.relsPK-!P E*drs/shapexml.xmlPK-!5drs/downrev.xmlPK `}   fExample: Iron Works, Inc. E    x mOxaxa?Rectangle 3"u o 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!Ny'Idrs/shapexml.xmlZ[O8~_iRze Be4#7ql'k;iZC˱}|>ϋD9W:N倞~Se .%02J>\vuFPX~6Sc~)Of\"/JU jR\fP"jz]KX,Q6T6·vzN4{(1Z!0q3](vQ&T=ЃOjRÔPd[s .uPMy̠8 )_ hkڝFU¨`WH%jqi4vκJ֛zݪ|aHN hvݳSkzUf}m߀GFP3@(UO<({s8%o 3Mqfقj=g#*3&:2^I̍e}ɔ6oLeQMGSq'7Xe]ԛV"G=MYҳ |n "؝3JHe'Г$=ii +pv#rJs銌e"kW\h[t CVbԭK|Ѷ,E+l.\;ί[nx "BRfJ#] w^ )bLY Smʔ~û*GKP Pc IBv@<:%3}s4Ԕȅ(q!X+G IZE-0Jȅubg+XS6љ]Mƥk o((LFEXv1d0Jcep0!ˏd#V-*vl~#s}vC| ?y"Ǒ |F2]Zy_J,b4Xv90Kt_7Y_nc%>,K _:Oo'7l~^g -]ib76XD.Ȓ),cq 瓭q8c N}ݵ.$լ XEA6[$^9v+߆W{Z}?/'cc~+ltg[0˃^==ZNPr~߁kVǸn^Oqb?jWoJ~<@.: ]V^~^~Y^fNI%0/:D)`\WQNX#V-?L_^q PM|/-O1_-bcWxJ/+xឋÏ=(?W_O0*_.m L{Di:e;P;_B`J6lϿA,.ѵҺkʰhe BfSe&:pCH uK8 --R)fضTUVr3.391[&6-n+qΐKYA$S ziZ՛z꺤•@zNXj)֪b#+yu dYJqntMrݸ(2t[(&A8Ƈ3kXМu_ݪn|ߴވlWiS&& asmA^pIAut5@:E-2~r4?;ƃ̣g LIh,o!_͎"j.70nKߗ fxE7臸ec.2]ib)BkjX̳g%.eRًz+%z*qM*B n Tެzm?QҼƣ/÷F39?XV\d [?w7+> k- m The monthly production level of product 2 must be less than or equal to u : x2 < u However, the production level for product 2 cannot be negative: x2 > 0^ Q  N  B  fMKC <  zA??IN00483_Picture 4IN00483_  3y___PPT10Y+D=' = @B +"v<!qS u;m; ;(    C Y/Gf21?Rectangle 2" 0  N   !    x Yxaxa?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!)yudrs/shapexml.xmlTMo6 x-BEbm#0,z\$Қ"Ur}$Nb@5Ù7o>>ɎZ> 9*E)򴺚qfV"gaݵm+)kh~ҭPЕ4p5AkʑCFZ\/Ǎauh>LQ[^ v]|B`W;L? R!jK qŽ1TX =byR>'x~? Sr*MDwd>DsvNx:yc9Գx~9 F\ĝtq3Fn48yvd[p2CpL&7ij5K-CHepy%V6>XtL˼ҁGk")Hw"۹3 }Kp 5d!m #(*0A$ Q>Q{q^Z=C݇GY_-xTF( mMؑ|lvo,D폮W}îfRS 6v/q4.G`(զll7/oJf]S7[IE)EV4R¯RS0ʷ'>)?e" WϷѺ mR ~Jr"=1&[ߝ 'guyB;PK!drs/downrev.xmlDMK0E!Sm4PK-!Zf[Content_Types].xmlPK-!1_a /_rels/.relsPK-!)yu*drs/shapexml.xmlPK-!drs/downrev.xmlPK `   fExample: Iron Works, Inc. E    x@Yxaxa?Rectangle 4" ð 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!G|drs/shapexml.xml][o8~_iUBiP騭ݕ @ڦنpVA9y'96M(3_&dE7GieēLv,t?KȘUp$Rd(d*I5Jh! 7(M*Jc\+;>w4Z=`^bV*z Y83`[ W`2[a*U]0T*{ iq+9ZX39gs^k֛g_kY;_,ݜyk:PBq[`04H x*lG-15,DQVk!Q?6N|7AU2+LǶQ<ߏ_pq2'Łj+_ 7 pqz~ 8rIDN,q2D?^,4VvVsɕ6\>psuG<ƒzKz4Nm(qKѻ\ݶp0R #XFvp4!D> X$} mo#RcA&ͥk ,ghb"ՙxd'<аGn vl-׸`*XԸ.QoVڟ\'P oՒ@C0Jb9PO/_'7!?0Ku؄ ĩ~q_bΑہy=~Q3^ O8= v .1tb%=]}V`ʬ6 tFܬdIE㒖@ʲ{be0G\'-ĉwIstđtP~\3T:wRVUr;/"Jdr }tHyAk QȮD 7WEĉ! yy1#bLc;O W\N/Y@΂1rwxYCGh!BvR5bF嘁 Q O/iroSH`cHLD/d⿾\y}yXЙN )!:%Nsxoz5E2:Cz͜^3_|~W)]Й|E+"_^u@²@sYsE{Y.i _Ѐ|E+*I\ўjX‡@g=ܦ??VQk0+B#4I3:0q,˱d$Kw { "tߝtK Y&v2zU-:8 ZCB%(Xz7LqF%&#JJ ! ˜N&uMFtvϦ {6<厼2t;osQbot؃Kuڼ}T&x%jxJIt1y3~9˦y5d\$'FYRHǫ%tL {DuAtRop8 ~9LiB ~dXAI cP-P@gAd# ҋxΚLɽP #tj.\H04\{T>4~JPJ~/ywQ#(KfǛ U/֬XQŒ*3O f9ЄXNfT{b};ڶ]6wr(7a\V`Q퉂.jv3O'V_kŗѥYM`_v \PpF5+ vm6PK!HdN4drs/downrev.xmlDQK0Co.uˆ*(>_ܔ$oAn48e,A\[q[YcoLa` :>CmC&[2gv :!FHᦗ$y;-R]L}N9/FSPK-!Zf[Content_Types].xmlPK-!1_a /_rels/.relsPK-!G|*drs/shapexml.xmlPK-!HdN4 drs/downrev.xmlPK @  MMathematical Model Summary Max p1x1 + p2x2 s.t. a1x1 + a2x2 < b x1 > m x2 < u x2 > 0  f 0//    C  YG%\Hiv^21?AutoShape 5#" zPK!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![ x drs/shapexml.xmlVKo6 x-~$vlcˆK5E$G~}gE[ĽH7o~+(cЖB.b E`s0Ϊܫ ?j*6\XZT ძų"e*(!ҴvUUͼyo:AgIaD: *%z%@.[ 0-znv&޻JA0 dŰ-LQD/ۯ.GX+ _;^1?H#]w2贻JH!~QlTVK]uƸ:㰹-&HQӳ#zn{tOy.>'FJO1FYxq%6mb^Q9,k\/,6:CYg$ W߽撅/ qT Nc0m*#"T,~Uk^Ȇϧ'tQca?8Kzt$-DX`1xH{I%Hg}^s̙b<]pBX'+Rqpdn+&`mq~* ~l>RKI*ߊ`b4-Gq0KuM6:2xaMjrxan[tVS( 7l>(DΪ_J{ M,LZ Q7?*^,C:gE⽃G?PK!eNdrs/downrev.xmlDN1E&CLhA)DLƍl=o۸ͽ97g]+bYh@4\kؽ?f bB6z& 'Z-0:lS-2clJ]!e,-9Ca10xM e`|X}đ I`߽N4aG2$RKIZ)4(M9`ctB{m:f@`3n|O,ܗr޾jxR0T ,0@}WBLǬ5vPK!c z( drs/shapexml.xmlVKo6 x-~vcwaYX%"U#3Cqrh 7oӾ2b|f++]eV`U< ?zjmי\X;UძwDNUP6BDGQm=E=$_s/t]$ NkN☹|Z0#` ; aJMw"`B[aZ^,wbŨ`/}u)*R3o],!?BXI;B: i>/]JLTRuP`k"YoU{O2X-qu} s[A0(J(؃b4»knLv9U8DcrhP݌U\B׃Qf"vU0Nf0Ui c'sg`  ;msQ ElJ,BF䦡A|mmȳWh۴8dP:'|h Kmp%״p5cIu>cvި:o5T^xd0xM e`|X}đ I`߽N4aG2$RKIZ)4(M9`ctB{m:f@`3n|O,ܗr޾jxR0T ,0@}WBLǬ5vPK!U=#n& drs/shapexml.xmlVKo6 x-~; ۃ0,z,FeqM*I_Pvź:H#q8>~:Vu>9:3ۄ{^8sthp|fYyz빬 c+j '*^R{4zm}ݯ-yg!:PEͦZzq v?&p`)aMA R*um5OK걄);Xmgjr,H۔ԻUTWB.x:@iU0l0̔pZG>^duA/{i$|2@ 83M:9D$>wv^ʱ+$<丫VI/,SBnVa?Së8C_L DHσTNDQc D։ӬG)7b|*4\ *\HP{7 uG X[rQRhÎX /b_yIK0p6JjBHLF\S@yx0f˿ଖ>+PI'~ԉTUUF@duVzg]о؈a5fyPK!8drs/downrev.xmlDAN0EH5HluRBUThxDvjIzZ,`9[o'ձk#`+#[] ?G-3\v3[c&ͨ J_.C}ƹR' }8mͥ1UQ [魡ꧼ(1M|/X%st! p?^ysq(/!jƟޯ߶:OV@ PK-!Zf[Content_Types].xmlPK-!1_a /_rels/.relsPK-!U=#n& *drs/shapexml.xmlPK-!8Xdrs/downrev.xmlPK`  B:2___PPT9  m Constraints  G    zA??IN00483_Picture 9IN00483_?0 3y___PPT10Y+D=' = @B +""tS  (  !    x @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!z3yudrs/shapexml.xmlTMo8/H'Eb aI"$}$Uah}g437dalUG V~^]M9TAR+?۹m k烁+ѐ[`+iA5AkʑCAC \i1^ʟ"(jV!km 2|)A*#Ҳ»R * jU[1wjN < gxvFo XwY\%O܁hN NXtCMC&2v :!FWKpp$[ Pu,OF9%Ӝ?nuJ]_MO M9-+/* һLJhsx] 􁜂xPK-!Zf[Content_Types].xmlPK-!1_a /_rels/.relsPK-!z3yu*drs/shapexml.xmlPK-!drs/downrev.xmlPK `   fExample: Iron Works, Inc. E     xYxaxa?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!D .drs/shapexml.xmlYo6~ąRmP}2 lB}N)=Lm'#y};I. ŖҺ}p&uj\uΙBgB-rJ ʄϽ/K)Bx4]ZCQN]\K,rd)[,˳ώ8Ӣ{ˆ옷k8EI6Fc2+L_-\!fmZ8"s `೭-u +'&[sJxOϺz^/:k̼ZǸc8{^?+a%gw g9Nl誸1*DF&so z48G*LGjt=)QS(Vy2ϕ(l)]!-k9ݗEAnDƋ>/ ztR(H4sEmFfR66=EWpߊ"Wwosa]ZdmN}^Lb~rV `."/yMԭocp:F`8D\ýp!0Sqxl!-p|J5WKQEKI,aldgW%EXTJb=Ψ{  V~x܎x{J8 6*X0e_F tSOs™0+h,NE8z=+ziQ[w=yDMJ2Ș^p`ՠ ܳM[}ky#*@`k.g;"4]֭U0I=[3Iw.}]DP9ǣ'IՕ;2CPK!`drs/downrev.xmlDMK@Eaxwv~NUQ5kͼ 36]r/rVtHηqeu˵Ϗ;ˤ`$ 3mOӱ*hB3)}ՐA?=q 1Zj7I4r|h`I9e-!oJ]M;?N__yF=k<w9@NAPK-!Zf[Content_Types].xmlPK-!1_a /_rels/.relsPK-!D .*drs/shapexml.xmlPK-!`drs/downrev.xmlPK `  Question: Suppose b = 2000, a1 = 2, a2 = 3, m = 60, u = 720, p1 = 100, p2 = 200. Rewrite the model with these specific values for the uncontrollable inputs.   f  U   zA??IN00483_Picture 4IN00483_[ 3y___PPT10Y+D=' = @B +"2#yS 1)@(    C Y/Gf21?Rectangle 2" `@P N      xZ0e0e?Rectangle 3"ìPK!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!9Bdrs/shapexml.xmlUKo8/@HnĀw0JbDQjdIʱRRbՁ!÷b|ct/ߏ9Zѻ~\]p钔2'Ż?n[e6uv>yQ˖{c[e\Kۍ^@Z5W0ݸHƱrƙnR  r !{?C%2|/T.lMe 9TK*}FKAǨl"%98f|:MgWדAi{ {S4/ (zV-R{:rNr:ECb'`KqviTՌ8e}aZKas+h:_YI $5Y!{.hD7Ax]+*Ԓ[Al84D'*eHE<`woetKJX-LHG[(VjyL^V?˾A]~!7RcWr4^$MsM d]۴kӃ3.+ oDEk5{6y8K!/ R=qRͳ;oe6Θ*Ѿ K%)ىq*OmVR}7ި 7+M_xZ.bUPty]>BunKe?ܠMW6  *M^mz[T]~S㥵V(ٝ g ^Qۨ ? Q25}*3?ۯb4`\aM"8A&N4Kv0xM e`|X}đ I`߽N4aG2$RKIZ)4(M9`ctB{m:f@`3n|O,ܗr޾jxR0T ,0@}WBLǬ5vPK!Wi]drs/shapexml.xml\]O8}_iRJaHT2G&Nmdm~ivTP{o|nξγ̸TI.zI a%bow(D\>rEYSAczE@'ZFC1%/@Yˌi\q\q@Yh5FAѕ 4gl IlA2 {C1N9iFU5aSU ^"L$f&S9Ę ) g21n U@T#K1!V5.bYw%U*bx8.4JeQ9|Zx_^ccӿc&F*JDk%)ܩ{08rnqp49c=v +[3Y%B6\|"$#(QDlL!ȇ)CsU-%LN'4B9hn2c{2}rf1r:IS7wGiVr8`M\! ^x {mI"[{I5>}xLl.K.$?{_ۗowWb_;={jm?ٻ ;E-!ٝgw'|"q5vH==|C=5y~p|kk1cܞz"艠_~DWk0W^G%>j@S({#4{gYȒ&_IQ@wg;Qr %@쪼<,h#G6 םvTu͙;z"/;k`oZ5>93D`~AOI1aaɺkE T jUPFߖ炾cHL,]AVފ5j2(Ys>A~2,n)m[B8+ZqZ'9sRQҴU d>~;ޛu>0} m<V-S :#L!V*CAMeыj1K* V7u5C | @PWс#eDG%z|uO2jfSRkocb( bQE^2ZI4,°)-1/iy19/$9^8n똺ן{ķ"7l=O-"eww¿Ϛ{h!81WxM6q a(RI[`FqcQtG u8/\'pj5CZwO`frjJܙ/PK!J drs/downrev.xmlDN1EMfH|VY),X?`݅mi+,o>޹ssf޴L>4Jx `d+%| XhΒ+Xw3̕Q!G u]yj2F#c^sc!&`cB5UM9+=mqڇ)X>?"[ӭC+ DKHdLPK-!Zf[Content_Types].xmlPK-!1_a /_rels/.relsPK-!Wi]*drs/shapexml.xmlPK-!J Y drs/downrev.xmlPK`  C  ,Answer: Substituting, the model is: Max 100x1 + 200x2 s.t. 2x1 + 3x2 < 2000 x1 > 60 x2 < 720 x2 > 0x % f)?>  -  zA??IN00483_Picture 5IN00483_0 3y___PPT10Y+D=' = @B +"^$|S ]U`=(     xZxaxa?Rectangle 2"íPK!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!iA9Edrs/shapexml.xmlTn6?Y+7Q5E$>RJCQtu g͛|;J[s~!LjaVsi}5)e˟ o_؜7!dE#;wql~bR pԩ4n&/>v$[*yvsÙnwR l'`Bcc r !k4;Fiw<7*$F1*۰p7AI򦼼}2*ACZ՜86=,.1|x:Iβ(!y hʤ@ǍKݴ(p ~}%= u6)m$# @$ڣV,^lEà/i![QI>V kDV^O< ފHRYƃ}U:x[+N ز/^5x.rmM$V'tS}m[qإ3NJIJ86VÉ7aK`3#j,;5Yq%ژ>HW43+UvT9 Yy۠ݦaAn^P[=яr"^k5 `́bpf 5u:$!e"}* _Wb G`@dაY +.^'DoPK! ^=Qdrs/downrev.xmlDMO0DHkQ(ԭJ@. %KGudM8q47zlq%; ֫qmuǍCdeRftB#"} \J_dЯHuCfIJLJG:TQ`.~/[q.?~}J'?ΪZ_*,Kuv.r _ ?PK-!Zf[Content_Types].xmlPK-!1_a /_rels/.relsPK-!iA9E*drs/shapexml.xmlPK-! ^=Qdrs/downrev.xmlPK `}   fExample: Iron Works, Inc. E f   xZxaxa?Rectangle 3" Ô 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!e_,,drs/shapexml.xmlY_o"7`ABNIPBNx27l[KH>}c/J\c:Wl%ˌOmΤN<#hBυ2ZtůCW0k7,F|}1l\pL!5`ڇVa rV.2/0^MVrXG|0hO9"Dzw2Jު"c,]Ō7̭x;|0m~kV֚DžsGX*R,*̟8_xs=vz]D/ Ss14iʰt}oÎO`{F\{>85F=8CENbWI6X&ZJyXgߥ3ځ5:nA6d e~mT fqYl^{@~EB$Ka_`tsk QȀ VcJ^ph?#ߨ`M(ZA,'v<'p?r Z@?`Wez/fg%b#c}eA˩2̄#!u E jRDe+1e,qLa΀4v  KSƶlj3 -ΖO(*, iJ*{.YyM1ih_+)<ħ&S* GQٜìVz_4HP јK;]LN 4p;N0@ѓ W%;Tygr!Kj2o>R>Q==@*m`Q&!:0}BE?Hy`7u,N<֡SDP*'NxVU4.A-F?hcE"-p,/}ʼ,($l94>?`)xpo 7P76:vl1YKh-l{h ys^u]GʁjPNT߯TBQY6%IsKfCms޵]?vso{k:c6uTn0 ( Q0ihlgd2ҤJ N(ҎH;`U?ǎ_pAɣx]JjA6 kLEL SHFͳTjO?+(Y"])>AeG5wmI>;|h{q&:3vF."1i(vs}ܸ t.c#C\Pd1@c%m/ZHzj*O6TӜq9{UvU<)icE YK;S`5$dLAn~PK-!Zf[Content_Types].xmlPK-!1_a /_rels/.relsPK-!e_,,*drs/shapexml.xmlPK-!bKdrs/downrev.xmlPK  Q  Question: The optimal solution to the current model is x1 = 60 and x2 = 626 2/3. If the product were engines, explain why this is not a true optimal solution for the "real-life" problem. Answer: One cannot produce and sell 2/3 of an engine. Thus the problem is further restricted by the fact that both x1 and x2 must be integers. 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    tOn-screen Show (4:3)um88 A GaramondArial Wingdings Book AntiquaMonotype Sorts Arial NarrowTimes New RomanStream 1_Stream IntroductionSlide 2$Problem Solving and Decision MakingSlide 4Slide 5Slide 6*Quantitative Analysis and Decision MakingQuantitative AnalysisModel DevelopmentAdvantages of ModelsMathematical Models Slide 12&Transforming Model Inputs into OutputExample: Project SchedulingExample: Project SchedulingExample: Project SchedulingExample: Project SchedulingData PreparationModel SolutionModel SolutionModel Solution Model Testing and ValidationReport GenerationImplementation and Follow-UpExample: Austin Auto AuctionExample: Austin Auto AuctionExample: Austin Auto AuctionExample: Austin Auto AuctionExample: Austin Auto AuctionExample: Iron Works, Inc.Example: Iron Works, Inc.Example: Iron Works, Inc.Example: Iron Works, Inc.Example: Iron Works, Inc.Example: Iron Works, Inc.Example: Iron Works, Inc.Example: Iron Works, Inc.Example: Iron Works, Inc.&Example: Ponderosa 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Slide 47"The Management Scientist Software Slide 49&Example: Ponderosa Development Corp.&Example: Ponderosa Development Corp.&Example: Ponderosa Development Corp.&Example: Ponderosa Development Corp.&Example: Ponderosa Development Corp.&Example: Ponderosa Development Corp.&Example: Ponderosa Development Corp.  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