ࡱ> % -bjbj%% GG}'0l@@@@<<<PR$R$R$8$,$P<%%"%%%-j=.$a.$‹ J-<u.,0-u.u.!1@@%%@!1!1!1u.@&%<%!1u.!1 !1+7ef<i%% Ƃ9g2PR$Q/*FiV0/:,{0,i!1PP@@@@ISyE 3104: Introduction to Supply Chain Modeling: Manufacturing and Warehousing Instructor : Spyros Reveliotis Spring 2006 Solutions for Homework #3 Problem set: A. Answer the following questions: (Pg 549 Question 6) Describe the differences among product, process, and group technology layouts. Describe the circumstances in which each type of layout is appropriate. Product Layout: Departments are placed to conform with the flow of materials required to produce a product or group of similar products. Process Layout: Similar processes (machines) are grouped together. Group Layout: Parts are grouped to form product families and individual areas are laid out to conform to the flow for a product group. For high volume standardized parts, a product layout is probably best. Job shops that produce a wide variety of low volume parts would be best served by a process layout. A group layout would probably be the most appropriate for several high volume parts. For each situation listed below, recommend the type of layout, among the four discussed in class and listed below, that would be most suitable for an effective operation. Explain briefly the reason for each choice. Type A Fixed location layout Type B Product layout otherwise known as flow line Type C Product family layout otherwise known as cellular or group layout Type D Process layout otherwise known as functional layout or job shop General Electric (GE) dishwasher manufacturing facility. GE is the second largest manufacturer in the U.S. of this type of appliance. B Second largest means it has high volume production, and dishwashers use standardized parts. A large business center that serves many different customers in a major city, such as a Kinkos Center, with fast and slow copy machines, graphic arts equipment, binding machines for report assembly, computers for word processing, etc. D Kinkos customers usually route themselves through various equipments in the facility, so a process layout is appropriate. A large automobile dealer repair/maintenance facility, with services ranging from minor diagnostics and repairs to engine/transmission work to body repair. D Their customers can have a high variety of service needs. The volume is regarded as low because a unique process is set up for almost every car and is not repeated in another car. An electronics appliance repair shop that handles a wide variety of products, such as televisions, video recorders, stereos, short-wave radios, microwave ovens, burglar alarms, etc. C Appliances can be grouped into product families according to their types (one group for televisions, another group for stereos, etc), and there will be designated areas for each product family. Manufacturing a luxury cruise boat of a capacity 100,000 tons (this is more than the Titanic weighed). A The heavy weight mandates a fixed location for the boat. Manufacturing aluminum ladders that range from 12 to 24 ft. long that sell in the range of $200-500 each through large discount stores and through catalog retailers. B Ladders are rather standardized with the only variety being the length. Since there is very low variety, a product layout would be appropriate. If there is substantial variety among them with respect to the required processing and the applied material handling, then a group layout might be more appropriate. A large sporting/recreational facility that contains tennis, squash, racquetball, diving pool, lap pool, sauna, basketball court, running track, exercise room, weight training room, fitness diagnostic room, locker rooms for men and women, bathrooms, shower rooms, offices. D In a sporting/recreational facility, users will route themselves through the facility in the sense that they walk from one area to the next according to their needs. No standardized flow or grouping is necessary. A mail service company that prepares mass mailings for customers. Services may include: artwork, printing, printing of items, printing of envelopes, insertion of items into envelopes, sorting of envelopes by postal (zip) code, imprinting of postage meter imprint. Not all customers need all of these services. C or D It is a high volume, high variety activity. The high variety requires different processing for different types of mails. On the other hand, the high volume might justify the dedication of different cells to different types of mail, i.e., a group layout. B. Solve the following problems: Pg. 547 Problem 2 The following tables show the distances between the department centroids. The table on the left shows the Euclidean distances (i.e. the direct distance between the two points), while the table of the right shows the path lengths along the arrows in the figure. The latter is a more appropriate measure because it is the actual distance traveled by the material in the material handling system indicated by the figure. Note that the Euclidean distances are symmetric, while the distances based on the paths in the material handling system are asymmetric.  Calculation of distances in the second table: Adjacent departments connected by a direct path: AB: = 45 AD: (552 + 702)1/2 = 89.02 BC: 25 + 20 = 45 CD: 50 + 15 = 65 DE: 65 + 15 = 80 EA: 55 + 10 = 65 Departments that have at least one department between them: AC: AB + BC = 45 + 45 = 90 AE: AD + DE = 89 + 80 = 169 BD: BC + CD = 45 + 65 = 110 BE: BD + DE = 110 + 80 = 190 BA: BE + EA = 190 + 65 = 255 CE: CD + DE = 65 + 80 = 145 CA: CE + EA = 145 + 65 = 210 CB: CA + AB = 210 + 45 = 255 DA: DE + EA = 80 + 65 = 145 DB: DA + AB = 145 + 45 = 190 DC: DB + BC = 190 + 45 = 235 EB: EA + AB = 65 + 45 = 110 EC: EB + BC = 110 + 45 = 155 ED: EA + AD = 65 + 89 = 154 Pg. 548 Problem 3 Number of trips requiredProducts(Forecasted Prod./50)1421838413 Results in a matrix: ToABCDEA121318B12FromC178D35ECost of material handling between departments = distance * # of trips * cost  The total cost under the current layout is $17,835 per week. According to the matrix in part (a), the traffic intensity can be categorized into 4 levels: 35, 17-18, 12-13, and 8. These four levels receive ratings of A, E, I and O, respectively, which are shown in the matrix below. The blank cells can be regarded as having ratings of a U.  If the areas that will stage the various departments can be physically relocated, then, it might advantageous to try to bring activity D closer to the center of the facility, since there is a large volume of traffic between this facility and the other departments, in particular, A, C and E. However, if the departments are already constructed and they cannot be moved, then a layout change can be to move the activities from their current location to another location. Noticing the proximity requirements in part (c) and the corresponding number of trips stated in part (a), one might be tempted to consider the following alternative:   However, the evaluation of the material handling cost for this new layout, provided above, indicates that it fails to improve the cost value resulting from the original layout, and therefore, it is not a viable alternative. In fact, it seems that, under the assumption that the physical locations available to accommodate the various departments and the interconnecting material handling equipment will not change, the original layout is a very good one. Pg. 549 Problem 5 To come up with a suitable layout, we first consider the locations of departments that are associated with the strongest ratings (As and X). For example, the department for cooking burgers and the one for fries are put on the opposite sides of the area. Drink dispensers are close to the drive-up window and not far from the counter. The desirability of closeness for other departments is accommodated next. After the layout is completed, a review is needed to make sure the strong ratings are observed. If not, a better alternative should be sought after by trial and error. A suggested layout is as follows:  The accompanying table lists the sequence of machine types required for nine part types produced by a manufacturing facility:  Set up a part-machine processing indicator matrix for the data in the table.  Determine machine groups and part families using the Row and Column Masking clustering algorithm presented in class;  The product families identified are {1, 2, 5, 8} and {3, 4, 6, 7, 9}. the Similarity Coefficient approach, with the clustering threshold set to 0.5.  The machine groups identified are {M2, M3, M5} and {M1, M4, M6}. C. Extra Credit Let yi be the units of technology i to be leased, xij be the capacity of technology i dedicated to producing the product family j (in machine-years). Note that xij can be fractional. MP formulation: Objective min 125000 y1 + 75000 y2 Subject to 50000 x11 + 0 x21 e" 100000 & & .. (1) 25000 x12 + 45000 x22 e" 100000 & & .. (2) 30000 x13 + 45000 x23 e" 100000 & & .. (3) x11 + x12 + x13 d" y1 & & .. (4) x21 + x22 + x23 d" y2 & & .. (5) y1, y2 integers & & .. (6) xij e" 0, for i = 1, 2, j = 1, 2, 3 & & .. (7) Example of using the Excel Solver to find the optimal solution: The objective is set to minimize the total cost, which is the sum of products of the leasing cost and the units to be leased for each technology. The decision variables (changing cells) are xij and yi. There are four sets of constraints. Non-negativity of technology dedicated to each product family.(Constraint 7) For each technology, the capacity dedicated to each product family is less than or equal to the units leased. (Constraints 4, 5) Integrality of leasing quantity. (Constraint 6) For each product, the dedicated capacity is adequate to meet its demand. (Constraints 1 to 3) The optimal solution is found to be leasing 2 units of technology 1, and 5 units of technology 2. The screenshots and answer report are as follow:         ISYE 3104 Spring 2006 Homework 3 Solution PAGE  PAGE 6  EMBED Excel.Sheet.8  wxx  o [ x 0  U5HI#Z[bGIMNORpžŵžŵžŵžŵžCJPJ^JaJ CJ^JaJCJPJ^JaJH*jCJUmHnHtH u 56\ 56\]5\5\^JaJ^J 5\^JG3Qp|}xD$`a$$8^8a$$ & Fa$$ & F ^`a$$a$$a$2---?  n o [ x 0 1 TU56I"#$8^8a$$ & F 88^8`a$#[bc-DM [$\$^h-DM [$\$^h & F-DM [$\$$a$8^8 & F 88^8`4@\n4Qn-DM [$\$^6Sop $$Ifa$ & F 88-DM [$\$^8 & F-DM [$\$-DM [$\$-DM [$\$^ JV$$If08##X 62 22 24aG $$Ifa$V$$If08''X 62 22 24aG$-DM [$\$a$ $$Ifa$V$$If08##X 62 22 24aG     !"#$%&*+,-./01235689:;<=>?@ABCDEGHIJKLMNOPQRCJPJ^JaJ CJ^JaJCJPJ^JaJ[ $$Ifa$$8-DM [$\$^8a$8$$If֞Qq 1 { '0''@'@'@'J'Jt 62 22 22 22 22 22 22 24a` $$Ifa$H$$If֞Qq 1 { #######t 62 22 22 22 22 22 22 24a`   $$Ifa$ <$$If֞Qq 1 { #######t 62 22 22 22 22 22 22 24 / a`!#% $$Ifa$%& P$$If֞Qq 1 { #######t 62 22 22 22 22 22 22 24 / a`&+-/1369 $$Ifa$9: <$$If֞Qq 1 { #######t 62 22 22 22 22 22 22 24 / a`:;=?ACEH $$Ifa$HI 8$$If֞Qq 1 { #######t 62 22 22 22 22 22 22 24 / a`IJLNPRTV $$Ifa$RSTUVWi!{!###b$c$d$$$$$3%4%5%7%<%%%%%%&1&2&8&:&f&h&&&&'''!'+','-'.'6':'G'̿j <PJU^JaJj<PJU^JaJj<PJU^JaJH*PJ^JaJ PJ^JaJ 5\^J^J jU5\jCJUmHnHtH uCJPJ^JaJCJPJ^JaJ CJ^JaJ8VW $$If֞Qq 1 { #######t 62 22 22 22 22 22 22 24 / a`W  & F 88-DM [$\$^8-DM [$\$8-DM [$\$^8 & F 88x-DM [$\$^8 [./8-DM [$\$^8 8-DM [$\$^` & F 88-DM [$\$^8h!i!|!##-DM [$\$^ & F-DM [$\$-DM [$\$8-DM [$\$^8$8-DM [$\$^8a$###b$d$$$$$$$$$$$$$$3%5%^ & F Vh^h & F & F-DM [$\$-DM [$\$$-DM [$\$^a$5%6%7%8%9%:%;%<%=%>%?%%%%%%%%%%%%h-DM [$\$^h-DM [$\$-DM [$\$^ & F V^%& &!&"&2&3&&&&&'!'/'&(|(()^)))*@*A*$@ ^@ a$ $p^p`a$ $^`a$$`a$$a$^G'(4(<(N(V((((((((((()))))")()0)6)@)F)L)r)t)z)))))**++++ + + +.+/+{+|+++,,,- -!-$-%-&-,---.-/-0-1-𻮡jDx<PJU^JaJj?v<PJU^JaJjt<PJU^JaJ#jCJU\^JmHnHtH ujdLU\^Jjz U\^J\^J PJ^JaJH*PJ^JaJ?A** +/+|++-,,,- -"-#-$-&-'-(-)-*-+-,-.-2-4-5-7-$a$$a$$h^ha$$ & F a$$ & F a$1-2-3-5-6-8-9-;-<-?---------------------- j zUj G CJUVaJ0JmHnHu0J j0JU>* jU\^J7-8-:-;-=->-?----------------------h]h&`#$------------$a$ # 01h. A!"#$%@=(tLw5#O`fH8x[olE=(hH _=BQZZߊ!5-mM4ʇӈJ~0x0 o5DB4E(`X:Mow7Ѹvv{~gam^쿷+S`%-38gc Vm]I?O E4'ߩvn /չsD}1m ^5m氌5l#Nm6@Lfle,gPy yo$ƿ(Pvmŵ}9]|Ƒ? ZʡuoY˅lN-BAu@6zW]LG׹mدa!6Cpl7{DX{]w[[\9wۄ_Mڸ% Y=[~lX*(;D7 Ӓ]irnGُ"q7jzMPqoAlnXswAܙk˓9{sX s6*s6's6wlcZth〈ibڠ*6lܒ;H`ʱ!faɽir,=fāهr7>m%Wdr,="W}#5_bG3qM[*#x_UyUGJs«0|:}@fk0rj#W:zL`=z ̥"1_Zbʱv.v`\/٣QT\:@pIť>A`v)qǸ ^Aǽ %ަ;0#(H`F41ݜ!0w)\jC.E .a.!t0w;J`vv6*lC~F ~z8؆b'p0&Ӻ6{ָn<ָָnaQC.u\id%er,Zj#7K9]rɍ)_G. ܘr,NI܊{$S 51CTQBژLG wcb_@$\유6|)D.U\*\Œ\# jA=rcʱLكrf6ʥBR%/ |)D.U\{'uژ*P+gnOn]3xt!1RN 6ѾD?XcCn}ާE,F&bn7ƵSٿZw弎qu ǃ9|IH q͠Oؼ'K 2,+79~97W \*\Wxo>9 .Ia_5aras뻮>a\5V9EUmZ=5?hώg,-}q:=_5rMjDў-|o/}tLmn} p&'>r 'f .|e+Bi)d߃^m6ϮORUfaf+|&;N0N[A6a^-iK:bqje$u4W 7faIc{wEK̊O,q]LƩW{ۇSs}zjOЧ/OЧG}:,|:Od}musu_r ϶ORקUiS5GN~3 $Vm@=+^R1+ҍAPS\O&"8xŘKAǟٵߒŰ7BCk {;Ħ+`W :Xb^"{!3wQOЭc*C7Ʊ>2wS y((O$PL0UaB$IMHu[fccKD?@i}UaQE|&#{ehO f92Rc _31PPzݙn 4Nׯ/mkXP3As c~Kh~ZS@ LvRQ}?Lx#/mm],aY]Fwmmp/]6{lZ;s[<%(p~՘jmjn&3픗wffsJfn/ C!f- Gg egtc9zq`6a+*eסLݶ_=WnU`83eߣfa1qd6`[(9'{􌲞s,g==-V|Ƶ2+>i>Z|kDuUҺK,ֈ%Ʊ.R,K7|}ӁyZۍ ̈#zcfl"=(^f^- GFqm̸3fn e=o z:0/[zFnL`FI{hLݖM|ݪ\qf&5;Ťt?4{=qϚGq_Ms6l)7o&y;3`9RIs(wt|T[t[>>S2o=6 .6]9oLPq2B*U4}ۆ.o)iƺK34b?{~%76P; gz3Ybuub}o \ۛGț><.`!thnmD.и8 .BxڵOOAl #?'/KbK[ %LLL7dM ,rZ>iG_DNjy/f63o7V@0 9le' 'c+sCEg2<">8Ύ$x6'k%lr #V2|@~=\-_SlxY`|["pqMp689pTBO%u ?QL]V2Elo`"C-;cgOǙ}t}7MnsmMnd!~3PfW&l2Gd|1 yF&V+go='gsiI7UoqjoO9P`Uj9*Wt:xn5-c:Cһyoa躗 ǿweX๊jVTzdr*ϷUcfjY-ϰlV۰:luVǰzlVϰBB֐ֈ֘֬&5SQ-ZVeX[ՊD|irۤ=?r@=ݱ Sb/&"еxXKQk)Z,E?jiP\0+Ce)`%bc<Kt2M,:۝w =oޏ̛73|܅|V>!w@A]@ +ۍ8U_ zp |4vL_䧾 !X~mF>&Ϭ2l ڣH6l\8A\SSSg3ls )tCfy6:Lܗ1e<ϻ,CcGP kn/sḛX5ٴCאU#u܇;p w8k^\To>W4+kokêW懓*؉(z&Rt>Ӻ`tZa|>oRA=yM[a1n $GH 47J3 V^;A{ ۸m%SV%۸--*k=cmv n.i۸\#:f9Mh̩mpsSV ۘy=?h"+ٟlAzUEvxLcss-iG:{,:O >*#)CCB,lݎYR9 fΩGh߸iu%y EEșƾQoBoԡ&> !>` 6MM,6MM'&x_'e$I!?$mU2?ӂ-Re̽ަ{K sA9|oRq~bۮ3m[5izlUk;?tՠz=Jj6k.a.B-ej!k|uISDdc/06gj,ac՗_S;_f66GxŇXuM?8XRPU/R'j0EqRҸ=9\KH#Q@=c MaLg .]4CxZ]LTG{/"Ԧhj IKU?Dhbmb+X1ͦ}1 4}EIڤ}RyP9wٝ;{BMN9s9sή!hxky!\(DB"9!>K^WnCyjkfYWb*) 8=l;˃yF~l^O (4: U!tMݢM/ZQQ,v½  Igα ^ocyKurr)[zDƿ Dn3P.|}½.3w {J `OXEs~ oМ>ivk5ayr:$ܗoetqQ) PpfdY$a ?57ۼ}6mJGS=arf\_xv=0~#؎x }Rn\OLsq]ݸ&"mZjا_Jx]\Oa >2Se}$Q%sSk`:1ٖsO?F~Q &f8*.ۼϋ$Ņ_Rn~d#*~4k'h,Fm\;<q.bC byBz6!Hz>s{W̉/8O-'-umUN{A; P>dS7_yq9Wj"p@jVҟgkK10Ǿ85GEhX|ڋ䤙'Uft <\>ot6-FpXC2nm)D- AJu&nU1l!=mJ%}YD^җW:nu :nuĭ^֭pvMz$OnA[Ѕ[ J 0qt?EnQnQt? І܊]iq[M:Ig$n']qSčuqsR pmgn1[̅ n11R-\`/nM &nܶ5̭W3fz:n33΍u֐f]umG~n!q{3r+q +΍u*Z]q63~[ 7n;@}vSvӅ#n7}vNYC{*ݷ En nu.[ɭ[­H܂ qt?nana6*~r*ܢ.ܢ-&~re[onk돓6y|3=L ,x(=C <5A!#vhH3b֋0C=Pa|W b251aq<VTXAAxB]҇K[?ۮaQػB7 o> »z>L)vݨ(i6 1]K0A@(H ޻1K0>xQh7^fc"v]LAƬBc*2n XrJsDy^9 @ۜX-|x\?C]L3C-܏,\, @= 8OCfZ;:EdX,wI.Q x\olgc1!J|6C$P͟&' ( DZ 5U|@#"BZU@ժ%jb¥TU ۹o.g!(Q ˶0"!~Lg_xNCth0Ho`2!nFlnٰ}{hF m0`JtZǟmȶu}18p||sȎFzmW$~i߬mķ6'NjlQ-ڬpB}cn5~rۇ'ji{'-`?im<0ܪ11 g,}n 5R1bb/T(3|Iv}?%;ZYq_Gv8ƫOԊgaطP+"b|= ?*fP̒ıJ w) GQB{c7A9ĺ+i)|Rcl? q~9=p8w1>ǼY4^pMYe1Uj>>|\HPx$+y5Cx5ԃF5<=?;XӾ̚^MV!!VikWkIwaPclvtm+֬z f\Kl3 _͙/ݲ/G2w?/S"V c~/sNpy;NfKT[K$冫oea6ւ_;Z30Nzmmlz]km_t %i(QdYCh"9-%$UƲligk$~m oŲ]J~hwζϼ'۝UՍwR$'$_J~!:b|gY"WKO*򭽪e,*{(γ5ÿ:DiM [|bKkTXӖ.; MCY5 `MSm,z6X65 1`MSl*kf@i\kZ#Ovjcm,,Npvul/uMH_ҨVB‡-ŀ5K2#_'l7):[-{XT,G'l*l gĬ: f Hb6@1;@Mib6@1;Y:9fÔg41#ZrȳaM̆sY[y6L1p1]l]<٥<%Mb!&_?m|r` U,+t&cy=jm,,yXAQLhp<Xy'-MPk.!QLŲcTT8LDz(` U,"(419M1Eo~[,{,֛5H?\B"E-g}pV\m-n Y[+JWt?E=gA4OHyIZ{}ʄ8?rYuU'ɜh3ڼIÉ63Jc@mfN'6i8Dqbmfa:mĉMN{=KR,( v>rV令ԋOKykKyόz`Y1tt66XV`ctrB=ao-\oT,+ }^~|/p;,W.~^٫RV*5#9cYI=Wij|&OP6ϡhx0{I˯em:\gGΎk;c%kx:Z`:[iy:iE$TŲ~qxcY!<:dYu%:<$YO']n=])ʢ|!Ojx~1 OU|,+y,-P[Z_[|~/klAM䳊eQءw=ϡ;4u.whb^PQimU[:ihMO5B$i9lhQTn Ta?\wἛwE} gNJ޷6Vv4Z-Rl6x;gLnN_ul3M!,w_[qjM98{ ~FYO\&p7V}kCC~dfceǰ[^k{*'|{jcOXM 1+?5/}d猆뮭 vo3v,FHݴt$PNQ}tq@zQZp\e'ߣ|f$4Y'7QtgUkQl^qW 6 D+FPy7W`4&Kl>$|D΋Nq2gcUlԋLj<>]:O髼?Y^"cL80II~r(Ϣ9C~r!0Ϥ}([\y}byϐtj͸,r 3p WDhaB]nI| [yA?yC9s~ ɇQVB~nn4~ːU'p2go@M6?\hgђ]C#Vi݀^,Pb'l r齃ߪ;f 'b#62O>O}L9(8^sd{9:S~\6_&l DIjmR6Mtd-j5ƶXclD^a]IVD6M2De4llelcۥ!&RȒ[-aK`K0R%a paƦk-a`0R%y |yƶka+`+0e^Kll"F՜Ou\#ώs՛(=|H|Ϲ}vNL(#1J=]zfy }rΠd[){#mw(3E{f1d>ջm $2XUJݶeHdU0tJw(Pӡr+cI'G6)eS2G0PX]9xWkSAMJ[cmRj A`mf{PRjE0׀\? JK_K.hkDPR3l3yݒagfw~3;TƐ?t}@A+Soތ8Vk׼0mȷ$b?d1A !$TM: :?GMx=D\ s ,m},:2m҂*7zdb<\g# 'n}p27e ^~Ko{'q9PzwVi};?l' \ μR/X TG.$(I3y (_y=#cܛH~^466 ȊzVbs-@=Gz|UN(Hy]M\!x<-x%xZ]lUE Fm_PlMCmƒ--PJbU(FP +M$UbL 1V0F~& HLLL-DL g9<݂mPe|xU}K!|>_, =ԯX<>jPIzz~%QZ R QʩS{ {(}q1/ 0CM2:6лV'Yϛ 9x6ʞe MoM+@IM~|],Yu}~|zfg s~KCc/6|C}pU7SS^mbP;@xmU2`zqC)nZ} cոa|7>7&C40FmOC{cW/DD߹9lh&=B?+s^'-D_>2tyb&|E􋐭Sjz? FY~;=]DtOpTLe?ZFt3ѼS?9S}-sl6}8gۿՌI[lqTVG*TiP9dRro'C;$(wI\@>Uh"Z2Tӯ"jkJ 'j%ꡅ9jȻ7Ejr>xڥj5\/ \vjE¬b.j~V5*+*b6$w[nͥtwit2{/z9*5CC%io7E]Va|'_+3[[Em&gZqoV7ua2%oK#$Rbgջ[fZ2T%eJnrԄHƿ+IM n hIY R$kIoz7UqO_Pu9]uACD߄A$@=+̏#fCGt]n: mxYMlU>3AmM0R D&H mA4ve".5 ׺ƠDc ac=gyw=tϹ~o3^Ri]8Hm۵_a{^[pˬܾl-X^m\\^䲍 M#Y9S[KDGCd/Ha$b|Xцm,*o4HNecdðC vmp^#J8d~|ĪҬzv_IvP%v=VzKSvϭN>g|vay$cxtwgAFy~EIqZBO۩g7y\ߏa;x~x t/rJy*二?p*"Ќ(a{^/s>Fpz#v)O>p ]甭x J;V}&<>;G/[۽xlAI}+BK-(ka= ]( OI/Vx*R,i +۞O|ϊc3?3bǽgf 0 Wr9@aq3l§"xYxv搾,Ⱦ3δg1VmXô yu*k5Ӿ3\6;Gs$iڐXy:|=[yc=[n孥uQ_Tj2|_eM۟З/I}BGUZE*0}Q:vGGl:*1%[9I'.?VN^tRfx\6_&lKlIaj&u6QlmlڊmX6MtGpMiئB6Udl˝\lT&M֡a&.kkc-`&UY}غ5l!غZ/&A `AvBۨm4(cS6a6.(bbѰ̈́`alJ*\lV065DF9G&Bi?Lj.}x FbO\QFsѭuw ֙Ae(Wѕ^G`;UZsɿ{Rضw~^-}#9mz787 Vk.PRO^m_ϙUsfД=:gfo'O4|*X䉷f WŶZoo,oC^_ Wϥ/:gQZQ Rk{p_j_U {ZgA1}z|m0U0{tzU{23귣R|]0N$=)#˞1 Q3 rf;kzW39rުXzv[܏ݧa}ڞAw]8~3{w睿Cg TMMo?Vӟ͛MM(h:lMNVtA:2aK6M7;+)93c3<،l;k06#bl҃M`cYdbs`uul1mVD jhM G[уؖ#Ge Y`ҵjj8rDtcy"7%GYil]Prبݫ?GޱQA?ȻrZ'M M߱7'"7Dd\  C *ABD15058_"@@bZ >ěLfz5%KnZ >ěLfz5%PNG  IHDR [AsRGBPLTE3ff3< ( cmPPJCmp0712>1tRNS@f2IDATA s$#AL* ==pA4p|zyIENDB`Dd\  C *ABD15059_"@@bU=1M*| ߨ1n)=1M*| ߨPNG  IHDR a`PLTE!!!ZZZkkk> tRNSJO cmPPJCmp0712HsDIDATWmI lAb8E&Et`&KޣHCU(0&-ox~IENDB`Dd\  C *ABD15057_"@@bO9@[?Vy nO9@[?VyPNG  IHDRysRGBPLTEZZZEfP cmPPJCmp07128I tRNS ATIDAT Av0d4 U TCX*XSŸJFeπ t*hS u5CB>_IENDB`@DdJ >  C AbX@Q2䵩@?4@ n,@Q2䵩@?PNG  IHDR'̎JsRGB pHYsj?IDATx^;Ѡm_$0Dp$6d2?K Ech!ɦl,lQeZ==/^̙]]T:=535/ &SN-y /'/kICN:='}.>ƅ 6k:@ 8|RBߦ8 q݊o][3so:udF or/{G3v:3Sަ"G[MFNKtHMG/Y}zR:I.BH`@,@Ϲ8Rޗ}y[o{&e`tFիpǭz}H$(眯~@\΄T蚬G% 5!F|jK#wNlyj.KcS[(w0: 8; \>&>B X?z֭ya w}U:dw9 P4kA9@^z}@6 }-Rw鸝Ancǎݽ{wwLlt$N[o߾qFJG 4.(KRp=-"z[_.Cܿ 5pRl۽ɓ'xܹs޽sd޼yS>:|kGח.]mSi&rG1kDͷ4nUUrT= 3pdy2X!Gdy4e׭_}5=Г'ODq`pgNb +{ e=2no~ZlG/_t =fх ^refuf;[izG5&#cl< ۷o;Μ9e!Bi:ǃCU R%C\05+f Ǐw\sU҆vEqܹ#^C~[tР=~x4,jqF%jOM_I ~D[ِsoze{52u[p>}*yFd>{L%. dl(X7}K:?sE q̬G+}L pw ޵XZMČ޵2mQG֒߿=~$O>OuDOG i1˯.i'NH} #G&%Z:eϛA* m.YJ0=}R&Oy Bevi㮧2نhY8U LI6uԧ*|tM5.95Ggϊp%3壋/J3{&2Ga׼[[͸!kEwh 9ë7 Q}AMrLꆓՏBZ:r>^%#!KW/Udڣp^*EB,em )+r pȩ+L>3H, >Ljʼn\4Rq p@8-Zr` Z\p͕GdؚrRkCFG.b LEV%dCKZ`y0%!PB/HNSRz ^_rg씄첬BV6cݪ -XQ<m@0Nma8Rc{ }kF'@qc ?J,KKƅ POx:oT!ji@m'ڶ lDXBσ(C@hx%2a D (4 z%2Q , Urgt:'yV0@ k,A!@xe2@؄7P@n|^8=؞B/o}G9! {m"/zϯ 52" P2mE~sҁ%']$@VP'NxYJkI @v:xvY3իW/_իWm eAzmڵk3O0~xo޼y69 V ׵ex#GJ6ЯZ>=?^Z;eKxšCn޼W[Y ѧ:J@Ҭn}є6!:M*+eꨋևyfVz&0k:9SR.\=*ݻwCЎM}=ajx h @  m^5zi<#VM.C"kj;~Gf#i9kGd֪[dBQ"k\C@uߘFrڻf @/nߵ%Nq۷vQN;at@q^AWel 0 QȼwpKK>#+I14N!"ܸJᩋkO9*ʴg}s{˳%8SŤtaZ#SI6ULtiT}Up (S)>x"(atQvD 7]Bbճk1D x DZ?+zm/^,"r{ *uL``tiΉ \[{ [VjX̭]9ZҨSE2Ց"p t= _.>=^ U n7hMN2ap9K-Vs۳O?i-/-m O+5w寞ŻH/^uR0P@Ƚ*'Oe\<7nݪG8a]`r@[KNH$ 1aɁ z+filjčfPޣ"qF&vRiJO\rz%C ąWA R$ ]=&d]l1%š-#W; \ Ӭ׮N7 . o@f -  eS-/!_&赮d`W8(Q(x«*B ֺ`l[m[PMkHܵeu ŲjI1Jdf][ٵD@ ZP(KP~ZNˡRW;r]^7[hrٝC5 Phזm@F=_5+^uJ6bof3~Cەö/^mY[W2?uΤëSм*m26xj68͜)C^3zkF5 :WCs!K^bwjlO7ҹTTK#l#=۾l*HjPxj$F^uRc{tމ͢m@8:RdZ$˔]-]tRcZul537sjX5X+/V%uJ}bb^V \`Vi 0ʬUc{FBn+XvjlpgUkkkӛcV(Lk6@ #igДqPNOmE)Z(coL|m!-F${Ek@v^3PEƐL,= 崽ػ(SŠܫ]?ZBݽތ (JrWv⩬^elS::PgA`1«]3[T l^!` HPN&V7|p !yvTo(v $9ЛDZ  r^=P9Q$;:WNw.¬&to?K;m#`~_@bLHL9m/6{W/AD[xcJԣF`R%-!D BTk.{sk] ^ZuUrE~Wz6Y u}S[8w0: 8Nm5`̃rWbV.-@uUPZh @0:@+"+[q:v@{x O!Bz5Oid xC ƀ Yd}as0&Ƚnr@ t +s&`-D<@*j>_^$Y׭i}n;HgXVw< 6Tqo`<;sxZAv 2r-{ <N-h\Oͭ[l{̳},P%$@˟̔V}Nr=VphQ3ײ@vkr`.j05atj v`ZnQʄؘ=܎NշNH=3N6![Nx\ړ{M0#YlvQ`Qr ![Cls% ٩x4(ObX[_`:Cr~ZEVZ.K2aEm΄RQn+0ϹIjRTӡؙn`nlQe9Q2׽7 kPSFWŶN-Љ*o+d7޵@HHZ8DHmJC.@n+Jdw @-026l #@W?^K՝k*^׭i|$iٽ5 U3)t=^޾S[yCV<@ OxO`Tݙƅ P&Jl-ghTA`2> U@AI@V# m@  pj@ k ^@@J@ -x  ^ t *A- El $ WbqyVD%@4^K@ 6H̀J#EוV/ HrځjmV{Y؞B/o}G9! {m"WN[ ?ҍTdc^.]2F5 V Db毙gu޽ǏUc rMq]@/_a4@[q$D=yݻscǎ=\>'Oԝ򩼕n~ϯ'O^ܽ{7HT1kB P/ ]&D9ѝ;w$)/^~]o޼ygϞ}|˗/?|pUTFoQ!Q5\2l|P} O>}kTU$#h@\xM… rHb)_ S>2ѣG%jڄÌ"Iؐ3mFKIw@yU/t@+M9Μ9#+SݯyJi駟?~4:FFrL{7U,Q&! tQEB8rKeH)wt`dKe5W n"@zQ[5[^v#@9P3 .r}k!P?r lFf @ 5  = > QA/zd(ƫUbwM.Gl-߫ ;D\]BxscJwH> ]lek%\ 7v7EE8/%g-< &`B؇@OsLdvGѓ]l91W#a(mnb,y>:<[/b3~f@3s;1sףsr8WVUքd9z8:XS[bVbVOS7aGoQ"v(|UM0^˟2s@!1tz3.žT:F~eϙ9LːlL'ec{J4C : ԏ.m5:8Ù5(:x[ޖHj+3TKT~M(ϩRΰ9 ZEĮ2!kYmLgu9tk"!s~_RmoU㬵\b63V>DB@ޥE[("':xz]UV}f͗*KlT7;|{g8gA;]BUiX2QSLX0Ђ.'^"«d]'ڲfy%x]0+Jpw1 hkQFҼGBr8>Ul˦TJ0}+3FaˤF&^jkV3S(&k5`(4V6͈_EN[N;(/a.iQß|q L"p{tNO'bԍ7;l,}XH? \]%Bk Er]G,CKҧc!^:%6KyDxM}40z:EmԨg YfM k =BAm0e'mƂ:" wv폄Kq۷vߩ$"F%@xmֵ%0k ydt@x u0" P/:|LF9 D? j:C ,]+p)*Be e* ^b,؇2N-ڙLcX@9 Dלj26 = Xҵ6G/ 7V{g<@N(7qƃ:!@9]{Y`{ }kF'@qc @\9meRq+_Qr{T{qb6*/ݎ@t9mޭ4C/[{۰]6F]ÈfTL@L,UO/6yia=NiMKvv=SH2ھ@ i$^W@^0ӎkӉq~L;".{l{aӰMu«x a3b`B]-/!1xQ}WfHYDxKF?m:T`A ^B&Ҩd3-}:EN}Zd ezy=,yy2پIճ*6/}(63#I!nRҵ'7'U-isOA>vtƯ+;GLvIe5W39!fi&D^0+$s (=^#VW:R.!0z,ȭO϶:^+SN\O\v綗??אb/-m O+5~g[mv^{{ig/! {3 ?``uZy\։O+z{d%"luyu嵞mcrNi-MU8y%=q׼g00i X v#}jĚ&v & ąW;pIO`5zrE6ƅN7qdWJ*CUUIkRo=܀؞ _|:%['>5<)R=+SDi8e J,p:o_-b'  u7zAvSDiSVeن 8 q&j4PV9K%ހk^:B gD @ D6\2|(tٙ@%V6 g(mp@_6JJ{mUWo2zi7!+ vӟF ,)Me2AԖI@!@q)^/]ɽUK[eW^k~B x$Pύ^_V9Tm1ƅƌCZ/҄ʩR9m* n.ms)<-rrڑ+kymʼ/u()=5̅+ XV; Z ^kzCvJRI q q&j4PV9K%ހk^:B gD @ DvETuEl iW7#iOVgmvbjiۦ^+(w-rڿܘw-#K/ֽv8rZ.)];h;@"fs>kF/3 P I@'RW(Ռ#k36c%@l-5 #zqjk2e܊ExkKӽXXup;9eg沁鑫%崽#r F64T)nƖL63LrL P=k.@L2Vvnm*ݕ"Zk,VRehz^}888ribMjS[xZA@Ƚ6`̃ri:VuI5kE $ c3eQf:u[0w[PՅ"ϸu8"e<eL \W DfU]. OmCSCNt3݇ 4B;vŬASspޚ~ dūz/KFk)Y;D6NC L05 H†ϙZ+80nC4fn h >E[PU+8__3 :OZ@؍u7 Er}k!PN{7y,q 5lOov@Ƚ6`̃r+H(QiK.0. *7e? ;[] noxMI|;S϶6V*UoR25T}m ^W}bߔM0{}ٵ(sq-#sSrY{l{ݎמZw[RT,$9гUaσ9UwS^vafQ=^4ASMmݓ׽1Mv9m5:%[]gCfW"wc@(ʁF%@ #4$@xmJISN^m$4ێO+؎m~_+daI<G'kxxj6} ^:B0:,XH- F ?_NXMhE`*vVzeC*-j &mx;&uF }v5ۺawkFfT@ }(gS5jk56 X w=@就 ?>`' L1']}0baѐ[FX vA(h I`ի6]xnʒnjxS %Gxݚ]SygEK4I`\o FA NUSF&`٢Y44Q5|(ouky-;:]LGo) %LaatG=[GB6 !@! ^vA ;4&@x-=(KZ(h P/kCs@hn h^4,z  ?9CmYYhW{}*!ḽ^ڶwh~߆*i-pDzeV[˿UXGҰђR^ڿ/|_,OXrcC\䀨9!k(H .hwmʄ43KT%(JDe$s9#uqB 00Ueuǽ@4+df9xeѰյx*UטNU;`3L#vO}J\x]+:XyE]hmuV=[]s׽.;5a۵y [ڍU;6.^m,LX׽; Bq(fO`Kg9_W~3C`lbB!d"Y[LbX@&"^t{5@ij$qYPQD Y[ӷ 6ʁ:@K@ ԁZ!@9V<@a>?V~_֒t%N!)w;hy@.(7sJu!ǎ{y.#͸Ҕ׮];|4me;zfTL>~uJ3X&Pu[ܷێCsqhwsQ2۾U8q(Q:,% sUӑ.QҥKzHrMcyKt[vj3YbP[9#k:tH{<}(SPCUD7Y&25T7Gk*3j-v8*3cc]Ul[g{e:k&+xߙx$:۷od6%jѣGj7n/_my{EY +PmU3u2^SD۷oCU$"{T7Nt3P{5*ʼxkˌ]yg|UT=З{v2y8lj`id_)o_L bP"=zW.S@֌%~iX4rFlQ %f ϟW932*jtPc M5_Q{cjQe k Qͤ#Cv:~, .שغl:tH;J RgլjC1|CX/S U(A_֭vBcJx-rb,KCAir`׆ˀ/뵫a6X1UY.\P4_pK5#G21}*6zygH>}z;A15t-rb VreӦd mp;Pu7wݫ˳:'8=#b5\JGKC4v2v߯JJƢ^M%Rpv$KVx#{-6kUi+Ё_e#򈕚%=TeK۱7uIGʚ4q̙3z}ff[re|_T&ؚF%f dFts ]LVt\yE٢HuP#vtPZΖ^[ؾlwC'^֏Lܖ^Q6d8j+*S% NqϞC`vZ C ~`) NEɈ P/x{ד~s֭UD!dR `{ }k׼! {m"0^?rQ.ˡף4JعJw=?'[`"lܒ}I~j@i'L .}W 频9{+؏qWnBF^uaBHn f ut]v3:nJ!6Bi4uc,vXD9Vυu.)_@U3iwu{ypIJþnSN{yXvLIz}}r qCOc5 9io > PNq^8=؞B/o}G9! {m"QNsK.o1. Prv-mU! ,/@"Kr}#ȩ @`Ix-Aot P8xu֪,] (A+]Ҩ@|qYQ4 !0w+^$Ԁj$QNF@.s)ʸ"r.{@!85 PN5b Pi∭Ԩ,q lOov@Ƚ6`̃r(-*5+N:%ڵkǎıHɓ'uǻwD?y:8t&+ Q;; D;b͟vׯϝ;$>{͛72߿+-QŚ7Q`^xQ!y7̳gϾzJKV .ؓ͛/ِ&|gH1:>qe޽+R*~'"]o(5Pܹ8rÇᅲm#/y+q6 ]^ow@''*=U!nQ=P-?>ӣ͆G2u(sk8K)k[СC&h^zU\`8tIk^6|gpPUvuqYi۲ؔ y+eQuC+e[-?/xt8=JUD@'>=zT#Yu˗/e>/Ho$L^M¨zHhz,mdթC.2: tYn|:NE O>y%L|t=f @2Ӗ yIgɄG= , /p8Y(I*[2\(%kHSXhM ĕ^E'FF]=}ygi3߿Օ+W,?4"pa{KPKlT4M:m(Ui d(-MUdC:/'m}}WEV&7:^})W: 8Bb,anj/@2 Q;W4QXNԩSլ=7?%{Ksn(g&/=/ EM[¨4#Djfp~A:^-k+(\ۃ\wȆ0ӳ=`dK8qk )H)wt;h¬` m^ZTɭOi~^PGSq \R.Ʃ]:VY/pIIl/-r]#! ^gΈ@zL04s@(a0{!{m̡B`axLl)ơ |< ~m峔!J a0:2 dxLP@4V1 0yݫ/1[r}L !0yݫ(-:ԑt@@03E" ! 6!V`bIENDB`6(Dd{y>  C Ab'm& Aޜ'Lnx'm& AޜPNG  IHDR sRGB pHYs+' IDATx^]Y-YU/"!F0usF D xBxVBC+> ڀz4GhAZޮԪZjO;3UY{ ܹw x @{ ( w3coo/N|#Da.9=r}c׭ "@ɛ3݈]Nc9iSLOmo>N|Ϊ}pkU q͞;M\g,9s4צkaˊҋ_{=,b/M?!("@ `!ԓ#3=트ݐpO9<;7/ü‡^Cg7_&" 8O'Ԅf)w)=?W=W7:|cԜ|ͯ~¥|O{SI{=woyO^7_W?vrS.]}SwTK|j}Ƌ_yg|z㯼Ɨ՜|ï5/i0_ЎO(ү M\@`Yp*:yS_)ԌM.s7wYej?;~'L͙}̋3SKϿ O~͋3Ժ4^2SK榗旞e֔Z< BGi1P)35O &Dqf-O:NY8=egy2gp_z>޽5~ az4O\x꥗eQI'l>/2AlcKP͏ۓͯ62<%L'˒Tȓ_R{v,O@ј /q3_ˋyJ!3fJP LC,Þ8{F;p2WgKuz݄ltRrd 2pw۶IΤٺd 2LA'?&+İщVr .AǭhʧvRW3ixsd65,6:!ˆo|4IYR@xl @_  E @h@: 3# q@o:L-@l,ʉN6: z#pf7i`}ppЯ_|R@t+$>֙\5k}]|yᆽXM7-<'ea{|y'ۉfI&:}3o~T__&3]GgZy!3]^+㋗o=[fD`C4|3 'tn=Dg` L PT- tr@%9Vt 6<.\8hdj@%Ϻ,5MWzI'+,Z0#l'3lU)B( ҋҒ1-Lߤ3._{οLuP%IdJE)Hj Vku]܌5DLZȦ`"Ackԕeʞ5˗Oq>fV$M)9Qe>UnAB (eDIҔ2KIoկdjI੹4LrɜעPTv$ tZ8.Ip{?Olt ɴ]ޖ<42k2vj؆Lljd:N]\+d_ @d4>lԓL@ -@`( 鞎 ӡY|2B?]$əxIOW/ʶF@vV;Z5~ n23g9#lzqGn*-u(i" ɮ?!H Sv.rhϺ@@@Z%Z]mK=h:XuƛNZ7_O^$%; @lt!v dh7@ B m 8 )@ B@d6ȴP  * U*@h_3%X d*w5mR9P FB\7W1~h9dZDy hQI58]Oia S {U4y09X`=^o;⋗o=6H>R2524+QjPEl)5( [n93@"PJҞJTPҖS^jP^p(]ey\px]7Ȕdy)zEʸ׿9Ca{5!.5iH,޴‘EBj[nmhY.93s%w C L6VOјiqUϸ>ƻ!O4h׹5(Rd|(ӫAat3d FJp[րg;w;yt#bؾ/"$R_ѓA8@>@'!"~3RsY j4H%ҐjpdPnCRCT+h!nXjn>'̒3ĘήQtɏ042bl˕WjPJ2WZݤ;M~NkyWdIݤRX0ʐҙ t\LF6+Hނ/ýb%e+/._)kI !0fPW^% F^P(@`iL~tXߒŸ*ɐ,e7UoܓqdRh@ @lrl -MCLD3,yΫ DWMrPr9ZB=m"3~;{NO@ɖ!C'Sbdjg3l4cҳmʢ2呩y\q=M!J$44RisC5ǔ&.F-j@g,r]$$o:$8Xɗ9χ.d"Z\P d*=}7FE4R[d]ʓuI2FaU$+ 9X3r"`.: pd$)Lpz?! En7 :K,06veJ]Ն"@@sۙnl0G28B'#`a4JR˜Xk"̩:2' P랤3r Ԓ(KrR/ B!0ɘL-L[ @ Nô[ɔJd B@8 S @z,گ&T 0$t<ǩj-o952 G ê~LoJ3hIG@s_vG3 PkrZG#CA)6pDGt 7:!`*6MG'of+8AL5x%)5(Ū7]̢Aj fW=YN!R2UIqҖEaRD{?U*jlyCN5 °fk׮"2%{\RGzh15^n5 FMaHrehfF #@=>]v߻2!I<[a m)J@C!,aPf7$&t<(zl gyѾE#KlQl Oc99א)!ħ&'lq Sr("S&IN7ǔ2.J=ޔ0bEcFO@s\ELILj$rfZ4fw7E2| 4)JT*Kg\++^R "-MJH S"PDJJ1y 1V_j%kZIfL0U5ijB~)Et;.QJEZaʓbLfQ'<"A@v A҄hd'Ssqe+ju>;Ive3*dtO?^XW ( iY 2uQ+ A)G;JTid*5(ŪY4Qmi T_HS`Ҵ8{KW}sm\F>LwdxF&^aJ J* J@f3Mb4`v*U͗z̈I^UUPܽEZzX-0fZ Iq("S^Ĝ|ƒZ~$׊Tc"|oR3|KA LO.l]/+'%'zgR֓dj^IGNx䴻~kT$ 2iN#{:y"q+4* z\O' t3~Jɔ&xd5.d_H,gRB㕮Z2Y*"++/+ |2T]S2XJfj!fJ0X)j+L<XJTYb--35dקJ*[R2]Pp R&T 8f*}6*[ ?fYd.]N9b^(]O\xH-R0Qj(AH2ǡ%-ljf i("VJFزE&4 z 0./]% $㐤vq£eG(b!괮X>ICV>M*l+y'K[JJ!Ր]9)+0d}xx_|Af\i.inr̴L2&^Ҝ%c 2BaRP)7e޷XI"uLE3@H2a<$>5Vۯd;6fǖ(ѓq%r$| d:In֖AٮI!p[#!laKWIL1_?POO!0/揙0yGdK.Ud*j |:4!/LTYUYq O=K~XISiT> \'u]U653bJpw(nU,U*O%VQ̂2Y`$Tz3SmmJTidpk4hd4*XWjPyd֣7v#\]OL8\*BhMN)RùȀL1 tb>uw\+ol:(D O-j;$q-TYUX}7_' XUHbҌuI[%vJzUwFL)鈵r|cRݳd:; .b.x:L1C -" ftc] ֘FѪؒ Cq $>5%)% 'QpL[l26Z 2͌@Rhl@ďIjMZ\͗>0 `Nskt-.н8n J$  L~:ywW$**5BDdEtF@ZLW<ȴ?vg_m nB2vEn`MiWal{螻;+OSF3XF;E֔իWIUI*L֙ޞ^e;O%'MEIk{+wUu5*P:^[MLr&m(3: &A8 NGkTdZ H@IjYil3l nPkFdEl@tC m~7`E 0t#h%څ@tC NF dڭX'q2]g̾ 3Nu#R "2m.T @۩kD @Cb B5kA<(&uZ:ȴ90X _KM" FPs @FL@`LWQ]*s#2`U wpp@@`N`U6`IENDB`Dd\  C *ABD15058_"@@bZ >ěLfz5%tnZ >ěLfz5%PNG  IHDR [AsRGBPLTE3ff3< ( cmPPJCmp0712>1tRNS@f2IDATA s$#AL* ==pA4p|zyIENDB`Dd\  C *ABD15059_"@@bU=1M*| ߨ1vn)=1M*| ߨPNG  IHDR a`PLTE!!!ZZZkkk> tRNSJO cmPPJCmp0712HsDIDATWmI lAb8E&Et`&KޣHCU(0&-ox~IENDB`Dd\   C *A BD15057_"@@bO9@[?VyxnO9@[?VyPNG  IHDRysRGBPLTEZZZEfP cmPPJCmp07128I tRNS ATIDAT Av0d4 U TCX*XSŸJFeπ t*hS u5CB>_IENDB`>Dd  J  C A? "2hnmD.и8|* `!thnmD.и8 .BxڵOOAl #?'/KbK[ %LLL7dM ,rZ>iG_DNjy/f63o7V@0 9le' 'c+sCEg2<">8Ύ$x6'k%lr #V2|@~=\-_SlxY`|["pqMp689pTBO%u ?QL  !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abdefghijklmnopqrstuvwxyz{|}~Root Entry  F#9g2@Data cK}WordDocument ObjectPoolv9g2#9g2_1200560905 Fv9g2v9g2Ole PRINTHCompObjf  !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLNOPRSTVWXYZ[]^_`abcdefghijklmnp[*    ''  '  '  Arialw@ }ww0- 2 6 Part type7.'..2 Machine sequenceE.*...*.....*. 2 p1. 2 p5,3.. 2 2.2 2,5,3... 2 >3. 2 >6,4,.. 2 4.2 4,6,1... 2 5. 2 3,5,.. 2 s6. 2 s1,4,.. 2 7. 2 1,6,.. 2 A8.2 A3,5,2... 2 9.2 6,1,4...' FMicrosoft Excel WorksheetBiff8Excel.Sheet.89q 0@\pISyE Ba=& =--z  <X@"1Arial1Arial1Arial1ObjInfo WorkbookSummaryInformation( MDocumentSummaryInformation8QArial"$"#,##0_);\("$"#,##0\)!"$"#,##0_);[Red]\("$"#,##0\)""$"#,##0.00_);\("$"#,##0.00\)'""$"#,##0.00_);[Red]\("$"#,##0.00\)7*2_("$"* #,##0_);_("$"* \(#,##0\);_("$"* "-"_);_(@_).))_(* #,##0_);_(* \(#,##0\);_(* "-"_);_(@_)?,:_("$"* #,##0.00_);_("$"* \(#,##0.00\);_("$"* "-"??_);_(@_)6+1_(* #,##0.00_);_(* \(#,##0.00\);_(* "-"??_);_(@_)                + ) , *  " `Sheet18e Part typeMachine sequence3,5,23,54,6,11,46,41,62,5,35,36,1,4 S 0@  dMbP?_*+%MHP LaserJet 6P/6MP PostScriptS odXXLetterPRIV0''''\K\K=&}"dXX??U} $ } m    ~ ?  ~ @ ~ @ ~ @ ~ @ ~ @ ~ @ ~  @ ~ "@  >@7    ~ ? ~ @ ~ @ ~ @ ~ @ ~ @ ~ @ ~  @  ~ "@  >@   Oh+'0@HXh spyrosISyEsMicrosoft Excel@qI@")՜.+,0 PXh px gatechh Sheet1  WorksheetsOh+'0|  , 8 D P\dl]V2Elo`"C-;cgOǙ}t}7MnsmMnd!~3PfW&l2Gd|1 yF&V+go='gsiI7UoqjoO9P`Uj9*Wt:xn5-c:Cһyoa躗 ǿweX๊jVTzdr*ϷUcfjY-ϰlV۰:luVǰzlVϰBB֐ֈ֘֬&5SQ-ZVeX[ՊD|irۤ=?r1Table,SummaryInformation(UDocumentSummaryInformation8\CompObjojt Chapter 1 hapNapapapNormal spyros 2yrMicrosoft Word 9.0@F#@?%@L0g2@L0g2 ՜.+,D՜.+,8 hp  COMPAQE'  Chapter 1 TitleL@/ _PID_HLINKS_AdHocReviewCycleID_EmailSubject _AuthorEmail_AuthorEmailDisplayNameA$0[;+' BD15058_Z;,' BD15059_T;-' BD15057_ -$-[;.- BD15058_Z;/- BD15059_T;0-  BD15057_X n Solutionsilschoi@isye.gatech.edueShuk-Yin Fion Choid  FMicrosoft Word Document MSWo i<@< NormalCJ_HaJmH nHsH tH@@@ Heading 1$$@&`a$5\<A@< Default Paragraph FontR^@R Normal (Web)dd[$\$PJ^J_HaJnHtH.U@. Hyperlink >*B*ph,@, Header  9r , @", Footer  9r &)@1& Page Number`RB` Body Text Indent 271$^7`CJPJ^JaJtH `CR` Body Text Indent 77P^7`PJ^JaJtH >V@a> FollowedHyperlink >*B* phFS@rF Body Text Indent 3$8^8a$ ./D(       2 ./2     D(3Qp|}xD?no[x0 1  T U 5 6 I"#[bc4@\n4Qn6Sop  !#%&+-/1369:;=?ACEHIJLNPRTVW [./hi|b d 3!5!6!7!8!9!:!;!!?!!!!!!!!!!!!" "!"""2"3"""""#!#/#^#####$J$K$$$%V%z%%H&x&&&j'k'm'n'o'q'r's't'u'v'w'y'}''''''''((((((((((((((((((( (!("(#($(%(@(A(B(E(000000000000 0 0 0 0000 000000? 0?0?0? 0?0?0? 0?0?0? 0?0?0? 0?0?0? 0?0?0? 0?0?0? 0?0?0?0?0? 0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0? 0? 0p?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0? 0p?0?0?0?0?0?0?0?0?0? 0p?0?0?0?0?0?0?0? 0p?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0? 0?0?0?0?0? 0?0? 0?0?0?0?0?0?0?0?0?0?0?0? 0? 0?0?0?0?0?0?0?0?0?0?0?0?0?0? 0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0?0? 0? 0? 0? 0V%? 0V%? 0V%? 0V%?000000000000000@0@0@0@0@0@0@0@0@0@0@0@0@0 00000000000000000000000 }RG'1--'5=?#%&9:HIVW #5%%A*7---!"#$%&()*+,-./012346789:;<>@A- }!!)+2:(?D"$(tLw%"$^R1+ҍAPS3"$+Vc\' 2$hnmD.и8|"$Nt RCF_"$[NoI] ."$ݱ Sb/'"$c MaLg"$8OCfZ;:E "$|T*jD"$~( ES֮qΨ"$}=Xx>S2s"$c枸,oq "$z|UN(Hy]MO"$aqa3a ׿X("$|1,۬9ś+ "$c t<'"$b,i"$+̏#fCGO@  (  H 2 C A ?6 d  A6 f  A6 j  A  6   A6   A 6   A 6   A 6   A6   AB S  ?b 3!!w'D( TM t TD7t TSt Td t T* t28K 4d82 t  J tf8tj[ t OLE_LINK1_PictureBullets _1077031098 _1200560905y'<(<(E(@@m|'<(<(E(7"9"U"V"e"h"""""$!$+$,$J%M%R%T%}'}'''''''''''((E(Q]KP\` !!# #:#E#q#w#######$$$!$%%}'}'''''''''''((E(33333333333333333i|#####$$$}'}'''''''''''''((E(ISyE schoi8C:\Documents and Settings\schoi\Desktop\Hw3-Solution.docschoieC:\Documents and Settings\schoi\Application Data\Microsoft\Word\AutoRecovery save of Hw3-Solution.asdschoieC:\Documents and Settings\schoi\Application Data\Microsoft\Word\AutoRecovery save of Hw3-Solution.asdschoieC:\Documents and Settings\schoi\Application Data\Microsoft\Word\AutoRecovery save of Hw3-Solution.asdschoieC:\Documents and Settings\schoi\Application Data\Microsoft\Word\AutoRecovery save of Hw3-Solution.asdschoi8C:\Documents and Settings\schoi\Desktop\Hw3-Solution.docschoieC:\Documents and Settings\schoi\Application Data\Microsoft\Word\AutoRecovery save of Hw3-Solution.asdspyrosWC:\Documents and Settings\spyros\My Documents\Courses\Ie3102\Spring-06\Hw3-Solution.doc 7.I0 ":"A!VfK[8JWN yj$E4+4!IMf+ ^yj$4 {nB!R.%Z('BL+|\wK0J[l103b-[4P>*U5i @-z]ACXX`_DF `E8JWk#K׼2XLL: PR^NUȟ>l=*^*`>o(. ^`hH. pLp^p`LhH. @ @ ^@ `hH. ^`hH. L^`LhH. ^`hH. ^`hH. PLP^P`LhH. ^`o(hH. ^`hH. pLp^p`LhH. @ @ ^@ `hH. ^`hH. L^`LhH. ^`hH. ^`hH. PLP^P`LhH.h^`B*OJQJo(phhHhpp^p`OJQJ^Jo(hHoh@ @ ^@ `OJQJo(hHh^`OJQJo(hHh^`OJQJ^Jo(hHoh^`OJQJo(hHh^`OJQJo(hHhPP^P`OJQJ^Jo(hHoh  ^ `OJQJo(hH^`o(.^`.pLp^p`L.@ @ ^@ `.^`.L^`L.^`.^`.PLP^P`L. ^`o(hH. ^`hH. pLp^p`LhH. @ @ ^@ `hH. ^`hH. L^`LhH. ^`hH. ^`hH. PLP^P`LhH.^`o(()^`.^`.pp^p`.@ @ ^@ `.^`.^`.^`.^`.PP^P`. IL+B!-[4E P]ACU3wK0!`_Dk#KR?O,k.%I0 i @K[dV@v4 `E*U5+^N 7XL('Hkl1l=