Extra Notes_location (2)

8/13/2019 Extra Notes_location (2)

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_ . / ~ .. - ~ - - -banks OUl :side their own country, locatlon ( : ~ ~ d s l o n s now t f < i l , p - . s ~ c n d r.arional borders. :In f ~ \ i : t , as figure 9.1 shows. the sequenceof Location decisions often b . e g i ~ -with!choosing a c o ~ m t Y in which to operate. Before Germany's M e f c e d i e ~ d B e n zd h . p ~ e Al- .abama ;liS' the location of its first major O V ~ f s e a S plaJJ.t, it first consi'd!eTed Mexico. In .

l ~ ~ end!, the fe;t· of marketing a $50,000 Mercedes that was Made in Mexico" drove -

the f i f t H bock to the United States. The POM in Action box that deals witl-lMercedes'. .

decision provides aJ,fl i)ntcl-esting insight from A ~ a b a l l 1 a s ers ec ive.Once a finn ~ l i c d d e s which cOlll1try is best for its ocation, it focuses on a region

of the h o s e l l c f ) ~ ~ I l ~ t yand a community. In the United States, the $'duth has Become-popul __~ ~ - : ~ - 5 . j [ i l o n - f oa varktY o t t ' c a ~ 8 n s , including the hospitality so often found

in s m a ~ ~ _ ~ , u , ~ < . ~ t is easy tpsee.why e l h a d ~ l ' s N 0 . r b ( ) r d n d , l I ~ t r i e s found :1 home inTUlPdodfJIDili$JS1 SSlPPl,when you read the POM m Actton box telling that firm s :;tqry.. 1 F l ~ . e ~ I § t < ; p in the IDeation decision process is choosing a sp'ccifu: si te within a

e O ~ 1 l l n w i . i t Y . Tlrccornpanyrnust. pick the one location that is best suited for s l ~ i n g

anCf"recelving, zoning, utili ties , size, and!cost. Agail1, Figure 9.1 summarizes this'series

Q f d e d s ; and the factors thaLi-Hect them. . -- " ~ ~ i d e s g l o b a h z a t i o ~ ; : -a number of other factors affect the location decision .

~ ar ; 1allQr:qrt:k!uctivity, forc(¥n exchange, and changing attitudes tciwardi 1 i , ~ l i t ~ ~ \ ~ ~ 1 S , emil:l;wment, ZOl1l;;i, po ulion, taxes, and so lorth.

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- ~ - - - - - - - - - - - - - - - - - - T H E O B J E C T I V E : : O L O C T I O N S T R A T E G Y

The best location for a given firm depends on its typeofbusiriess. Industrial locationdecisions focus on minimizing <:osts, whereas retail and professional s e r y . i c e - o r g a n l z a ~

ti;ons typically have aloeus of maximizin revemle. W r t ~ e h o u , s e location, however; .l'lJl.;\l,¥ be determined by a combination 0 - cost anc speed ofdeiiv'ery. In general though, . . . . .

til1l.;e(i).wH/€(;£,ivcof locaiion str(J.(cgy is -tornaxirnize the bcneJfilt Qf location. t o tl'le N(l, iim;.~ : > : ~ ' i _ : . ,_ ."'_'_. , . -_;"--= . - . ..":__, , ~ : . _ , . - . ~ . , : : , . ~ ~ _ ~ - . - c . . - . . . . _-'8

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Case I: $12 W,lges per t iur _ $12 ; $1)601.25 Units pro<.hiccdlp Cl how: - 1.25 -c •

. $10. Wagesyci' h o u , , = $10 =': $10.001.00 Units produced-per hour 1 . 0 0 '

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, -.,.,

1 E J q 1 \ l U f l ~ { W ~ c , s w i t h poor trainin " 1 9 ~ ~ ~\;ducntion or lOOt: \ ~ ) I k h n h i n H n < l ~ , n ( n , b e a Ag O ( ) d ' l ? ~ \ I ' ; : Y I i ( ) ; j t bw wages. y t 1C s iiH¥c tokel1-; ell:lI Yloyec:; who c a n l 1 0 t ( ) t t \ ~ T H i \ , { ) f ; t l - : S

ways - 1 ~ i i i i f @ l r t 1 x c i r p a c c of work arc n ( l ~ ~ ~ 1 l \ k h g o o d to.the o r g : m i z a t i p j l 1 . c v ~ nat: low:::iwages. La,hor COSj; per unit is 0 1 l 1 e t i l l l q S : ~ i : · m e d the a b ( J r c i ' n i c c n c o f : t h : i · i ~ ~ ~ 1 ~ I : t l : C t . . 01. ~ e J

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.. ~ : ~ ~ ~ r }S . l v 1 1 a t d i u f a b · c ~ i J r f i f n g Labor Costs of 17 Nation's; 1993; Ti ese avcrairc hourly

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M,ay ~ ~ ~ ~ ~ ¥ . : . ~ ~ I k > t w . a ~ i l ~ _ e ill \ DeuescheM , , < t ~ , D;wlv.

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Exchange,Rates,Although wage rates and productivity may makedifferent countriesseem cconomical, unfavorable e x c b ~ l l 'e rates mi h t DC "ltG)JIwsnvings. Sometimes, t h o l g h , e o

panies ¢<In take a vantage 0 a particula:ic>) ; ~ t V O j a i ~ ie'ex<;hange rate by relocat1ng,qrexponirtg to a foreign country. Howcvc«, the vatues of fordgn currencies contiL'1 iaUyrise and fall in most countries. Such h a n l f , e ~ could well make what was ,1 g o ~ d

tion in L995 a disastrous one in 1999. Many of the maquik dora l f J k ~ f i t s , U . s . ~ O , \ : 1 ~

factories in Juarez, Tijuana, and Matamoros, Mexico, opened shordy a f t ~ 1 f th.e M e ; i ~

can peso decreased by 200% in relation t the dollar in the 1980s. ' ,

Costs

Attitudes' C _ ' , -

.Attitudes o f n a t ~ ~ 1 1 f ; l 1.. s t ~ e , and heal governrngnts toward private ) [ 0 erty, zoning,;paUutlc)[l,and e 1 ~ 1 \ l ) f ( ) y n l e n t s t C 1 b i l i t y ll1ay beii1 flux. Governmeritaatt i tucks at t h e ~



351ETHODSOF EVALUATING LOCATION ALTERNATIVES

time a toe.ation d<o:cisipI). i s ~ . ~ jl1ilY n o t be lasting aries. Moreover, managementmayfind tl{at these attitudes,ca:1be'in#luenced by l e c i d ~ r i ; t r i p .

M E T H O O S O F E VA L U A T IN G

. J , . . .OCATION A L T E R N A T I V E S

r,There are four majm lincdhc :,)tflS fot' solving locasion problems: the 1 ~ K : t o ~ ' - F , H i n g

a : t ~ o d . , 1\0£.J;·onal break-s:ven analysh, the center-of-gravity m e { ( l l l ~ I , and the l ' l \ j I L ~ -. ~ .

' ~ ' .

: . ~ t t ·

I ~ ~ 5 1 t i n g Method., C ~ i '.. . . . . . ~ . . : . Factor-raring J i l ~ i e i l ' l l i < o d 'T h e t e ~ ~ ~ many factors, both qt.mlitative and qllClntitgtive, to consider in choosing a

~ ~ l O C a J ~ t t B . : s o m e of h ~ \ $ ~ & a ( ( : : l I o f st r e more importarii:' than others, so managers can lise\ v e i g l ~ t t l 1 g . s to make J ~ d i e ~ l S i o n process mare objective. The fador,ratitl i ~ d l Q d is

o ~ b , e c a p ~ ~ N l I 1 ~ ~ : . ~ ~ l f ~ e t y ',l,f factors

f r O l n ~ ~ i l ~ ~ f \ t i o n to re'tteation

t o l ~ i t ) ~ ) r skills AssetlQJb,typlants

O p ¢ w q l \ l i ~ ~ g

can ~ I n l ; : l ~ ~ ~ .' .. ' . . a l o n ~ g n t f } c Mcxicansidie ot the--1 '\,To g . i ~ ; ~ I ~ J l i I i ; ; j l j I I 1 . ~ , - ~ e a .what a set of typical l o c a t i o l ~ . factors and tL'l,eir lielative bordee, from Tex<l15to( . g l ' l . t s a e ~ l i t ; 1 l o l < i l \ I i i l . l l l i ~ c t l l r m g , we present Table 9.1. This table was dieveho,ped by Californin, are calLedGrant Thil- rntmfl"mconsulting finn heuclqunrtcrccl-in Chicago, based on a survey of IJwl/iiiladOl'as. Some 1,400

t a l e < l ~ l u f ( l - C l i ' l \ l l F ' i l l ' l ) gassociations. . . . firms such as RCA, Genera!"," ' M t ) t l l l : S ~ Zcnil:l.l, Hitnchi, -a''\t -· .. - .,

. dE operate these plants,

1 J ~ ? 1 ~ m ; : i t ~ l W h i c h were designed t o u d p' - both sides of thei H f f b ~ L O W I N G 19FA CTGili/S HAV.E BEtl i l '1ll\liENT-l'FIED AS J.MPORTANT TO MANUFACTUR1N,G FIRM S: impoverished border r e g ( O > H . ~

After the 1982 devaluationf ~ ' l t T > ( 1 m W E I G H ' ' r ( % ) FA C T O RW E I G i - I T ( ) o f t i , e p e s Q . , t h J e l { ~ l l l 1 b e

' ,..... lHa(jHil-aJorf!l6 l>le,l,r;)yt,riplcd,Labor' c o ' s ~ s . G 6 v ~ ( . n m c n t fiscal p ( ) ~ ~ l « i , c S and it isbdliieveG! t' n0.itby the

Wilges $ ; P e r s i . : } l l ~ J income growth 9 year 2000;;\15 m ~ i t r y <i16thrce .Uniontzati on 6 i;'IXdi[I(;:rt 4 million workers wil:t:be

employed in these crossChahl,'Cs in W;(gcs 5 Ch.lngcs ill ' taxes 4

border plants. Mexican wages. . ~ h a n g e s in unionization . .... -....... --. S i l ' , ~ \ l i e b ~ l s , i l l 1 i e s s incc 11I'ivcs 4 arc l o ~ v , ,uid at current

Z4 21 cxchnl1ge t;i\ite's,companiesS t a t c . r e ~ u 1 a t e d l l 1 p l o y n ~ I ' t f i q l t costs d o r l ' d 1 0 ( o ) k u ~ )th,e Far East as

they n i n ' i ; ' e ~ 1 i ~ kWorkci's' compcnsatir(1f\ insurance' '

!l21 Sclcctcd:mmlity-of-Iifc issues

E\.lilsatio11Ctj:it ott iving

Trampbrtation

Health care

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: s C t ; h ' : S I I ( \ n \ I \ I ' ; l I G t ' ; @ : j · H ( ; h ~ t . l ; I M H n \ l { C n ' r i l l g . C l i / , i a t l 's\lidks.111CiilctOrs were i.lc"d\lj:;ed indisv h h : , ~ t m c 1 , ~ l a i 1 1 1 f ; ( c n / r l i ) J r i S S ~ ; d ' i t i , ( ; i l S ,star e cC'lrililllit (IcVd(lpl11e{l,tdirecr()rs, )lI1d ·i;tareGhal11hers· of

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Ullcl1)ploynicll t cc1mi'i<:ns;IrilHl5 bClldhs 9

. Aycj'iigc iusurnucc costlier case 5

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_.352 CHAPTER 9 LOCATION STRATEGIES};

T h e f a c t o r ~ l : a ~ i n g method has six steps:e

1. Developa list of relevant factors (such as those in Table 9.1).2. Assign a weight to each factor to rehect its relative importanceiatjse C Q m ~ ~ ~

pany'sobjectives, , . , . . ~ - .

3 Develop a scale for e,{ch factor (for example, 1-10 or ~ points},

-. 4. Have muuagcment score each location for each {actor, using the s C a a l € ~ i t l l Sl([CP 3.5. 'Multiply the score by the weights for each factor,'lnd total the scone ftoa:cach lo

cation.. ~

,6. Make a .reeommendaeioo based on. the n:wxi:liRlNll point score, c o : r 1 6 ~ d l C r i n : g t h e

results of quantitative approaches as well. --" *

~

;i

BILLINGS

(.05)(60) =

(.25)(60) = 15.0

ST. CLOU 0

SCORES,

(OUT OF 100)

ST. CLOUD

.25 70 0 G ( ,Z§)i(}!Oj = 17.5

.05{ ] GO (,;@ijj) {50)

= 2.5.10 85 $0 ( 10)(85) 8.5·l9 75 7< 1 . 3 i ~ Y ~ : l 5=29.3

. 2 ~ ~ i , ( ;ii(j) 70 (.2 )(<i()) = U ~ : @

n f I @ ~ { 'f(l4

Example 1 shows how to lise the facror-ratiog lililcthod.

, FACTOR,

TA l L E ;;).2 . . W I ~ i H SSCORES, AND SOLU'l'l!(i)'N

L\li'flrcosrsan'tlattii\idc

~

' , · i a b l e 9 . 2 < l l s p , . s h 9 ~ ~ - t h ~ ' , w ~ l t g ; a hl J I ~ d to evaluate altetnativgsltelL?cations.0iv::cl1"tl1eqpticjn oLt00ff i in ts assigned tto each filCf:Q't, the St. O'BiHdlocat'.)n isd r e ( e r ~ l b l e . Bf<%angingth'0]xiints(ir wdgh,tl> slightly for some tacwfs;·WC can ana- 'Iyzc the sel1sitiiiity elf the decision. 'F,()F instance,We can see t h ~ l J changing thescores for labor costs and ,rttTrlitks by W poilits<:anchange d ~ e 0 1 i e c i s i o O.

, : ~ J i c l n { ) i s ~ ~ , V e L J i I l d ~ 1 C o s ~ 1 ~ . e t k s of New Hampshire has decided to expand its prodlJetton of Mtl'Sdt Co[logil'lIC too opening a new factory location. The expansion is dueto limited capacltv.at its exiisdng plant. The rating sheer in Table 9.2 provides a lis,of qualitative factors that manugcmcnt has decided arc important. Their weight- 'ings and their tilting for two possible s i tes-St . Cloud, Minnesora, and Billings,

, Montana, arc shown.

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¥ E T H O D S OF EVALUATiNG LOCATiON ALTERNATiVESt·:". When a d e ~ i i i l l o ~ 1 lhi sensitive to minor changes, further analysis of either the

353

weightingor dlrepolnts assigned may be appropriate. Alternative ly, managementmayCdllclude that these irlhlngiblc factors are not the proper criteria on which to base aocation decision and tH<lY therefore place pdm<lry weight on the more quantitativeFpects of the d e c i s i o ~ · .,'

LccationalBreak-EvenAnalysis. . '" . . . . .

L 6 c a t i o l l ~ l Q t g ~ l S , , i Y ~ 1 1 a n a l y s i s is£he usc of c o s l ; : ~ t Q l ' J c l m e 'anal sis to lWlke a ne c o-r O I ~ U C C O l ) ) . y . : . _ : ~ ' : . : : < , > .parior} a l t e r ~ a t l \ ' c s . y lc di;ftil ' i r ~ ~ l g l x e ( anevar i accos tS andg ~ ; i p rng l ' ~ ) ~ . T ' e c r c i ocation, wec?n clcrermtae whlch one provides the lowest

:ost.This : t : ~ p h i ( ; . a p p r o a c h also. provides the range omvolume over which each locat i 6 n is preferable, " ,

, \ . '

The t h t ~ ~ steps i\QJocational break-even a n a ~ ' L s are:,., . . .."... -._.-.-..-; - : '-,' _. '. . '- :- .

Locatiooal break-evenanalysis

, ~ ~ .

i t . ~

; ' ~ ~

J

l O i f . ~ ~ p u i ~ ) ~ ~ l t < ; : 6 2 < ; ~ g a p . d variaple ~ o s t for e a ~ . h J p c a t i o n .

~ 1 G J . i ~ $ t Q i : : ~ ~ l ~ h l o c a t i o n , with costs 01; t h e ~ e r t k a l a x i s a i t 1 j ~ ' ;. , . : , : L ; : ~ : ~ , l ~ K ~ e ; ; ; . · . · · · . h . o l i i i ; i i i z _ o _ l l _ t _ a l _ · a _ ·xis, . .

of the graph and

3 seu .a.t:has the lowest tQt,ftl cqst (or the expeqed production;:: ,v o . § ; i e C ~ ~ · ~ c . ~ ..~ -

Example 2 shows li1 O'\>vto use locational break-even analysis.'

manufacturer of automobile carburetors is considering three locations-Akron,.wling Green, arid C h i c a g o - ..for a.new plant. Cost 'studies indicate that fixedstsperyear.at.rhesiresare $30,000,$60,000: und$HOiOOO, respectively. Vari}e costs are 75 .per unit, 15 per unit, andf :251P€ww.i1il'rt, respectively. The ex

; . - ' ~ t e d selling price 'of the' carburetors produce-dillS $120.- The company w['Shes to~ t ~ n d the most economical location for all. expected: i f i ( J i l i . J . i l J l ) , ~ of 2000 un t t sg[ yeaf., ~ \ , . For eachof the three, we can- plot the fixed costs Itbose at a vo urneo zero1 ~ \ ; 1 J 1 i t s ) and the ~ 6 l a l . c o : ; t (fixed c o ~ . E ?..~ . ~ : : : ~ i ~ l b l e costs) at the expected volume of~ Q p t p ~ t . These lines have b e ~ 1 plotted 111 FIgure 9.3,

1 <:;'il::F ; o ~ C b t ~ o ~ "

· I D ~ ; l ( } w e s t < x > . s t ~ < n q l ) , q ] ~ e € f ~ ~ ~ t ~ ~

;. . ; .

' ~ ? . ForAkrQI). .. . . . ' ~ ~ ~ , . ' T tf11 cost =$30,000 7 5 ~ 2 ; ~ ~ _ O ) =$180,000

1 t 0 1 t t ~ ~ c i 5 ~ ~ ~ . $ 6 , 0 1 0 q 9 + $ 4 . 5 ( ~ ~ ~ ) ± $ 1 5 D ~ o o e ~

.,yW i ~ ~ ? g ¥ ~ ; ; r ~ : : ~ i Q ± : ~ : ~ : : i = ~ l : g Green provtdespQfitlS'. .

T ( ) t ~ l revennc .. , - - , t 9 J a , l F ~ ~ ; ~ : t : ? Q ~ , 0 0 0 ) i $15q,000;' $9.o,gOQ/y,ear. ... z - _ - ~ ~ .._ ~ __"

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CHAPTER 9 LOCATION STR TEGIES

IFtGUI\E 9.3 m Crossover Char t for Locational Break-Even Analysis

$180,000

$160,000$150,000

$130,000u;o ·

_

o ,

c ·c« ,

. , . . " - ."

1000 1500. 2000 2600 3000 · · ' 0

VollU!l'l'lte

...The.chort alsotells us that for a volume of less d:> an 1,00.0, Akron would be. preferred, a l i l ~ i p r ; ~ J l l 4 h \ l p e area te t h a n 2 , ~ _ Q ) 1 C h . i C M Q W Q ~ M y l ~ ~ t l h greatest

. J : : r o ~ t . l h e ~ f ~ ¥ ~ t P 9 J l t ~ are 1,.000 a I 1 ~ t J , f t K ? . ..:. c .. .: . _ .

(9.1)

Ld W ii

ic x =



ihto rmal areas; it also saw the exodus of corporateheadquarters from city centers to more congenial'suburban sites.

The third wave--<:aU it the fiber-optic w a v e -: ' ~ ' : ~ T h e Third Wave of Urban Emigrationis electrifying the United States by crisscrossing it. , 'Leads to a New Geography with glass fibers. It has taken scarcely 15 years. The~third wave is one reason why Fidelity Investments

Why would Citicorp locate its credit card operations relocated many of its employees in 1993 from Bostonn South Dakota and clothing vendor Patagonia put to Covington, Kentucky. Now employees in the 10\'1-

s customer service staff in Montana? Why did Utah cost Covington region connect by phone line torn into a national center for software develop ~their colleagues in the Boston office at a cost of less

ment? And why would U.S. \X1estpick tiny Lusk, than a penny per minute. That is less than FidelityWyoming (population 1,504), as a telecornmurssca spends on local connections. .1 o ~ 1 i center? The answers are the same: explosive. Who will be the winners in the fiber-optic loc l ( \ I ; < i J l i \ C e s in fiber-optic cables, digital switches, and cation movement? States with smaller tax burdensD C D l i l 1 l i P u t i n g make sites. in the previous hinterlands a,nd owners of property in fringe suburbs and scenicV€ifcloser, "Geography is irrelevant" in location sc rural areas should come out ahead. And so should E"~ ~ ~ r u l l l ) ; , says real estate consultanr Chris Leinberger . . mail providers (like MCU. telecommuting s o f t w a r ~ . Employers have, of C O ~ l f s e , been trickling oue: makers (like Lows), videoconferencing firms (like

rtD4 g cities for a long t i ~ l l , e . ~ i i 1tt'le first wave of urban Picture-Tel), makers of office electronic equipment~ i ' Y , ( ? t i c 1 , manufactusers tool their factories out of (Iike Dell and Hewlett-Packard), ancl deliveryfirmsT ~ ' , ~ areas and put c : h e Q i } ; 1 ~ : ' e i e v e r electric power (like UPS and Federal Express). ..

~ ; and railroads readh,edi. T ~ 1 e interstate highwayystem was the driving fm "ce in the second wave, Sourc es: Forbes (N.""emhcr Z3. 1992): 184-190 and Telemarketing

which c l ~ a s e d more assembly lines and textile mills Magazine VoliZ (Feb. 199'4): 4?-4J .... . . ;

L diy iC _ _ _

(9.2)s : IW

i

here c, = x-coordiuate of the center of gravityC, =y-coordinate of ch.e center of gravi ty . ,

.. ali> : = x-coordinate of Location i .

iy = y-coordinate of o c a t i o n i .Wi = VQlll\iliLincof goods lHo'Ved to or from location i .

l o ~ :tilh.0.ItlI(j1\lli 1Itiiion l.iS{.9'.lli~ i l l \ l J l d 9.2) include the term w, the volume of suppliesm{crrea r O ® i j J f f n < D ~ \ l i ) :1loclLItHioin t. .

Because llJ1Qicj L l l l t l ~ ~ i l l i e i J . ' of. O J J 1 ; ~ a i n e r s shipped each month affects cost, both volme and distanc€ilililiJLtlt ilhc COQGtiSiildleliedin the location decision. The center-of-gravity

ethod assumesd ~ a i J t t CD SIt

iiSdJittccdy proportional to both ' distance' and volumepped. The ideal IOC:IDllriilOilfliits trlft-a,twhich minimizes the weighted distance betweene warehouse and its, t e l t a i ~ ou\tllets, where the distance is weighted bythe number of

mtainers shipped. ". .xample 3 shows how to use the center-of-gravity method to choose a wareLise-location. ._- . .



• - ~ ~ _ . . ~ - • .: : _ ~ --. . .=: ' --; .---_._'-_.' , - ~ _ - . - -". - -

I Consider the case of Quain's Discount Dep@drtmerlt Stores, a d 1 a ~ n of four t<;lJrgeKMart-type outlets. The firm s store locations are in Chicago, lPli 1 i : 1 i : s l b u r g h New York,and Atlanta; they are currently being H I P I i J ~ i e d out of an old ailild. inadequase we,rehouse in Pittsburgh, the site of the chain's {fwsilIstore. Data on dtetnand rates :i1lt eschoutlet ar e shown in Table9.3 .

T B L E 9 3 DEMAMilD FOR Q U A I N S•DISC0.w;Wf STORES

f iJ WlfMhliUEROF CONTAI,M/ E; R5

STORE LOCATION I ; l ; I ' ~ P E O PER MO'Mllilfl,

: ~ :

~ ..

. - - {

))

Chicago

Pittsburgh

New York

Atlanta

2,000

1,000

1,0002,000

i t ·

,, 1..' New York (130, 1;3101).1 C l t l ~ l : : a g l 0 (30. l' 20) (8

12 0 "r

- ., ~ ' ' ' ' ~ 1 0 t:: : 9h 00.ltO} 6t1' 1 I, _ I90

,

60

" 0'-,,1:;.'.

30 I . l

( 30ArbHrary0fiQiin

Y , f ~ , . 1 1 1 .. , . . ' ~ ~ ~ f e l m i t ~ rof gravity (66.7, 9 3 . 3 ; -

•:to-

AlIaiija16rOJEast-West

60 90 120 150

Tlhle iiiinmt hilllS decided to find some centrul location in which to build a n e w,

warehouse. I i ~ s current store-locations arc s ~ h · o w n in Figure 9.4. For example, locat ion 1 k ~ { ] l l . i / < l : l ~ O , and from T'lblc'9.3 mf ldi j F i ~ ~ f r e 9.4, we have

dt,x ' JiQ

dry ==i112 O

W1;==H)OO

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Extra Notes_location (2)