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Appendix A

RZDEFINING THE HINTERLAND

"Unless there is a favourable 'hinterland' to a portit cannot prosper." Cunningham, 1926!

The seaport and its hinterland...the traditional

approach has been to evaluate the potential activity of a

seaport in terms of the economic health of its hinterland

or inland market area Ffrench 1979!. Geographers over

the last 60 years or so have had a substantial interest

in the extent of the hinterland served by particular

seaports. Once the extent of the hinterland is

delineated the inference is that one should be able to

evaluated whether it will generate increasing or

decreasing flows of cargo through the port in question.

However, by identifying a structural difference between

captive local demand for port and shipping services and a

more competitive market for inland transshipment

Bennathan and Walters �979! depart from the traditional

concept of the hinterland. They argue, theoretically,

that. the hinterland of a port can be divided into two

parts, the captive local market and the inland market in

which more than one port may compete for customers.

Thus, there are qualitative differences within a port's

hinterland. Because this argument has not been

empirically tested, and because the distinction is used

131

in this study, it is important to support it with some

statistical evidence.

Numerous geographers have contributed to the

development of the concept of the hinterland. Sargent

�938! recognized that the area serviced by a particular

seaport may depend on the structure of the landside

transportation system and is, therefore, limited by the

extent of investment in landside transportation,

geological barriers, political boundaries, and the

proximity of other ports. He also identified the

influence of the weight and value characteristics of the

cargo. Morgan revised by Bird 1950! elaborated on the

concept that heavier, lower value cargos ores, gravels,

grains! which tend to be much more economically moved on

water, are moved through the closest port, giving the

ports relatively small compact hinterlands with respect

to these cargos. The higher value, lower weight cargos

machinery, consumer goods! can be transported overland

for substantially less cost relative to their values.

Thus, the shippers of these cargos are more sensitive to

time factors and the hinterlands for these goods tend to

be more extensive and, possibly, even overlapping.

Similarly, Hoyle and Hilling �984! noted that. goods

shipped in large quantities to or from a limited number

of points in the hinterland are most economically moved

132

by rail and, thus, their hinterland is dependent on the

configuration of the rail system. In contrast, goods

shipped in relatively small quantities to or from many

dispersed points are more economically shipped by truck

and their hinterland is strongly influenced by road

network limitations. Kenyon �970! used the definition

of one night's truck travel to delineate the extent of a

seaport's hinterland.

Given these basic parameters, the hinterlands of

numerous ports have been delineated Weigend 1956,

Patton 1958, Hoyle 1968, Hilling 1969, Kenyon 1970, Bird

1984! for various cargos, during various historic

periods, and when subjected to political and technolical

changes. But once these hinterlands are identified,

there is little evidence in the literature of any effort

to assign values and predict the implications for the

respective seaports. In the applied seaport literature

market. research reports make use of the hinterland

concept, but this research has a large subjective

component. Apparently, both the applied and academic

efforts in this area are severly limited by the

difficulty in obtaining sub-national data Patton 1958!.

The difficulties in operationalizing the hinterland

concept have been further exacerbated by the

technological change to containerization. Although

overlapping hinterlands and variations in extent for

133

different cargos were reported prior to the general

adoption of containerized shipping, Hayuth �982! reports

a substantial restructuring of cargo flows and port

hinterlands due to the growth of containerized shipments.

He notes the dissolving and intermingling of the

boundaries of the container cargo hinterlands for the

same goods. Port hinterlands are "...'shared' by an

increasing number of ports." Hayuth 1982! These changes

make it more and more difficult to identify a finite

hinterland for a specific port and, thus, to gather data

to evaluate the prospects of the port. Hayuth's analysis

is supported by Bobrovitch's �982! identification of

over-lapping hinterlands in his data set.

Only rarely have empirical studies of port hinterlands

the density of cargo traffic at various distances from

the subject port Patton 1958! has been reported. In the

majority of studies, hinterlands have been identified

only in terms of their physical extent with little or no

effort being exhibited in the evaluation of the

qualitative or density characteristics of the

transportation of cargos within the hinterland. If, for

instance, one item is transported to the end of the rail

line, that point becomes the location of the extent of

the hinterland, even though 80 or 90 percent of the cargo

may only travel a few miles from the port. This approach

134

has probably been due to the interest in the extensive

boundaries as foci of competition between ports and to

the lack of accessible data.

Although Bird �982! mentions the possible

significance of the local market, only Kenyon �972!

attempts to empirically identify the local market.

Wilder and Pender �979! show a significant concentration

of cargo movements within the first 25 miles of a port,

but they do include any distinction between markets in

their list of port demand factors. It is only in

Bennathan and Walters �979! that one sees a theoretical

distinction.

If it can shown that in the United States ports and

ship operators face two different markets and that most

cargo movements are associated with one market or the

other then this distinction should be incorporated in

cargo distributions for the United States. In addition,

if most cargo originates from or is destine to the local

city economy then data from the local economy might be

considered as a significant proxy for the larger, less

distinct traditionally identified hinterland and this

data might be used to more accurately evaluate the

prospects for port growth.

Data on the domestic origins of export cargos and

destinations of imports in the United States can be

obtained from the cargo manifests filed with U.S.

135

Customs, but it is not regularly compiled or published.

This severely limits academic research in this area.

However, in 1970 and again in 1976 the Bureau of the

Census conducted and published special studies, Domestic

Trans ortation Part A and Part B, on the domestic

transportation---origin, destination, and transport

mode---of international cargos. Although this data is

now somewhat dated, it provides the most substantial

statistical insight into the density distribution issue.

And, as data gathering efforts go, this one appears to be

a particularly high quality effort.

For the 1976 study a sample of 72,DOO shipments

through ports within the 4S contiguous states was

selected from the customs manifest population. The

weight and value data for the shipments was taken

directly from the manifests. Detailed information on the

domestic origin or destination of the cargo as well as

the mode and cost of the domestic transportation was

solicited by questionaire. The response rate on the

questionaires was an impressive 76 percent. It is

important to note that these data were aggregated bycustoms districts. Thus, while the transportation data

are based on the specific port through which the cargo

actually move, the data for several ports within a

customs district. was combined. It is tempting to read

136

the data as representing a specific port, but. it must be

read as representing regional aggregates.

The series of graphs at the end of this appendix,

figures A-1 to A-20, present data drawn from Domestic

Trans ortation Part A and Part B, but it has been

modified to focus on the port hinterland issue rather

than on the national transportation demand. The

statistics have been converted from national percentages

to actual values and then from the actual values to

district percentages for the nine customs districts. If

P equals the percent of national shipments transported a

specific distance to or from district ports; N, the

actual national value; D, the actual district value

transported a specific distance; T, the district total;

and Z, the percent of cargo passing through ports in the

district that is transported the specified distance,

then:

PN = D and D/T = Z.

In addition, the first two mileage categories, less than

25 miles and 25-49 miles have been combined to conform

more closely to the extent of the Standard Metropolitan

Statistical Area SMSA!, which is the most readily

available statistical representation of the local

metropolitan economy.

l37

The first pair of graphs figures A-1 and A-2!

illustrates the distribution of the national totals.

They are followed by a pair of graphs for each customs

district. The first graph in each pair provides a

comparison of general cargos, imports and exports, by

value and by weight. The general cargo classification

was chosen because it most closely coincides with the

flows of containerized cargos. The second graph in each

pair compares imports only for all vessel shipments with

those for bulk cargos by value and by weight. This data

set was complete only for imports, but it is most likely

that it is closely paralleled by export patterns. It is

important to note that the vertical axis on the graphsare calibrated in percentages not in absolute values.

So where distributions appear similar the actual tons of

cargo moved may vary substantially.

Clearly different patterns emerge from the different

regions, reflecting variations in the development

patterns of the port hinterlands. However, for all

regions general cargo distributions tend to be flatter

reflecting higher value to weight ratios and the

particular advantages of containerization in the

transshipment of these cargos. In some instances

irregularities in the distribution can easily be

identified as specific origin or destination cities. For

the Los Angeles region the hump 150 miles from the port

138

Figure A-1

139

Figure A-2

140

Figure A-3

141

Figure A-4

142

Figure A-5

143

Figure A-6

144

Figure A-7

Figure A-8

146

Figure A-9

l47

Figure A-10

148

Figure A-11

149

Figure A-l2

150

Figure A-13

151

Figure A-14

152

Figure A-15

153

Figure A-16

154

Figure A-17

155

Figure A-l8

156

Figure A-19

157

Figure A-20

158

can be related to the cities of Santa Barbara, San

Bernardino, and San Diego similarly distant from the

ports of Los Angeles and Long Beach although in different

directions!. Several regions have a secondary high point

mid-range {20-749 miles distant! that can often be

related to the distance to a specific inland city, but it

is always substantially lover than the local less-than-49

mile peak. While the inland cities served in this way

may be as large or larger than the port cities, they are

probably located in the overlapping hinterlands of more

than one port and, therefore, in the competitive market

sector identified by Bennathan and Walter �979! ~ If one

reconsiders the diagram from Bobrovitch's �982! model

see chapter 2! one would expect the actual density of

the generation of demand for cargo movements to be

associated with clear concentrations of economic

activity. Thus, figure A-21 shows a hypothetical pattern

Figure A-21

C

o

Q

Inland City

Distance

Port City 1 Port City 2

159

of the distribution of density of economic activity

between port city 1 and port city 2 and an inland city

served by both ports. Figure A-22 shows the distribution

of cargo movements to or from port 1 a! and port 2 b!.

Then, diagram c! shows a composite with a concentration

at the inland city that is the result of service by both

ports. While transshipment data for each port will show

the inland city as a relatively minor concentration, the

addition of cargos transshipped from more than one port

will result in a volume more proportional to the

concentration of population.

Figure A-22

0

V3CIO CO

4Q

C

Pott I Port 2 Inland City Patt 2Potr. I

Some of the cargo distribution patterns are

surprising. One might have expected both Chicago and

Houston to have relatively more transshipment traffic

160

connections with the mid-west heartland, but that is not

substantiated by the data. The concentrations in the

Miami Customs District, which includes the states of

Florida, Georgia, South Carolina and North Carolina,

portray a surprising amount of transshipment. This may

reflect cargo specialization of the smaller ports in the

region in order to capture the economies of scale, and

then general distribution through out the region. With

small port cargo specialization, one would expect a

substantial amount of cross-hauling of cargos. lt may

also reflect the transshipment of fresh fruits and

vegetables from Latin America to the Northeast.

The concentrations within the first 49 miles from the

ports may reflect the wholesale collection and

distribution networks or the location of import dependent

industries near the port as suggested by Alonso �973!.

Imports only, especially bulk--clearly delivered to the

port closest to the destination. Bulk cargo by value is

surprisingly slightly more concentrated than by weight in

several instances.

Generally, however, this series of graphs supports the

expectation of more transshipment of high value, low

weight cargos and less transshipment of high weight, low

value cargos. They also show a substantial difference in

the volume of cargo generated within 50 miles of the

ports and the volume generated beyond that boundary.

161

While it is quite likely that this concentration reflects

the concentration of port related industries as well as

the structure of the distributional networks, it does

provide evidence of variations in the nature of the port,

hinterland as suggested by Bennathan and Walters �979!.

Et is not incompatible with the overlapping of

hinterlands in the service of inland cities.

162

Appendix B

SPREADSHEET CELL-FORNULA PRINTOUT

163

A4; [W45]A6: [W45]B6: ' B

C6; ' C

D6: ' D

E6: ' E

F6: ' F

G6; ' G

A9: [W45] 'Market for SeapoA12: [W45] 'COMMENTARY ANDA15: W45] 'Demand for ShipA17: [W45] ' FunctionalB17: 'pl-al-blqC17: '1

D17; 'p2-a2-b2qE17: '2

F17: 'p3-a3-b3qG17: '2

E18: 'and

F18: 'p2+p3-A-BG18: 'q2A19; [W45 JB19: ' al - B20

C19: 'bl - C20

D19: 'A - D20

E19: 'B - E20

F19: 'ql - F20G19; 'q2 - G20

A20; [W45]B20: 80

C20: 2

D20: 75

E20: 0.5

F20: 20

G20: 21.5

A22: [W45]B22: 'pl � C22C22; +B20- C20*C10!D22: 'p2+p3-E22E22: tD20- E20*E10!A24: [W45] 'Ship Operator'sB24: 'TR - alqlC24: ' - blql"2D24: ' + Aq2E24: 'Bq2"2A26: [W45] 'Ship Operator'sB26: 'MR1-al-bl

C26: 'ql andD26: 'MR2-A-Bq2A28: [W45J 'Ship Operator'sA30: [W45] ' Functional

B30: 'TC - C+gC30: ' where

D30; 'Q- ql+q2!

rt Services

NOTES

Services: local�!, inland�!relationships

Variables introduced

Estimated value of variables

Total Revenue TR!

Marginal Revenue

Cost

relationship

Functional relationship in cell ID's

Functional relationship in cell 1D's

165

E30: ' and

F30: 'C - Cs+P

A32: [W45] ' Variables introducedB32: 'C - 333

C32: 'Q - C33D32: 'Cs - D33

E32: 'P - E33

A33; [W45] ' Estimated value of variables333: +$D$33+$E$33C33: +$3$44+$D$44D33: 40

E33: 3

A35; [W45]B35; 'TC � C35

C35: +$3$33*$C$33A37: [W45] 'Profit Maximizing Condition for ShipA38: [W45] ' Operator: MC � MR338; 'when

C38: 'C - al-2b

D38: 'lql andE38: 'C - A-23qF38: '2

A40: [W45] 'If * denotes an optimum value, solvingA41: [W45] ' for ql+ and q2*341.' 'ql* - alC41. '-C!/2blD41: 'and q2*E41: '- A-C!/2F41: 'B

A43.' [W45] ' Variables introducedB43; 'ql* - B44D43: 'q2* - D44A44: [W45] ' Estimated value of variablesB44: $B$20-$B$33!/�*$C$20!D44: $D$20-$3$33!/�*$E$20!A46: [W45] 'Ship Operator Demand for Port ServiceA48: [W45] ' Functional relationshipB48: 'P k4+k5

C48: 'QD48: 'dP/dQ-k5A50: [W45] ' Variables introduced350: 'k4 - B51

C50: 'k5 - C51

A51: [W45] ' Estimated value of variablesB51: $E$20*$B$20!- $E$20*$D$33!+ $C$20*$D$20!- $C$20*$D$33!!/ $C$20C51: -�+$C$20*$E$20!/ $C$20+$E$20! +$E$20!A53: [W45] ' Functional relationship in cell ID'sB53: 'P 354,C53: 'C54, D54D53: 'dp/dQ-E53E53: +$C$51A54: [W45] ' Estimated values of P given values of QB54: +$3$51+ $C$51*$C$113!C54: +$3$51+ $C$51*$C$137!




D54: +$B$51+ $C$51*$C$163!A56; [W45] 'Supply of Port ServicesA58: [W45] 'Port's Total RevenueA60: [W45] ' Functional relationshipB60: 'TRp - P*QC60: ' for Qp,D60: ' Qt,E60: ' 6 QwA62: [W45]B62: 'TRp-C62; +$B$54*$C$113D62: +$C$54*$C$137E62: +$D$54*$C$163A65: [W45] 'Port's Marginal Revenue, derived fromA66: [W45] ship operators' demandA68: [W45] ' Functional relationshipB68: 'HRp � P +C68: ' dP/dQ*QD68; ' for Qp,E68: ' Qt,F68: ' 46: QwA70: [W45]B70: 'MRp-D70: +$B$54+ $C$51*$C$113!E70: +$C$54+ $C$51*$C$137!F70: +$D$54+ $C$51*$C$163!A72: [W45] 'Port's Total CostA74; [W45] ' Functional relationshipB74: 'TCp - k3QC74: '*3 + k2Q"D74: '2 + klQ +E74: ' ko

F74: 'where; kO

G74: '>0, k1>0,H74: ' k2�, K3I74: '>0, k2 2�k3klA76: [W45] ' Variables introducedB76: 'k3 - B77

C76: 'k2 - C77

D76: 'kl - D77

E76: 'kO - E77

F76: +E77

G76: +D77H76: +C77

I76: +B77

Z76: +$C$77"2K76: 3*$B$77*$D$77A77: ['W45] ' Estimated value of variablesB77: 0.0026

C77; -0.225

D77; 6.63

E77: 3.596

A78: [W45]B78; 'TCp- l66

C78

D78

E78

A79

B79

C79

D79

K79

A81

A83

B83

C83

D83

K83

A85

B85

C85

D85

E85

A87

A89

B89

c89

D89

A91

B91

C91

D91

E91

A93

A95

A97

B97

A99

B99

C99

D99

$B$77*$C$113 3!+ $C$77*$C$113*2!+ $D$77*$C$113!+$E$77 $B$77*$C$137 3!+ $C$77*$C$137 2!+ $D$77*$C$137!+$E$77 $B$77*$C$163"3!+ $C$77*$C$163 2!+ $D$77*$C$163!+$E$77[W45] 'Port profit TR - TC'TRp-TCp+$C$62-$C$78+$D$62-$D$78+$E$62-$E$78[W45] 'Port's Average Cost[W45] ' Functional relationship'AVCp- k3Q'"2 + k2Q'+kl + k0

'!Q

[W45] ' Functional relationship in cell ID's'AVCp

$B$77*$C$113"2!+ $C$77*$C$113!+ $D$77!+ $E$77/$C$113! $B$77*$C$137"2!+{$C$77*$C$137!+ $D$77!+{$E$77/$C$137! $B$77*$C$163"2!+ $C$77*$C$163!+ $D$77!+ $E$77/$C$163![W45] 'Port's Marginal Cost[W45] ' Functional relationship'MCp - 3k3Q'Q"2 + 2k2Q"'Q + kl

[W45] ' Functional relationship in cell ID's'NCp-

�*$B$77*$D$113"2!+�*$C$77*$D$113!+ $D$77!�*$B$77*$C$137*2!+�*$C$77*$C$137!+ $D$77!�*$B$77*$C$163"2!+�*$C$77+$C$163!+ $D$77![W45] 'Pricing Strategies[W45] 'a. Maximize profit MR - MC![W45] ' Functional relationship'MC - MR

[W45] ' Functional relationship in cell ID's�*$B$77*$C$113*2!+{2*$C$77*$C$113!+ $D$77!

+$B$51+�+$C$51*$C$113!A101: [W45] ' Arranged in terms of Q 6 set - 0B101: ' 0-

C101: �"$B$77*$C$113 2!+�* $C$77-$C$51!*$C$113!+ $D$77-$B$51!hl03: [W45] ' To solve the quadraticA104: [W45 ] slQ"2 + s2Q + s3 - 0 where:B105: 'sl - C105C105: 3*$B$77B106: 's2 - C106

C106: �*$C$77!-�*$C$51!B107: 's3 - C107

C107: +$D$77-$B$51B108; 's4 - C108

C108; +$C$106"2-�*$C$105*$C$107!A109: [W45] ' Solution of the quadratic a!B110: 'if s4

C110: +$C$106"2-�*$C$105*$C$107!D110: '>0*

167

E110: QSQRT $C$106*2-�*$C$105*$C$107!!Bill.: 'if s4

Clll: +$C$106 2-�*$C$105*$C$107!Dill: '-0*+

B112: 'if s4

C112: +$C$106"2-�*$C$105*$C$107!D112: '<0+**

B113; 'QlC113: -$C$106+$E$110!/�*$C$105!B114: 'Q2C114: -$C$106-$E$110!/�*$C$105!A115: [W45] 'b. Maximize throughput P � AVC!A117; [W45! ' Functional relationshipB117: 'P - AVC

A119: [W45! ' Functional relationship in cell ID'sB119: +$8$51+ $C$51*$C$137!C119:

D119; {$B$77*$C$33"2!+ $C$77*$C$33!+ $D$77!+{$E$77/$C$33!A121: [W45] ' Arranged in terms of Q, multiply by QA122: [W451 and set - 0B122: $B$77*$C$137*3!+ $C$77-$C$51!*$C$137"2!+ $D$77-$B$51!*$C$137!+$EC122: '- 0

A124; [W45] ' To sol~e the cubicA125; [W45I tlQ"3 + t2Q"2 + t3Q + t4 - 0A126: [W45I where:B126: 'tl - C126

C126: +$B$77B127: 't2 - C127

C127: $C$77-$C$51!/$B$77B128: 't3 - C128

C128: $D$77-$B$51!/$B$77B129: 't4 - C129

C129: +$E$77/$B$77B130: 't5 - C130

C130: $C$128/3!- $C$127"2!/9!B131: 't6 - C131

C131: $C$128*$C$127!-�*$C$129!!/6!- $C$127"3!/27!B132: 't7 - C132

C132: +$C$130"3+$C$131"2D132; ' if

E132: +$C$132F132: '>0, one rG132: 'eal root

H132: '6 pair ofI132: ' complexJ132: 'conjugateK132: ' roots,B133: 't8 - C133

C133: ISQRT $C$131~SQRT $C$132!!D133: ' if

E133: +$C$132F133; '-0, all rG133: 'oots real 168H133: ' 6 at lea

I133: ' st two arJ133: 'e equal,B134: 't9 � C134

C134; QSQRT $C$131+QSQRT $C$132!!D134; ' if

K134; +$C$132F134; '�, all rG134: 'oots realH134; ' irreducI134: 'ible caseJ134: '!

A136: [W45] ' Solution of the cubic b!B137: 'Ql - C137C137: 42.691

D137; $C$133+$C$134!- $C$127/3!B138.' 'Q2 - C138

C138: - $C$133+$C$134!/2!- $C$127/3!+ gSQRT�!/2!* $C$1B139: 'Q3 - C139

C139: - $C$133+$C$134!/2!- $C$127/3!- QSQRT�!/2!* $C$1A141: [W45] ' Test of roots of cubicB141: +$D$137+$C$138+$C$139C141:

D141; -$C$127

B142: $D$137*$C$138!+ $D$137*$C$139!+ $C$138*$C$139!C142:

D142: +$C$128B143: +$D$137*$C$138*$C$139C143:

D143: -$C$129

A145: [W45] 'c. Maximize Social Welfare P - MC!A147: [W45] ' Functional relationshipB147: 'P - MC

A149: [W45] ' Functional relationship in cell ID'sB149; +$B$51+ $C$51*$C$164!C149:

D149: �*$B$77*$C$164"2!+�*$C$77*$C$164!+ $D$77!A151: [W45] ' Arranged in terms of Q 6 set - 0B151: ' 0

C151: �*$B$77*$C$164"2!+ �*$C$77!-$C$51!*$C$164!+ $D$A153: [W45] 'To solve the quadraticA154: [W45] ' vlQ"2 + v2Q + v3 - 0B155: 'vl - C155C155: 3*$B$77B156: 'v2 - C156

C156: �*$C$77!-$C$51B157: 'v3 - C157C157; +$D$77-$B$51B158; 'v4 - C158

C158: +$C$156"2-�*$C$155*$C$157!A159: [W45] 'Solution of the quadratic c!B160: 'if v4-

C160: +$C$156"2-�*$C$155*$C$157!D160: '�*

K160: ISQRT $C$156"2-�*$C$155+$C$1.57!!

33-$C$134!

33-$C$134!

77-$B$51!

B161: 'if v4

C161: +$C$156"2-�*$C$155*$C$157!D161; '-0**

3162: 'if v4-

C162; +$C$156 2-�+$C$155*$C$157!~<0***

B163: 'Q1C163; -$C$156+$E$160!/�*$C$155!B164: 'Q2

$C$156-$E$160}/�*$C$155!

170

Appendix C

SOLUT1ON OF FOUR SINULTANEOUS EQUATIONS

171

n

0

I0~ 92

D +

g 0+!ID8t+e t D'OSD $ I0Sr"

+

0

+

4+ 4 ~~ ~ 0

I0»

D0 »I ~ I

OO0nam

L L L000

000

»

0

0 O

I

0C

4

ID 0

D

I ~0

r C 0I

I

~ IC

0

C 0 C

0 0

0 I

8

I

~ g+

gOI0 LIw 0 0»

!I0 »»

»~ t ~2 C

172

0 0Orl0'4 D DD ++

U 0UD + +++ O D

DOOU 0 l0 e+

+D ~+g8$

~ ~ » PlI ~ I ~ ~

0 nil0

C»4IIIr0»

IIW

U

0 I00 Or e

I

n~ e I0»0»

IoC U

»0

'0 '0

h ' R~ .

D I4C ' 80

I +r ~ o

4 0 IC» V0 3

00 +

gU

I

I

I0

L 0

C 0

0 4 C0 0

I0 00 ~I

~ 6 8I C

g

R

3~I~ ~ 0O 0

Appendix D

IMPACT MATRIX CELL-FORMULA PRINTOUT

173

L50: ' S trategyM50: 'Profit Mx

050: 'Thrput NxQ50: 'Velfr MaxL52: 'ResultingL54: 'Profit

M54: +C79

054: +D79

Q54: +E79L56: 'ThrputM56: +C113

056: +C137

Q56: +C163L58: 'welfare

M58: $B$51-$B$54!*$C$113!/2058: $B$51-$C$54!*$C$137!/2Q58: {$B$51-$D$54!e$C$163!/2L60: 'Mat CostL61: 'x 1000M61: +$B$54*2000000061: +$C$54*2000000Q61: +$D$54*2000000Q62: 7.13*2000000Q63: +Q61+Q62

174

alonso, william. 1975. location theory. receional ~folic

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