Linear Programmi n g and Practicable
Farm Plans-A Case Study in tl1e
Goondiwind.i District� Q ueensl a n d
by
P. A. IUCKARDS
and
W. 0. McCARTHY
Price
:
Forty cents
University of Queensland Papers
Volume I
Department of Agriculture
Number 5
UNIVERSITY OF QUEENSLAND PRESS
St. Lucia
29 August 1966
Fryer
53
.U695
v.l no.S
WHOLLY SET UP AND PRINTED lN AUSTRALIA BY
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1966
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LINEAR PROGRAMMING AND
PRACTICABLE FARM PLANS
INTRODUCTION
In the decade following the introduction of linear programming to problems
in agriculture, an extensive body of literature has been built up. Candler &
Musgrave ( 1960) and Musgrave (1963) cite references to material of this kind.
Articles dealing with the problems of developing profit-maximizing plans for farms
are numerous-for example those by Peterson (1955), Heady et al. (1956),
Puterbaugh et al. (1957), McFarquhar & Evans (1957), Waring et al. (1963),
and Camm & Rothlisberger (1965). Most of this literature, however, is concerned
not so much with generation of practicable plans for individual farms, but rather
with presenting solutions for average types of farms. Swanson ( 1961) summarizes
this situation as follows:
ln spite of the voluminous list of agricultural "applications" of linear
programming, one finds virtually no documentation of commercial
applications . . . the solutions apply to typical (in most cases, hypothetical)
farms and the principal purpose of the work has been to analyze relation
ships within the firm.
The lack of commercial applications has a number of possible explanations.
Initially, many authors were merely attempting to fit the par ticular problems of
175
176
P. A. RICKARDS AND W. 0. McCARTHY
the farm firm into the theoretical framework of the method. Heady (1954) is an
early example. As well, extension workers who were the people closely concerned
with everyday farm planning frequently did not have the background necessary
to capitalize on the method, nor ready access to computers. A further complication
was the evidence that formulation of individual farm plans was relatively costly in
terms of the time and effort required to estimate input-output coefficients and
for use of the computer itself.
In an attempt to minimize some of these difficulties, the standard or bench
mark plan was put forward. A benchmark plan is an optimum plan for a
hypothetical or average farm which is subsequently used as a basis for advice in
particular farm situations. However, this approach only gave acceptable results
when the farms involved were homogeneous with respect to resource supplies and
technology and where the production functions for individual enterprises were
approximately identical among farms. In practice such conditions do not normally
prevail.
As a consequence of the lack of published studies in which practicable farm
plans were presented, some people began to doubt the usefulness of the technique.
Thus Clarke & Simpson (1959) put forward a "simpler" alternative, while Defries
(1959) stated bluntly: "I am doubtful of the use of (such) elaborate mathematical
tools in production economics".
An alternative and less pessimistic view is presented here: namely, that a major
shortcoming of farm plans by linear programming has been incomplete specifica
tion of the problem. In turn this has led to recommendations which cannot be
applied in practice. For example, the literature appears to include only two studies
(Woodworth (1957) and Coutou & Bishop (1957)) in which treatment of the
problem of soil heterogeneity is explicit and none in which planning is on a
paddock by paddock basis. To suggest that activities can be allocated among
paddocks or soil types after the programme has been run nullifies the whole
purpose of the exercise. Admittedly such restrictions make more complex an
already complex situation, but, as computer capacity and efficiency is constantly
increasing, so can the programming of the farm situation be made more realistic.
If programming is to be of maximum practical use to extension and advisory
workers, farm complexity and variability will need to be more completely specified
than hitherto. The extension worker should also consider the initially computed
farm plan as a draft subject to modification by discussion with the farmer and
probably recomputation at least once before the final working plan is decided on.
This paper is concerned with some aspects of these problems. Specifically the
paper includes soil types and paddock areas as restraints and indicates the
necessity for discussion of successively more sensible draft plans with the farmer.
This more realistic type of approach is one which extension workers will need to
adopt if programming is to become a practical aid in advisory work.
Of course the cost and time required for this approach may well preclude its
use by publicly financed extension services in isolated studies of farm planning.
As Musgrave ( 1963) points out, the most expensive aspect of programming
studies in an area is the accumulation of information and experience from which
the basic programming matrix is constructed. It would be reasonable to expect
that the cost of further studies in an area would rapidly diminish. Hence it is the
authors' opinion that, if plans for a number of farms in a district could be
generated by use of edited forms of the basic matrix, then this would be an
economically feasible method of district farm planning.
The current study, in which an individual property is considered, was
commenced early in 1964 and entails the use of a static linear programming model
to generate a practicable farm plan for the ensuing twelve months. The analysis
proceeds as follows: firstly the case study property is described and the problem
LINEAR PROGRAMMING AND PRACTICABLE FARM PLANS
177
delimited; next, activities and restraints are specified and a draft plan computed.
Initially the restraints include soil type but not paddock acreages. The impractic
ability of such a plan is demonstrated even though the inclusion of soil type makes
it more realistic than most plans found in the literature. Paddocks are then
introduced as a restraint and the ensuing plan presented to the farmer for assess
ment before finally arriving at a practicable plan.
THE CASE STUDY PROPERTY
The property chosen, "Trevanna Downs'? is located in part of the "brigalow
belt" approximately 30 miles north of Goondiwindi. Like most properties in this
district, "Trevanna Downs" is characterized by the heterogeneous nature of its
soils and the wide range of enterprises which are successful on these soils. This
leads to a multiplicity of production opportunities. Hence the farm manager is
faced with an extremely complex decision problem in determining an optimum
allocation of scarce farm resources among alternative production processes.
At the commencement of this study, most of the property had been cleared of
native scrub and 2,200 acres were available for immediate cultivation. An
accompanying map, Figure 1, shows the range of soil types, their distribution
and paddock layout in 1964. This map was constructed after identifying soil
production types and cultivation land on a scaled aerial photogt:aph. Shadelines,
wasteground, and subdivision fences were also located. A planimeter was then
used to measure the acreage of soil types and paddocks.
Having established the land resources of the case property, the operator was
then interviewed in order to qualify the level of production restraints. In addition,
estimates of production coefficients for enterprises which had actually been
carried out on any one of the six soil production types were determined. These
data were supplemented with information provided by members of a district
survey,2 local technical experts, and also from market reports. In this way a
relatively accurate description of all the production opportunities available to
management was built up.
·
CONSTRUCTION OF MATRIX A
The case study property demonstrates some of the problems of realistic matrix
construction. Activities and restraints are therefore discussed in some detail. As far
as soil type is concerned, each type has a unique set of input-output relationships
for alternate crops which are available to the operator. Thus in constructing the
initial programming matrix (Matrix A) the acreage of each soil type acts as a
resource restraint.
The programmed restraints
Five discrete soil production types were under cultivation on the case study
property in 1964. (The cultivation portion of soil production type 6 has been
amalgamated with that of soil production type 2 since these two soils have identical
crop productivity once the gilgais have been removed from the former soil type.)
The acreages of these soil types comprised the restraints R1 to R5•
In addition to cultivation land it was estimated that 5,494 acres of the property
were under cleared native pasture in 1964. This land was subdivided into three
'The plans in this study relate to the 1964 planning period, and hence the original
grazing homestead-block of 8,333 acres is considered. More recently the size of the property
has been reduced by compulsory resumption of 1,000 acres.
2 A survey of production enterprises on eight neighbouring properties was conducted
in order to provide a more comprehensive pool of information from which the ap propriate
coefficients could be selected.
N
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4.
Letters
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Mapping
No.
Unit
Production
type 1
Cultivated
Acreage
0
Major Characteristics of
Dominant Soil
--------· -------
Heavy dark grey self-mulching clays.
Weakly gilgaied
acid subsoils.
Production
555
3
Production
type 3
74
brown
Deep heavy grey
differentiation.
clays
clays
with
with
little
s trongly
profile
730
Weakly solonized red brown earths.
5
Production
type 4
Production
type 5
!69
Weakly solonized soils related to solodized
solonetz. red brown earths, and grey and
brown soils of heavy texture .
6
Production
27
Very strongly gilgaied grey clays with strong ly
aci d s u bsoi ls .
4
type 6
SCALE
cultivation
paddocks
519
2
type 2
distinguish
CULTIVATION
BORDER
Fig. 1 .--Soil production t ypes, paddock code, fencelines, and culti vation acreages-
Trevanna Downs--May, 1964.
chains
20
40
179
LINEAR PROGRAMMING AND PRACTICABLE FARM PLANS
types on the basis of pasture productivity,
constituted the restraints R., to R8•
and
the
acreage
of
each
type
R9• The maximum stud ewe restraint
The number of stud ewes was restricted to 500 as this was the maximum
number that the operator could manage in the 1964 period.
R lO· The lucerne restraint
This restraint ensures that there will be adequate supply of lucerne feed avail
able for those stock requiring it for strategic grazing purposes.
1?11• The maximum late grazing sorghum restraint
The operator has expressed a preference for a restricted acreage of this crop
and has indicated that 160 acres would be the maximum he would be prepared
to plant in any' one year.
R1�. The maximum wheat restraint
Wheat is harvested with an auto-header capable of handling 600 bags daily.
The safe harvesting period is considered to be twelve days so that an upper limit
of 7,200 bags was placed on the annual wheat harvest.
R 1:1.
R 11, and R15. Tractor hour restraints
The plant capacity only becomes limiting from December to March. Restraints
R1a to R1" constitute the level of available tractor hours in the January, February
March, and December periods respectively.
R1". Supplementary sheep units
It is the general consensus of opinion of graziers in the Goondiwindi district
that during the summer flush, from October to April, approximately five breeding
cows can be run to every 100 breeding ewes (or equivalent dry sheep) without
active competition for feed. During the winter months, when Jess tall feed is
available, this ratio falls to 3 per cent. This relationship was expressed in the R16
restraint.
R17• Arable type 2 wheat supply
This restraint was specified so that adequate wheat would be available to act as
a zero cost cover crop for lucerne on this land type.
R1s to R�7• Feed restraints
The supply of forage by crops and pastures and the demands for forage by
livestock were all expressed in Dry Merino Ewe equivalents (D.M.E.s).3 The
feed year was divided into four equal periods which roughly coincided with the
four seasons of the pasture year. In addition three feed pools were established
in order to differentiate crops and pastures according to the characteristics of
forage supplied for livestock production.
The first or so-called "transferable" feed pool collects all forage from perennial
crops and pastures. A characteristic of forage supplied to this pool is that it is
freely transferable at the cost of some loss in nutritional value from the period
in which it is produced to a future period. Livestock do not consume directly
from this pool but all feed, after inter-period transfers, is supplied to a separate
pool called the "consumption" pool.
As far as this study is concerned, the consumption requirements of livestock
have been broken up into two components:
(i) a requirement of oats forage for special-purpose grazing;
(ii) a requirement of forage of at least maintenance quality for general
purpose grazing.
"One D.M.E. is defined as the energy requirement of an adult merino ewe, neither
pregnant nor lactating, for normal maintenance and woo l growth over a one-month period.
180
P. A. RICKARDS AND W. 0. McCARTHY
Separate consumption pools have been established for these two feed
components. The "oats" feed pool collects all forage from grazing oats crops and
supplies the need of livestock activities requiring special-purpose grazing.
The general-purpose consumption requirements of livestock are met from the
so-called "consumption" pool. This pool collects forage supplies from annual
crops (excepting grazing oats during the May-September period) as well as
transfers from the "transferable" feed pool. No transfer activities operate within
this pool as forage from annual crops usually has zero substitutability with respect
to time.
The restraints R18 to R21 relate to the levels of supply of forage in the "trans
ferable" feed pool in the four periods of the feed year. R22 and R:!:l relate to the
levels of supply of special-purpose forage in the "oats" feed pool in the May-June
and July-September periods respectively. R24 and R27 relate to the levels of supply
of forage in the "consumption" pool in the feed-year periods.
R28• The grazing sorghum supply restraint
This restraint ensures an adequate supply of sorghum forage for the "crop
wether" activity which requires four months of crop forage during the April to
September period.
The activities considered
A range of no more than six alternative crops was considered for each of the
five soil types under cultivation on the property in 1964. The relevant crops were
wheat, early grazing oats, late grazing oats, early grazing sorghum, late grazing
sorghum, and lucerne.
The first three activities considered, X1 to X3, were grain wheat activities on
soil types 1, 2, and 3 respectively.
Activities X4 to X8 represent early-season grazing oats on soil types 1 to 5
respectively while activities x9 to xl3 represent late-season grazing oats on the
same soil types.
October-planted forage sorghum or so-called "early grazing sorghum" on soil
types 1, 2, 4, and 5 respectively is represented by activities X14 to X17. This crop
has a three-year cycle on soil types 1, 2, and 4, on which it readily produces
ratoon growth, but only a two-year cycle on soil type 5 where the ratoon stand
is not successful.
The next four activities X1s to X�1 represent January-planted or "late grazing
sorghum" on soil types 1, 2, 4, and 5 respectively. This crop is normally planted
with the auxiliary tractor so that activities X1 s to X21 are not competitive for
tractor hours in January.
Activities X2� to X26 represent lucerne-growing activities on soil types 1 to 5
respectively. A preliminary investigation showed that wheat production on soil types
1 and 2 is optimum in the programmed solution and hence wheat is considered
to provide a zero cost cover crop for lucerne activities on these two soil types. In
contrast, wheat production alone is not economically justified on soil types 3 and
4. On these soils the lucerne activities (X24 and X25), by definition, include wheat
as an initial cover crop. This practice seems reasonable as it allows the operator
to realize a net profit instead of incurring a cost in the year of sowing. A cover
crop is not specified for lucerne on soil type 5 because of the unsuitability of this
soil for wheat production.
Land under cleared native pasture was subdivided into three types, namely X,
Y, and Z, on the basis of pasture productivity. Activities X27 to X29 respectively
refer to pasture activities on these three land types. The production coefficients
used for each pasture type represent the seasonal feed productivity of the pastures
LINEAR PROGRAMMING AND PRACTICABLE FARM PLANS
181
and not a measure of annual production under some specific form of pasture
management .
The next ten activities, X:lO to Xa!h are fee d-transfer activities and relate to
transfer of forage within and among the three feed pools previously defined. The
first two of these activities , Xw and X:n, al low transfer of oats forage from the
"oats" fee d pool to the "consumption" pool. The rem aining feed-transfer activities
were specified so that the comp uti ng routine would be enabled to select the
optimum form of pasture management for the property .
Activities X32 to X35 allow transfer of feed within the "transferable" feed
pool from each of the four periods of the feed year to the following p eriod at a
loss of nutrient value. A nutrient decline of 35 per cent was assumed for transfers
into a frost-free peri od and a decli ne of 50 per cent assumed for transfers into a
period of frost incidence !
In order to relate the "transferable" feed pool, with its associated inter-period
transfer activities, to the consumption requir e m e nts of lives tock , four additional
activities (X36 to X39) were specified to allow the transfer of feed from any period
in the "transferable" feed pool to the correspon ding pe riod in the " consumption "
pool .
Matrix A was completed by speci fying nine livestock activities. The nutrient
requirement s of all livestock were expressed in Dry Merino Ewe e quivalents , one
D.M.E. being set at 36 lb of total digestible nutrien ts . "
The first livestock ac t ivity , X10, represents fl ock br eed ing s h eep and one unit
of this activity is taken to be a Poll merino breeding ewe and her normal support
ing stock-approximately 3 p e r cent rams, all lambs , and 2-tooths. It is implicit
in this vector that ewes and lambs are grazed on oats from May until October,
that ewes and weaners cut 12 lb of wool, and that lambs cut 4 lb.
X41 re presents the stud Poll merino ewe activity which is defined similarly to
the flock ewe activity .
The next two a ctiv ities X1� and X43 are Poll merino wether activities. In X42 it
is assumed that wethers are gr azed on natural pastures throughout the year and
cut an average of 12.5 lb of wool per head. In contrast, XH assumes that wethers
are given access to forage so rgh u m crops for four months during the winter and
consequently cut an average of 15 lb of wool per head.
Xu represents breeding cattle which are fully competitive with sheep as
r egards feed re quirements. One u nit of this activity is taken as a Hereford breeding
cow and her normal s u p porti n g s toc k-appro xim ately 4 per cent bulls , all calves,
weaners, steers, and heifers up to twenty -four months. It is assumed that all
steers and 70 per cent of heifers are fattened on oats and sold at twenty-four
months. The rem ainin g hei f er s r eplac e cast - for -age b reeders .
X45 repre s ents vealer production which is also fully competitiv e with sheep
as regards feed. One unit of this activity is as s umed to be a Hereford breeding
cow plus 4 per cent bulls, and all c al ves , weaners, and carryover stock up to
twenty -four months of age. It is assumed that all weaners are fattened on oats but
that only 75 per cent reach sale condition in twelve mont h s. The carryover stock,
with the excepti on of replacement heifers, are sold fat at twenty -four months.
The majority of graziers interviewed in the Goondiwindi district estimated
that the border between supplementary and competitive range of cattle grazing in
'F or a dis cus sion on the nut rition al value of subtropical p a sture s see R. Milford,
"Nutritional values for 17 su b tropical grasses", Australian Journal of Agricultural Research.
XI
(1960),
138.
The n utrien t requirements f o r cattle and sheep activities were taken from: Committee
on A nimal Nutrition, Beef Cattle and Sheep (Nutrient Requirements of Domestic Animals,
Nos. 4 and 5 [Washington D.C.: N ati on al Academy of Sciences-National Research
Council, 1959]).
5
1
2
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25
26
27
28
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19
20
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9
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Oct.-Dec. D. M. E.
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Apr.-June D. M. E.
July-Sept. D. M. E.
J a n. -Ma r.
"Consumptiou" feed
"Tfan;ferable" feed
Jan.-Mar. D. M. E.
Ap r. -Jnn e D. M. E.
July-Sept. D. 111. E.
Oct.-Dec. D. M. E.
"Oats" feed
May-June D. M. E.
July-Sept. D. M. E.
2
Arable type 1
Arable type
Arable ty pe 3
Arable type 4
Arable typ e 5
Pasture X
Pasture Y
Pasture Z
Maximum stud ewes
Lucerne restraint
Max. late 'grz. sorgh.
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January tuctor
Feb.-Mar. tractor
Decemher tractor
Supplementary sheep unit
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Oct.-Dcc. D. M. E.
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Jan.-Mar. D. M. E.
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Max. late grz. sorgh .
vvlleat max.
January tractor
Feb.-1\hr. tractor
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Supplementary sheep unit
Arable 2 wheat supply
1
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Pasture Y
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Maximum stud ewes
Arabie type
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Fig. 2-Matrix A (Co11tinued)
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32·1 32 ·0 12 8 12 8
58·3 46 4
12 8
29 6
20
P. A. RICKARDS AND W. 0. McCARTHY
184
associ ati O n with sheep is 5 per cent during October to March and 3 per cent
during April to September Consequently, it would be feasible to run a limi ted
number of e ither breeding cows or vealer mothers in a supplementary relationship
with s heep in addition to X44 and X45 which were assumed to be fully competitive
activities. x46 and x47 repr e senting
parti ally competitive
breeding cows and
"partially competitive vealers respectively were specified such th at the upper limit
of the se activities was set at 5 per cent of the bre eding ewe numbers (or 1.67 per
cent of the wether numbers). At this level X46 and X_., only become competitive
for pasture feed in the April-September period and even then 60 per cent of
their pasture feed requirements can be suppli ed without diminishing the amount of
feed available for sheep activities.
The final activi ty X48 repres ent s crop fattening. This activity entails the
purchase of thirty month old store cattle d uri ng May, June, and July, followed
by intensive grazing on oats and sale of fat cattle in Sept e mb e r and early October.
An a rithmetic descrip tion of Matrix A is included in Figu re 2. Only non-zero
elements a r e shown in the body of the matrix
.
"
"
"
-
-
.
TABLE 1
Activity
Xt
X,
Xo
X7
X12
X,,
X,.
X,.
X,
Xz1
Xzs
Xz•
X""
X""
Xs-•
Xaa
X31
Xas
X,.,
X-«>
x.,
X"2
X.,.
x ..
X.,.
PLAN I-THE PROGRAMMED SoLUTION
Wheat type 1
Wheat type 2
Early oats type 3
Early oats type 4
Late oats type 4
Late oats type 5
Early grazing sorghum type 4
Late grazing sorghum type 2
Wheat sown lucerne type 4
Native pasture X
Native pasture Y
N ati ve pasture Z
May-June oat transfer
January-March feed transfer
·
April-June feed transfer
October-December consumption transfer
January-March consumption transfer
April-June consumption transfer
July-September consumption transfer
Flock sheep
Stud sheep
Wethers
Crop wethers
Partially competitive cattle
Crop fatteners
Surplus Resources
&. Wheat maximum
R1s January tractor
Rn Arable type 2 wheat supply
Revenuel
FROM
Unit
Acre
Acre
Acre
Acre
Acre
Acre
Acre
Acre
Acre
Acre
Acre
Acre
MATRIX A*
Activity
Level
5 19 .0
1 01 .5
74.0
149.9
68.6
D.M.E.
D.M.E.
D.M.E.
D.M.E.
169.0
216.6
4 80.5
294 . 9
1,875.0
762.0
2,857.0
191.3
13,268.4
13,491.6
10,768.7
D.M.E.
Breeding ewe
Breeding ewe
Wether
Wether
Breeding cow
Steer
7.277.8
14,731.2
32 1 . 0
500.0
155.5
3,504.5
101.4
8.7
D.M.E.
D.M.E.
Bag
Hour
Acre
15,641.8
829.2
40.7
1015
.
£28,355.1
* Matrix A was submitted for computation to the G.E. 225 electronic computer at
the University of Queensland. Solution was reached in approximately six minutes.
t The revenue from plan is found by multiplying together the "revenue" of each
activity with the level to which that activity is represented in the plan and then summing
over all activities. T he "revenue" from any activity does not include an allowance for fixed
costs such as rents, rates, insurance, depreciation, or any other charges which are unaffected
by the level at which the activity is carried out.
LINEAR PROGRAMMING AND PRACTICABLE FARM PLANS
185
THE PLAN FROM MATRIX A
The pr ogr ammed solution to Matrix A, plan 1 is included in Table 1. This
plan re pr esents an opt imum farm plan for the case study property, given that the
location of crop-pr oduction activities need only be restrained by soil-type
d istribution If plan 1 was fitted to the property, according to the soil-type
boundaries marked on Figure 1, insurmount able difficulties would arise in
attempting to put it into operation.
This can be well illustrated by cons idering activity X1. which represents wheat
production on the 5 19 acres of soil type 1 under cultivation. This soil t ype
occurs in p arts of paddocks B, C, F, G, H, I, K, and L. Should wheat be grown
on these areas it would be i mpractical to use these padd oc ks for grazing purposes.
In other words, land under wheat should be fenced separ ately from that used for
grazing. To erect subdivision fences on each of the eight paddoc ks on which soil
type 1 occurs would scarcely be practicable from a managerial viewpoint and,
furthermore, the cost of this fencing would most certainly negate the economic
advantage of the comp u ted crop distribution.
Similar problems arise if an attempt is made to fit any of the other crop
activities into the property organization in the manner specified in plan 1. Clearly
the inclusion of soil-type restraints will not result in pr actic a ble farm plans except
where soil-type boundaries and fencelines coincide. This is an un i kely situation
in practice.
Hence, in order to generate p ractic able farm plans, it seems necessary that
crop-production activities should be restrained by the size and location of cultiva
tion paddocks as well as by soil type distribution. In the present study this step
necessitated the construction of a new matrix (Matrix B), in which acreage
restraints from crop-production activities were specified for each culti v ation
paddock. The way in which this was done is now described in some detail. In
addition, an arithmetic description of Matrix B is included in Figure 3.
,
.
l
-
CONSTRUCTION OF MATRIX B
The programmed restraints
Twelve cultivation paddocks, distinguish ed by letters A to L in Figure 1,
were available for cropping in the 1964 planning period. Restraints R1 to R12
represent the acreages of arable land in these paddocks
Restraints R13 to R23 in Matrix B are defined identically with restraints R6 to
R16 of Matrix A. In addition the feed restraints R24 to R3.1 of Matrix B are
identical with the corresponding feed restraints, R18 to R:!� of Matrix A.
.
The activities considered
Six alternative crops were considered for each cultivation paddoc k These
crops were wheat, early grazing oats, late grazing oats, early grazing sorghum,
late grazing sorghum and lucerne.
The vector of a particular crop activity on a particular paddock represents
the production process that would be operative if the whole of the paddock was
committed to that crop. This vector is derive d from weighting the relevant crop
production process for each soil type in the paddock according to the proportion
of the p addock which is made up of that soil typ e and then summing over all
soil types in the paddock. In other words the new p addock- crop production
processes are weighted linear combinations of the soil-type processes of Matrix
A. The procedure used to determine these vectors is elaborated by Rickards &
Musgrave ( 1965) in a recent article.
.
,
,
,
C:>
m
11
13I
7
8
12
9
10
34
33
32
30
31
24
25
26
27
1
28
29
23
19
20
21
22
18
114 1
15
16
17
_
1
6
5
4
1
2
3
R
..
Jan.-Mar. D. M. E.
Apr. -June D. M. E.
July-Sept. D. l\1. E.
Oct.-Dec. D. M. E.
Grz. sorgh. supply
July-Sept. D. M. E.
"Consumption feed"
E.
Oct.-Dec. D. M. E.
"Oats feed"
May-June D. M.
Jan.-Mar. D M. E.
Apr.-June D. lVI. E.
July-Sept. D. M. E.
r
�'Transferable feed"
as
Paddock A
Paddock B
Paddock C
Paddock D
Paddock E
Paddock F
Paddock G
Paddock H
Paddock I
Paddock J
Paddock K
Paddock L
P tu re X
Pasture Y
Pastu e Z
1\-iaximum stud ewes
Lucerne restraint
lVlax. late grz. sorgh.
Wheat max.
January tractor
Feb.-Mar. tractor
December tractor
Supplementary sheep unit
�
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D. M. E.
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s��>plemc_:ltary sheq:
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Feb.-Mar. tntctor
Deccrnbcr t1·actor
\Vhcat m<tx.
Janu..lry tractor
Lucerne res trairrt
Max. late grz. sorgh.
!\1aximum stud ewes
Paddock A
Paddock B
Padd o c k C
Paddoc k D
l>addock E
Paddock F
Pack\ock G
Paddock H
Paddock I
P ad d ock J
Paddock K
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I>asture X
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unit
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Supplementaiy sheep
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l\rfaximun1 s t u d � \Y C �
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, 24 ! Jan.-.1\lar. D. M. E .
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January
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P. A. R I C KA R D S A N D W. 0 . M c C A R T H Y
1 90
While a full complement of alternative crops w as initially considered f o r e ach
cultivation paddock, discu ssions with the farm operator revealed that eleven of
these alternatives were agronomically infeasibl e . A fter deleting these, sixty-one
crop-p addock alternat ives remained and the s e were sp ecified in activities P1 to P (n .
M atr i x B w as completed by specifying th ree n ative pasture activities Pr;2 to
P 6 4 , ten feed transfer activities P fj ;; to P74 and nine livestock activities P 7r, to P 8 3 •
T h e s e 2 2 activities , P t; � to P R � , a r e defined as for activiti es x 2 7 t o x -I H in Matrix A .
T H E P LA N FROM M ATR IX B
The programmed solu tion to M atrix B is included in Table 2. A compari son
of plans 1 an d 2 shows th at the grossly impracticable placement of crops in the
former pl an h as l argely been corrected in plan 2 in which th e pl acement of crops
is restr ained by pa ddock bou ndaries . On the other h and, inspecti on of the latter
plan reveals that four of the twelve p addocks , n am e l y B , C, I , an d L, contain
more than one crop . S u ch a solution would not nor m ally be acceptable to the
farm opcrato r . fj Thu s , while the construction and sub s equ ent solution of Matrix
A ctivity
P,
P,
P..
P,
P ,o
P,
P,1
P"
P,l
p,
p ,,
p,,
P"
P,,
P ,1
P oo
P ,m
Po::
Po,
Poo
Poo
P os
Po"
P.,
P,
P,
p,,
P'"
P,
P,"
PLAN 2-THE
TABLE 2
PROG R A M M E D
Early o a t s paddock A
E a rl y oats p addock B
Lucerne pad dock B
E a r ly oats paddock C
L ate grazing sorgh u m p addoc k C
Earl y grazing sorghum paddock D
Late grazi ng sorghum p addock E
Late oats paddock F
Early g r azing s o r ghum pad d ock G
Whe a t paddock H
Early o ats p addock I
Earl y grazing sorghum paddock I
Late grazi n g s orghum paddock .I
Whe a t p a d d ock K
W heat paddock L
Late grazi ng sorghum paddock L
N a ti v e pasture X
Native pasture Y
N a t ive pasture Z
May-J une oat transfer
July��eptember o a t t ransfer
J an u a r y- M a rch feed trans fe r
April-Jun e feed transfer
October-·December co n s u mpt i o n tr ansfer
Janu ary-March ronsumption transfer
April·-.f une con su mption transfe r
J u l y-September consumption t r a n s fer
Stud sheep
Wethers
Crop wethers
Parti all y compet itive cattle
Crop fat teners
P s1
Psa
Surp lus R esources
R i ll Wh ea t maximum
R,n January tractor
SOLUTION
FRO M
Unit
Acre
Acre
Acre
Acre
Ac r e
A cr e
A c re
Acre
Acre
Acre
Ac re
A cr e
A cr e
A cr e
A c re
D.M.E.
D.M.E.
D.M.E.
D . M .E .
D .M.E.
D.M.E.
D.M.F.
We ther
Wether
ewe
Breedi n g co w
Steer
B ag
Hour
A ctivity
Lew• I
Acr e
Acre
Ac re
Ac r e
D .l'v1 . E .
Breed i n g
M ATRIX [l
25.0
49.8
58.8
30.2
60 . 4
95.2
1 44 . 0
70.3
73.8
7 1 .3
1 90 . 0
244 . 5
1 07 . 1
505.9
1 7 8 .7
1 68 . 9
1 , 8 7 5 .0
7 62 . 0
2, 8 5 7 .0
1,83 5.2
32.8
1 3 , 1 94.6
1 5 , 6 6 3 .4
1 0, 8 0 7 . 0
1 5, 0 69 . 3
4 ,7 8 1. 8
1 5,687 . 5
5 00 . 0
7 64 . 1
3 , 65 5 . 1
97.9
1 1.7
1 , 07 5 . 3
83.1
Revenue £ 27 , 4 65 . 1
0 As
far as t his study is concerned a necessary co n dition for an accep table f arm
plan would be t h a t ( with the e x cep tio n of P addocks G , I , a nd L, f or which temporary
subdivision fences are available ) the whole of e ach c ultivati o n paddock should be placed
e i ther under a single crop or und er a co mbinati on of a gr o n o m ically compatible crops.
L I N EA R P R O G RA M M I N G A N D PRACT I CA B LE FA R M PLA N S
191
B h as resulted i n a n improvement o n real ity, i t appears likely that a rigorous
optimum which is also acceptable to the farm operator could only be reached using
integer programming techniques . This would involve specifying integer restraints
for alternative crop activities on e ach cultivation paddock so that each paddock
is forced to accept one crop alone in the final plan. Unfortunately, if the experi
ence of B ennett & D akin ( 1 9 6 1 ) c an be t aken as a guid e, probl ems of slow
convergence to an optimum can be expected with matrices of the size used in
this study.
Alternativel y , if the conventional stati c progr amming solution contains only
minor infeasibilities, then the technique discussed by Rickards & Musgr ave ( 1 9 65 )
for examining border plan7 information c an be appli e d Systematic use of this
technique in s uch cases all ows the programmer to re ach a practicable solution
which is not signific antl y different from the "true" optimum.
A closer l ook at the paddocks containing more th an one crop shows that the
misallocation problem in plan 2 is not serious. In f act the crop combinations in
paddocks I and L are q uite acceptable as the use of tempor ary subdivision fences
in these paddocks is normal management practice . P addock B is divided in its
use betw een e arl y o ats and l ucerne in the ratio 4 : 5. This is an acceptable
combinati on, however, since both crops would be required to provide winter
grazing for the 500 stud ewes of plan 2. On the other h and, the recommended
combination of crops for paddock C, n am el y e arl y oats ( P7 ) and late grazing
sorghum ( P 1 0 ) , is unacceptable since it is implicit that these crops provide forage
for different clas ses of l ivestock.
Clearly either P7 or P10 mus t be excluded from plan 2 in order to reach an
acceptable farm pl an . Thu s the border plan s at both the upper and lower border
prices for each of these two activities were analyzed . The plan corresponding to
the lower border price of P7 was sel ected as the practicable solution to farm
planning and is referred to as plan 3 in further discussion . The only difference in
the b asis v ariables of p l an 3 is the repl acement of P7 ( early oats paddock C) by
P9 ( early grazing sorghum p addock C ) . Thu s , a compatible pair of crops is intro
duced to p addock C. Practicability in the programmed s olution has been achiev ed
in pl an 3 at a revenue decrement of only £ 1 0.22, which is smaller than the
decrement resulting from other border plans . In the interest of brevity, pl an 3
will not be enumerated since it is almost identical with pl an 2.
While i t is reassuring t o the theorist that a precis e s olution t o a farm planning
problem can be obtained within the progr amming framework by the use of
sensitivity analysi s , the practitioner may argue that such techniques only serve to
introduce an unwarranted air of accuracy into f arm planning . For instance, an
extension worker, having arrived at plan 2, may feel that it is so close to a
practicable solution that he is prepared to make the fin al adjustment arbitrarily
after discu ssion with the farm op erator. Where the required adj ustments are only
small in m agnitude, as in the present study, this is probably an acceptable
approach. Onl y experience with the use of matrices which include paddock
restraints will tell whether an orthodox programming technique c an usually be
expected to provide a s atisfactory approximation to the "true" optimum. Such
experience should also indicate the usefulnes s of th e border-pl an techniques used
in this study.
.
7 Most
comput er routines for linear p r ogram m i ng problems are abl e to calcul ate
the mi nimu m change in the objective coeffi cients of each current b asis act ivity which
would be necessary to i nd uce a change in b asis variable s . Th e value of an obj ective
coeffi cient after adding this cha nge to i ts original value is called the "b order price" while
the new plan that becomes optimum at a "'border price" of an activity is known as the
"border plan " . Rickards & M u s grave suggest an exam ination of alternative b order plans
and selection of that plan which overcomes the problem of crop incompatibility with
the least decrem ent in revenu e .
P. A . R I C KARDS A N D W. 0 . M cCARTHY
1 92
EVALUATION O F T H E P R O G R A M M ED SOLU TION
Normative a p p l i cation o f the p rog ram med sol ution
Tr aditionally, the normative val ue of the computed so lution is gauged by
comparing th e reve nue from th e computed plan with th at for the observed plan .
In order to es timate the l atter v alue, the production activities included in the
observed pl an for 1 9 64 were iden tifi ed, as closely as possible, with corresponding
activities in M atri x B . T h e anticipated revenu e from the obs erved plan was
es timated to b e £27 , 2 3 7 . 0 , which falls short of that from pl an 3 by £ 3 , 2 1 7 . 9 .
This val u e , of cours e , does not include a n allowance for the costs of changing
enterprise combinations and is therefore an upwardly bi ased estimate of the
financial su periority of the computed solution when such costs exis t . Other differ
ences between the pl ans are sum m arized in Table 3 .
A CoM P AR ISON
OP T H E
Major Crop or
Li vestock Acti vity
THE
TABLE 3
LEVELS OF MAJ OR ACTIVITIES IN PLAN 3 AND
O B SERVED PLAN FOR 1 9 64
---
Wheat
G razing oats
Forage sorgh u m
Lucerne
Flock ewes
Stud ewes
Wethers
Crop wethers
P artially competi tive cattle
Ful l y competitive cat tl e
Competitive vealers
Crop fatteners
A.cre
Acre
Acre
A cre
!:lreeding
Breed ing
'Nether
Wether
ilreeding
Breeding
Hreeding
Steer
Level i n
Obser ved
Plan
Level i n
Pl an 3
Unit
------ ---
6 92 . 6
5 1 6. 6
60 .0
545.2
1 , 20 0 . 0
500.0
5 00. 0
755.9
25 9 .0
8 20 .2
202.8
ewe
ewe
cow
cow
cow
500 .0
754.0
3 , 674.0
98.0
9 3 .0
17.0
30.0
8 .0
--
Revenue
Difference
in Level
.£ 2 7 , 4 5 4 . 9
+
-
+
-
63.3
22 1 . 6
740.2
3 4 2.4
1 , 20 0 . 0
2 54 . 0
3 , 6 74 . 0
5.0
+
1 7 .0
30.0
8.0
+
+
I
T
- -- - ----
£24, 2 3 7 . 0
£3,2 1 7 .9
Differences of some importance are that all the flock ewes and part o f the
lucerne and grazing o ats acre ages in cluded in the obs erved plan are replaced by
wethers and grazing sorghum in plan 3 . This raises a pertinent question of
whether plan 3 could have been put into oper ation in 1 964 , given that it was
available in adv ance .
Certainly it s eems that there would be little difficulty
in adjusting the acreages of annu al crops in the observed plan to those indicated
in plan 3 . On the other hand the major reorganization required for sheep activities
could only be completed in th e short run by s ellin g all flock ewes and repl acing
the s e by purchased wethers .
Livestock trans actions such as this would inevitably result in long-run financial
and stock man agement difficulties . In the first instance the difference b etween
the s al e price and book value of flock ewes woul d be considered as property
income subject to taxation. Secondly, in purchasin g wethers there would be a
possibility of reintroducin g certain internal paras ites which had been eradicated
from th e property .
Hence in this particular study the normative application of the programmed
solution, while being feasibl e , is not a convenient plan for management to adopt
immediately. The apparent revenue advantage of the computed s olution is upward ly
L I N EA R PR O G R A M M I N G A N D PRACT I CA B L E FA R M PLA N S
1 93
biased b e c au s e of co s t s involved in short-run ch anges in the level of livestock
activities . This p roblem could be overcom e by introdu cing time as a variabl e in
the linear programming model . Exampl es of this type of anal y si s are provided
by T hr o s b y ( 1 9 62 ) and P e a rs e ( 1 9 63 ) , who us e d "dyn amic" lin ear p rogramming
to determine o pt i m u m p attern s of pasture improvement.
While the model used in this study f ail e d to p rovi de a p at solu t io n to farm
pl annin g for th e case proper ty, the aaalysis of the farm finn is still of valu e. A
ch aracteristic of the lin ear p rogrammi n g ro utine is that beside solving the
allocation problem it al s o solves the valuation problem . That is, it calculates an
optimum set of v al u es for th e resources available to the farm operator. Thes e
values are referred to as shadow price s . It will be shown below that, even in
cases where strict appl ication of th e programm ed solution is undesirable, th e
combined u s c of both the s olution its elf and th e shadow p rices p ermits the an alyst
to determi ne the de s ir abl e avenue of p ro p e r ty reorganization in both the planning
p e riod consid ered and in future periods .
Applicati on of s hadow prices to farm planning
Shadow p rice s are c alcul ated for all non-basis activities in the final solution.
In the cas e of re s ourc e s which are limiting in the final plan, these p ri ces indicate
the m argin al value products ( M.V.P . s ) of thes e res ources . In co ntrast the
shadow prices for ori ginal non-basis or "real" activities indicate the margin al
opportuni ty costs ( M . O . C . s ) of incl uding these activiti es in th e basis of the fin al
,
TABLE 4
MARG INAL VA L U E PROD UCTS OF RESTRAINTS IN LnHTED S U P P LY IN PLAN 3
R estrain t
Unit
R,
IL
R:�
R,
R,
Rn
R,
R,
R,
Rw
RLL
R"
R.o
R"
R"
R,,
Rn
R,"
R,
R,
Ron
R"'
R,,
Roo
R,
R'"
R2,,
R:,o
R"
Rn,
R""
R,,
P addock A
Paddock B
11 addock C
Pa ddock D
Paddock E
P ad dock F
Paddock G
P addock H
P a ddock I
P ad d ock J
Pad dock K
Padd ock L
P a sture X
P e� s ture Y
P asture Z
M aximum stud ewes
Luce rne restraint
M aximu m l ate gr azing sorghum
Feb ruary- M arch tractor
December tra ctor
Supplementary sheep uni t s
J anu ary- M arch tra nsferable D . M . .E .
Ap ril-J une tr ansferable D . M . E .
J uly-September transferable D . M . E .
Octobe r-D ecem ber transferable D . ,�l . E .
M a y-J une o at D . M . E.
July-September oat D . M . E .
Ja nuary-Ma rch consu mption D .M .E .
April-J u ne cons umption D . M . E .
July--September consumpti on D . M . E .
October-D ecember consumpti on D . M . E .
Grazing sorgh u m supply
Acre
Acre
Acre
Acre
Acre
Acre
Acre
Acre
Acre
Acre
Acre
Acre
Ac re
Acre
Acre
Breedin g e we
D.M.E.
P l a nting acre/ye ar
Hour
D . M . E.
D . M.E.
D. M.E.
D.M .E.
D.M.E.
D.M.E.
D .M.E.
D . M.E.
D.M.E.
D.M.E.
D . M.E.
D . M . E.
D . M .E .
M. V.P.
in £ 's
1 .34
6.4 3
5 . 60
3 .34
2.29
7.25
7.82
6. 0 6
4.53
7.82
7 . 47
6 . 00
1 .7 8
1 .32
1.18
5.88
0 . 1 58
7. 8 2
4.56
5.3 3
0 .49 1
0. 1 1 2
0. 1 7 3
0 . 3 45
0.082
0. 1 73
0. 346
0. 1 12
0. 1 72
0.346
0 .082
0. 1 55
P. A. R I C KARDS A N D W. 0. M c CARTHY
1 94
plan in the least sub-optimal way. These values c an be used to gauge th e
efficiency of res ource use within the farm firm .
Table 4 includes the M.V.P . s of restraints specified in Matrix B which are
limiting in the final plan.
The M.V . P . s of cultivation land vary from £7 . 8 2 on p addocks G and J to
£ 1 . 3 4 in paddock A . These values indicate the per acre economic rent earned by
paddocks of varying s oil-type dis tribution and p rovide a guide to predicting the
relative profitability of expandin g cultivation activities into new paddocks of
known s oil -type dis tribution . The M . V . P . s of grazing l and vary from £ 1 . 7 8 on
cleared brigalow s crub country to £ 1 . 1 8 on cle ared box-sand alwoo d country.
The l ate grazing sorghum restraint, R 1 8 , has an imputed value of £7 . 8 2 ,
indicating that farm revenu e could b e subst antially improved b y increasing the
acreage of this crop . On the other han d , the static linear p rogramme does not
take into account the high vari ability of ou tcomes from this crop . Thus the
operator's preference for restrictin g th e area of forage sorghum could well be an
expression of risk preference , in which cas e the restriction is realis tic.
The tractor hours avail able for cultiv ati on operations became l i miting in both
the D ecember an d February-March periods and M . V . P . s of £ 5 . 3 3 and £4 . 5 6
respectively were imputed t o these resources . These values are far i n excess of the
cost of incre asing the cultiv ating capacity by either hiring more labour or operating
a larger plant with the current labour supply. Thi s indicates a major weakness in
property organiz ation .
The M . V . P . s of limiting general-pu rpose feed resources indicate that the
m arginal value of a D . M.E. unit of "transferable ' ' feed varies from a minimum of
£ 0 . 0 8 2 in the October-December to a maximum of £0 . 3 46 in the J uly-S eptember
peri od. An apprais al of techniques for alleviating the acute feed shortage in l ate
winter and early spring seems warranted . Two alternatives are examined, namely
the use of purchased grain as opposed to home-produced sil age for supplementary
fe eding during the winter month s .
There seems t o be little likelihood that s upplementary grain feeding would
ever be j ustified in a normal season. For instance, the c o s t of feed oats would
have to f all to 4 s . 6 d . per bushel or feed wheat to 8 s . per bushel befo re grain
s upplements could be provided at less than £0 . 3 46 per D . M . E . unit. In co ntrast,
the profitable u s e of silage for s upplementary feeding seems plausible . It is
estimated that with a standing forage crop marginally valued at £0 . 1 1 2 per D . M . E .
during J anuary t o March and allowing 1 5 s . p e r ton harvesting a n d ensiling costs
and 2 5 per cent deterioration in feed value during storage, then silage could be
fed out for £0 . 2 0 6 per D . M . E . in mid and l ate winter. This cost is £ 0 . 1 40 per
D . M.. E. less than the value imputed to general purpose feed during this perio d .
T h e M . O . C . s of all sub-optim al activities will n o t b e included h ere due to the
restricted space available . Ins tead , only the v al ues imputed to sub-optimal live
stock activities are listed.
P75
P79
P80
P81
Activity
Flock ewes
Fully competitive cattle
Fully competitive vealers
Partially competitive ve alcrs
M.O.C.
£0.24
£ 1 3 .72
£ 1 1. 3 0
£ 1 .28
per
per
per
per
breeding
breeding
breeding
breeding
ewe
cow
cow
cow
While no flock ewes are included in plan 3, the M . O . C . of this activity ( £ 0 . 2 4
p e r ewe ) is sufficiently low f o r t h e programmed solution t o b e sensitive to changes
in the input-output relationships of flock sh eep. On th e other hand, s tud sheep
h ave been restrained to 5 00 in plan 3 by R1 6 which is marginally valued at £5 . 8 8
i n this sol utio n . These values indicate a disequilibrium with the market and a
need to expand the s tu d enterprise at the expense of flock sheep. Finally, the
L I N EA R P R OG R A M M I N G A N D PRACTI CA B L E FA R M PLA N S
1 95
M . O . C . s of P79 and Pso are so high that plan 3 woul d be completely insens ttlve
to an y li kely changes in either pro duction rel ationships or product price s of th ese
fully competitive cattle activities .
A t this stage, having examined b oth the programmed sol ution a n d th e avail
able shadow prices, we are in a position to d ete rmine th e direction i n which the
operator s h oul d reorganize production i n order to reach l o ng ru n stability with the
market. In brief , it appears that the followi n g steps sho ul d be taken :
-
The stud ewe ent e rpris e should be in cre a s e d at the expe n se of flock ewes .
The wether flock sh ould be increased by retaining the annual cullin g of
2-tooth males from the stud fl ock.
111 . The acreage of grazing s o rgh u m should be incre ased at the expense of
grazing o ats and lucern e .
iv . T h e possibility o f producing silage from s u mm e r crops should be further
inves tigated with a view to s u p plementary wi nte r feeding .
v . The w o r ki ng c ap acity of th e cu lti v ati n g pl ant sh oul d be increased.
i.
n.
Extension of experience from an i n d i vidual study
Exp erience gained in this stud y indicates that linear programming offers a
useful app ro ach to individu al farm pl anning. The limiting factor to its application
in isolated studies will pro b abl y be the high cost involved. For i ns tan c e given full
ti me devotion to the task, the pres ent s tud y would have taken the anal yst ap p ro x i
m ate ly three months while cash expenses amounted to £ 1 00 . Th u s the total cost
of th e st udy could be set at approxim at el y £ 600. Gi v e n the turn over of the
property, th is is s c ar c ely an exorbitant figur e but it would certainly fall ou t si d e
the budget of any publi cl y fin anced exten sion auth ority Hence, as far as isolated
studies are co nc erne d it would s eem that the farm op erator would h ave to be ar
most of the expense.
In contr ast, the use of programming techniqu e s for f arm pl anning becomes
more attractive as the number of f arms in a di s t r ict which require this service is
incre ased. For instance the auth ors consider that the cost of progran1ming
additional properties in the Goondiwindi district woul d rap idly diminish . While
it would still be necess ary to interview e ach farm operator in order to est ablish
the unique characteri stics of his property , m any of the i nput output coefficients
neces s ary for m atrix construction c ould be drawn from the pool of information
already available. Thus it is estimate d that a practicabl e f arm plan could be
achi e v e d for p r op e rt i es simil ar in size and c ompl exit y to "Trev ann a Do wns
in
approximat ely th ree w e eks
In additio n c ash costs ( incl uding data preparation
and pr o c e s sing ) coul d b e exp e cte d to appro a ch £ 1 00 .
Co sts of this order m ay still plac e linear programming analysis o f individu al
farms out of re ach f or publ ic extension agencies unless the farm operators
involved are prepared to bear p art of the cost. On the o ther h and, f arm man age
ment club a dvis ers and pri v ate consultants s hould find that the co s t economies
forthcoming as the number of p r ogr amm in g stu dies incre ases are such as to make
this form of farm pl anning fin ancially attr active to th ei r c li e nts
,
.
,
,
-
"
.
,
.
S U M MARY
While th e liter ature on th e application of line a r programming m e th ods to
agricultural problems is extensi v e , little attenti on has b een given to the use of
pr og r ammin g for p ro duction pl an ning on case stud y properties . Furthermore, mo st
authors who have concentrated on thi s 1 atter appro ach have applie d it to farms
with soil types which are, or which ar e assumed to be, homogeneous as regards
P. A . R I CKA R D S A N D W. 0 . M c C A RTHY
1 96
production . In practic e, in Australia for exampl e , such homogeneity is true of only
a small proportion of the total universe of farms. Thu s , the literature i s particularly
deficient in applications of linear programming methods to real farm situations
of this type.
Where a number of soil types are represented on a property, each type having
a unique set of production functions for feasible agricultural cropping, manage
ment is faced with an extremely complex problem of determining the optimum
allocation of res ources among altern ative production activities . Nevertheles s , this
study on a property in the Goondiwindi dis trict has indicated that even under
s uch circumstances a practicable farm plan can be developed. This can be done
by progressively revising and reprogramming the original matrix with the help
of the farm operator.
Normative application of the s olution derived in thi s way may not always be
advisable, particularly if it in volves major short-run adjustments to existing live
stock enterprises . This does not necess arily deny the value of programmed
s olution s . Rather it mean s that the programmed s olution cannot be used merely
as a blue print for farm planning but that a more skilful interpretation has to be
placed on the programmed results . Combined use of both the s ol ution its elf and
als o of shadow prices imputed to final non-b asis activities permits the analyst to
determine the direction in which the farm ope rator should reorganize his
production pattern in future periods .
If farm management workers are prep ared to adopt s u ch an approach, as well
as to specify the production planning problem more precisely th an hitherto, then
linear programming can be of much greater u s e as a f arm planning aid . Under
these circumstances the limiting factor to its application will probabl y be the
expense involved rather than imperfect appreciation of the method as at present .
A C K N OWLEDGM E NTS
The authors would like to express their gratitude to the eight graziers who
provided the survey information, and particularly to Mr. H. A. McKechnie,
M . L . A . , the owner of " Trevanna D owns ", and his son, Mr. D. McKechnie, whose
generous co-operation permitted this study to be pursued to its conclusion. The
work was financed from res earch expenditure provided by the Australian C attle
and Beef Research Committee. Thanks are also due to Mr. W. F. Musgrave for
his advice on programmin g techniques .
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