Group Title: Economic analysis of farm system constraints in St. Elizabeth, Jamaica
Title: An economic analysis of farm system constraints in St. Elizabeth, Jamaica
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Permanent Link: http://ufdc.ufl.edu/UF00071946/00001
 Material Information
Title: An economic analysis of farm system constraints in St. Elizabeth, Jamaica
Physical Description: 12 leaves : ; 28 cm.
Language: English
Creator: Tierney, Carolyn
University of Florida -- Food and Resource Economics Dept
Publisher: Food and Resource Economics Dept., University of Florida
Place of Publication: Gainesville Fla
Publication Date: 1989?
 Subjects
Subject: Farms, Small -- Economic aspects -- Jamaica -- St. Elizabeth Parish   ( lcsh )
Sustainable agriculture -- Jamaica -- St. Elizabeth Parish   ( lcsh )
Genre: non-fiction   ( marcgt )
Spatial Coverage: Jamaica -- Cornwall -- St. Elizabeth
 Notes
Statement of Responsibility: Carolyn Tierney.
Funding: Electronic resources created as part of a prototype UF Institutional Repository and Faculty Papers project by the University of Florida.
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Bibliographic ID: UF00071946
Volume ID: VID00001
Source Institution: University of Florida
Holding Location: University of Florida
Rights Management: All rights reserved by the source institution and holding location.
Resource Identifier: oclc - 74436738

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An Economic Analysis of Farm System Constraints
in St. Elizabeth, Jamaica

Carolyn Tierney

Department of Food and Resource Economics
University of Florida, Gainesville, FL


Abstract: The role of the small farm sector in economic development have been
neglected in past economic development policies. This study involves an economic
analysis of constraints to vegetable production in St. Elizabeth. Farmers cite
lack of irrigation, low farmgate prices and uncertain markets as the primary
constraints to increased production. Farmers are being encouraged to improve
efficiency and reduce per unit costs of production in order to produce more
competitivEly for export.
Data on costs of production and resource availability are being gathered
from farm records and surveys. A multiperiod linear programming model will be
used to analyze constraints, production decisions, effects of changes in prices
and resource availability, and the acceptability of alternative technologies,
varieties, and production practices. The model will be designed to reflect
farmers' actual choices and constraints, rather than to prescribe an optimal
alternative. A "safety first" approach to profit maximization is assumed, where
food production is given priority. Preliminary results indicate that labor
constitutes a large percentage of costs of production and that availability of
labor is the most binding constraint to increased production and farm income.
Low yields and prices also limit farm income.

ECONOMIC BACKGROUND TO JAMAICA
Jamaica is the third largest Caribbean island, with 4,411 square miles,
and a population of 2.5 million. The economy is predominantly based on
agriculture, but the bauxite industry and tourism are also very important as
sources of foreign exchange. Although Jamaica is considered one of the more
developed Third World countries, it is still plagued with many serious economic
problems. Unemployment has remained at about 24% since 1943. Income
distribution is highly skewed, with urban incomes being twice as large as rural
incomes (Boyd, 1988). A larger share of the labor force is employed in
agriculture (39%) than in any other sector, yet average earnings in this sector
are much lower, contributing significantly to the unequal distribution of income
(Jefferson) Jamaica relies heavily on imports, a situation which led to
widespread inflation and instability when IMF imposed devaluations led to higher
prices of imports, particularly food (Boyd,1988). The bauxite and tourism
industries have been a boon to the Jamaican economy in the past. However,
excessive reliance on these industries as a source of foreign exchange has left
the economy vulnerable to changes in external economic conditions (Girvan).
Since the decline of the bauxite industry in the late 70's, the tourism sector
has received much government support in order to make up for deficiencies in
foreign exchange earnings. However, tourism's net contribution to foreign
exchange is dampened by the large import content of the tourist industry, which
was estimated to be 40% (Jefferson).
Throughout the development process there has been a general weakness of
intersectoral linkages in the Jamaican economy. Industrialization programs have









failed to create significant employment and have been costly and ineffective.
Industries in rural areas have few links with the agricultural sector and have
been detrimental to rural agricultural economies by increasing the reserve price
of labor.(Jefferson)
It is a premise of this study that Jamaica's economic problems are due in
part to the historical neglect of the role of the small farm sector in achieving
long term, sustainable growth and development, and lack of recognition of the
critical role of this sector in achieving structural transformation. Moves
towards a more sustainable development path including efforts aimed at
development of the small farm sector, encouragement of efficient use of
resources, and development of domestic industry and intersectoral linkages, are
integral to the long run resolution of these problems (Johnson and Kilby).
This study focuses on vegetable farmers in southern St. Elizabeth parish.
They represent onL segment of the small farm sector, which comprises a large
portion of the Jamaican population. Identification of the factors which impede
these farmers in their efforts to increase production and income could serve as
a guide to development of more effective policies and programs for promoting long
term growth and reducing dependence on imported food.
REVIEW OF PAST AGRICULTURAL DEVELOPMENT PROGRAMS
Since the 1940's, the emphasis of programs designed to stimulate
agricultural production has been on subsidies and loans. Between 1947 and 1968,
subsidies, loans, and funds for land reform took up more than half the budget
for agricultural development. Most programs were failures in meeting production
goals (Jefferson).
One explanation for the failure of these programs is the emphasis on loans
and subsidies. This approach assumes that cash is the constraining factor to
increasing the productivity of labor and land on small farms. It is more likely
the land quantity and quality, insecure tenancy, fragmentation, poor technology,
and inadequate water supplies that are the chief constraints. Cash was usually
used for short-term consumption because farmers could not make productive use
of the cash on their limited land resources (Girvan, 1976). From 1946 to 1956,
37% of the development budget was devoted to welfare oriented programs such as
education, public health, and other public services. While these rural social
service programs raised the standard of living in rural areas, they did little
to remove the impediments to increased production, so have done little to
increase the productivity and profits of small farmers.
Past economic policy has emphasized industrialization, export production,
urbanization, and export of manufactured goods, while neglecting the problems
of traditional agriculture. Identification and alleviation of constraints on
small farm production could allow Jamaica to become more self sufficient in food
production, and enable the small farm sector to make its full contribution to
economic growth.
DESCRIPTION OF THE FARMING SYSTEM
This study is being carried out in South St. Elizabeth Parish, Jamaica.
The region was chosen because a significant amount of the vegetables, fruits and
root crops consumed in Jamaica are produced there. The indigenous dry farming
techniques developed there allow production of a wide variety of crops, despite
the harsh conditions. The focus will be on farms between .5 and 5 acres in size.
The farmers in the area have larger holdings than in other parishes due to the
low carrying capacity of the land. The elevation is between 1100 and 1900 feet.
The topography varies from flat to moderately sloping plains, with occasional
rocky hills, and is surrounded by mountains. Farmers mainly cultivate sluort term










vegetable crops including tomato, sweet pepper, escallion, onion, cassava,
potato, cucumber, carrot, melon, beet, thyme, yam, peanut, pigeon pea, and red
peas. Some farmers also raise goats, pigs, and chickens.
Production is primarily market oriented. The major cash crops are
escallion, tomato, carrot, thyme, onion, and melon. Crops grown mostly for food
or a small local market are gunga pea, red pea, cassava, yam, pumpkin, and
cabbage. An important component of the system is guinea grass which is used as
a mulch to retain soil moisture, keep the soil cool, and hence to promote crop
growth. Most farmers keep a portion of their land resources in guinea grass to
be used as an input to production.
An estimated 50% of household food is purchased, mainly things that cannot
be grown on the farm such as bread, rice, milk, meat, fish, and beverages.
Farmers reserve a piece of land to grow the main food crops, yam, gunga pea,
red pea, cassava, and assorted vegetables. Virtually none of the food grown on
the farm is stored or processed. When they do not have any it must be purchased
locally, so even these food crops are grown partly for the local market.
CONSTRAINTS
Farmers have identified lack of water for irrigation as a primary
constraint to increased production, although they also recognize that widespread
irrigation would cause excess supply and low prices due to lack of markets. They
also cite difficulty in hiring labor and the high cost of labor, as well as
uncertain markets and low prices due to the government's open import policies,
as additional disincentives. Many of the vegetables grown in the region can be
produced at a lower cost in other countries and farmers in Jamaica cannot
compete. Farmers are being encouraged to improve efficiency in the use of
purchased inputs to lower costs of production and become more competitive, and
to adopt drought resistant varieties of tomato which have a longer shelf life
and are suitable for processing.

CROP CULTIVATION
Crops are planted at various times throughout the year, but the main season
starts in August, when fields are cleared, and planting is done with the start
of the rains in September. Planting is done January to March for an early rainy
season which occurs between April and June. Some farmers plant a catch crop in
May or June in anticipation of higher prices during times of shortage, and to
get an additional crop out of the year.
Escallion is an important cash crop in the vegetable system. The purpose
of the escallion within the system is to maintain a steady cashflow throughout
the year. Many use income from escallion farming to finance other farming
operations and to maintain the family and finance the children's education.
It is a low risk, drought resistant, low labor input perennial crop with a ready
market in the tourist areas. After planting, escallion requires little
maintenance other than occasional weeding. Harvesting is carried out on a year
round basis. During the dry season they can be harvested every 6-8 weeks, and
in the wet season every 4-5 weeks. Prices in the dry season can go as high as
$8-$9 per pound (farmgate) but drop as low as .50 per pound in the wet season
when rain causes excess supply. Escallion is planted by transplanting bulbs from
another area. Farmers plant new escallion or enlarge their existing fields when
the price of these "seed escallion" is low. Production practices are fairly
homogeneous. Planting density varies, but is dependant on the location; farmers
at lower elevations face hotter and dryer conditions and have less trouble with
"frobt" which causes fungus and diseases, so they can plant escallion closer










together. At higher elevations it is cooler and there is more rain, so escallion
must be spaced more widely to minimize disease and allow more wind circulation.
Carrot and tomato are also common cash crops in the system. Carrot is a
low risk crop with a stable market throughout the year, and is not very
susceptible to pests so requires little spray. If prices are low when the carrots
first mature, they can remain in the ground up to 4 weeks until prices are more
favorable. Within a 12 month period, 3 carrot crops can be grown on a given
piece of land, whereas only 2 crops of tomato can be produced. While tomato is
also a common cash crop, it is considered to be a high risk crop requiring more
frequent spraying, but under favorable conditions it can be very profitable.
Marketing is done mostly through higglers, processing plants, and parochial
markets. There is a vegetable processing plant, Jamaica Vegetables Ltd., located
nearby in Bull Savannah, which could provide a market for much of the locally
produced vegetables. However, this plant cannot be profitably operated on a year
round basis and has been closed for several years. The higglers provide the
primary marketing outlet for small farmers. The higgler system has been
criticized as being costly and inefficient in the past. Lowering marketing costs
through provision of credit, training, infrastructure, more efficient
transportation systems, and other forms of support for higglers, may alleviate
the marketing constraint for small farmers. A detailed study of the feasibility
of such a program is beyond the scope of this study. Information and results
from the model analysis will give some indication of the value of such a program.
The primary objective of this study is to identify the constraints on the
farming system which affect production decisions and develop a quantitative
assessment of the most binding constraints to increased output and productivity.
Given these constraints, the feasibility of introducing new technologies or
production alternatives into the farm system will be evaluated, as well as the
effects of these changes on the farm system and production decisions. Changes
in economic conditions, either policy induced or resulting from market forces,
will also be evaluated to determine the sensitivity of production decisions to
these changes.

METHODS
Data will be collected by means of farm records and surveys. A record
keeping project was implemented, yet due to farmer's unwillingness to maintain
usable records for any length of time without frequent supervision, this method
of collecting data is being discontinued. Data is now being collected from
surveys of 25 farmers. Five farmers will be chosen in five separate villages
based on their willingness to cooperate. These farmers will be in close
proximity to each other to allow for several surveys to be completed in one day.
In the first survey, information on resource availability, land use, and
cropping patterns will be recorded. The proportion of land in each crop and the
size of each garden will be estimated and used to develop cropping calendars for
each farmer. These can be used to compare production patterns prescribed by
the model to farmers' actual production decisions in order to validate the model.
During the second survey, data on input requirements for each crop activity
will be gathered, and farmer's spraying procedures will be observed to obtain
uniform measurements of pesticides. Two visits will be scheduled during the
harvest season to gather data on yields and prices for the farmer's cash crops.
Cash available for farm and household use will be based on crop income
and any other regular income from employment and other sources that the farmers
are willing to divulge. Cash resources available for farming will be net of cash










needed to run the household. This information will be recorded in the final
interview. All of the information gathered from farm records and surveys will
be synthesized into a preliminary linear programming model which will be
subsequently expanded and refined in later phases of the project. This model
will be used to identify and quantify the most binding constraints and to
evaluate their impact on productivity, yields, and profits, as well as production
and household decisions. Parametric analysis will be used to assess potential
economic gains from alleviating the binding constraints.

MODEL SPECIFICATION
A multiperiod linear programming model is being used to analyze production
and constraints over a two year period. Each year is divided into quarters.
Only carrot and escallion planting decisions are examined. An option to purchase
guinea grass is included so farmers can augment their own grass resources if
necessary. Selling activities are included so cash resources in each period can
be augmented through the sale of produce. Land, grass, labor and cash resources
in each period are limited to 1.5 acres, 1 acre, 156 days, and $2,000
respectively. A demand constraint for escallion limits the amount that can be
sold in each period, which varies depending on the season.
Costs, yields and returns are based on data gathered from farmers' records.
Escallion costs are dependant on season, since planting costs depend on the price
of seed escallion which varies between seasons. Costs are distributed over
several time periods as they are incurred, which is reflected in varying cash
requirements in each period. Yields and returns also vary between periods
depending on rainfall and prices. The objective is assumed to be maximization
of the present value of net returns (profit) from planting activities over a two
year period. This objective is secondary to ensuring a minimum level of food
production, which is incorporated by deducting land resources reserved for food
production from land available for cash crop production. The matrix specifying
model parameters for periods 1 4 is presented in Table 1.

RESULTS AND DISCUSSION
The solution to this model over a two year period is outlined in Table 2.
The optimal solution calls for planting .3 acres of escallion in the first
period, producing 600 pounds of escallion to be sold. None of the available
resources in this period are constraining production. Planting is postponed
until future time periods when it becomes more profitable.
In period 2 the solution calls for bringing 1 acre of carrot into
production. These carrots cannot be harvested until the subsequent period, so
none are available to be sold in period 2. The escallion planted in period 1
yields 1200 pounds for sale in period 2. The limiting factor in period 2 is
available labor. The slack variable indicates the amount of each resource which
is not being utilized in production. The zero value of the slack variable for
labor in period 2 indicates that labor has been fully utilized. The shadow
price represents the value of an additional unit of the constraining resource
in terms of increased profit. This shadow price must be equal to or greater than
the unit cost of the constraining resource to warrant purchasing an additional
unit of this resource. Hiring labor in period 2 is not justified since the shadow
price of $27.96 is well below the unit cost of hiring additional labor.
In period 3, another .68 acres of carrot comes into production, and 3,392
pounds of carrot harvested from the second period's planting is sold. Escallion
planted in period 1 yields 1200 pounds to be sold in period 3. Again labor is











limiting increased production, leaving land, grass and cash resources
underutilized and leaving 800 pounds of unmet escallion demand. The shadow price
of $38.11 is not high enough to justify hiring additional labor. The analysis
of period 4 results follows the same reasoning.
In period 5 no new activities are undertaken except for the sale of produce
planted previously. This is not due to resource constraints as all resources
have positive slack variables. Sensitivity analysis indicates that it is the
price of carrot in period 6 which is limiting production. A $.06 increase in
the price of carrot in period 6 would change the model solution, bringing carrot
into production in period 5.
The analysis for period 6 and 7 is similar to that of periods 3 and 4.
An acre of carrot is planted, 1200 pounds of escallion are sold, and labor is
again the most binding constraint to increased production. In period 7 the
shadow price of labor is high enough to justify hiring of additional labor.
In period 8, the lack of markets for output produced is the primary factor
constraining production. No carrot is planted because the limited time frame
of the analysis does not allow for the sale of produce in the following time
period (ie, period 9), hence carrot planted in period 8 has no value. This
result would not be obtained in a more expanded model, since no other factors
are constraining production in period 8. Planting escallion yields a product
within the same time period but the demand constraint prevents additional
escallion from being planted even though the land, grass, labor and cash
resources are adequate for increasing escallion production. The shadow price
for escallion demand in period 8 indicates that for each additional pound of
escallion that could be sold, farmers' profits would increase by $8.75. As long
as this is above the farmgate price of escallion, it would be a worthwhile
endeavor to seek new markets for escallion.
These results indicate that availability of labor is the most binding
constraint, as it limits production in periods 2, 3, 4, 6, and 7. Limited demand
for escallion also limits production in periods 4 and 8, (the fourth quarter)
when farmers are unable to sell all the escallion that could be produced from
available resources. Parametric analysis of relaxing the labor constraint in
period 7 indicates that land is the second most binding constraint, since slack
land leaves the solution (Table 2). Labor available was increased from 156 days
to 236 days. On doing this, labor is no longer a constraint and instead, land
in period 7 becomes constraining. The objective function value increases by
$3139 due to an increase in carrot production and sales. In the extended model
farmers will have the option of hiring extra labor, but addition of a labor
supply constraint may alter this conclusion, leaving labor as the most binding
constraint.
Sensitivity analysis of objective function coefficients (costs of
production, input prices, and revenue) reveals that the model results are
sensitive to changes in the cost of producing carrot in the first quarter of each
year. Accuracy in estimating this parameter is important to ensure realistic
model results and predictions. Results are also very sensitive to slight
variations in carrot prices in periods 2, 3, 6, and 7. The likely model response
to an increase in carrot price in one period would be an increase in the area
planted in carrot in the preceding period, assuming that no other factors are
Lonstraining, as is the case in period 2 and period 6.












Table 1: Matrix of Input/Outut Coefficients C3 S3 BG3 SC3 SS3 C4 S4 BG4 SC4 SS4
-3800 -2500 -1000 +3 +2 -3800 -2800 -800 +3 +3
C1 S1 BG1 SC1 SS1 C2 S2 BG2 SC2 SS2
MAXIIZE NPV = -3800 -2800 -800 +1.5 +6 -3800 -2500 -800 +1.5 +3


= 1.5


1 1 0 0 0
0.3 0.5 -1 0 0
150 100 0 0 0
3200 1700 800 -1.5 -6
0 0 0 1 0
0 -2000 0 0 1
0 0 0 0 1


SUBJECT TO:

LAND 1
USEGRASS1
LABOR
CASH 1
CAR 1
SCALE 1
SCDEMAND1

LAND 2
GRASS 2
LABOR 2
CASH 2
CAR 2
SCAL 2
SCDEMAND2

LAND 3
GRASS 3
LABCR 3
CASH 3
CAR 3
SCAL 3
SCDEMAND3

LAND 4
GRASS 4
LABOR 4
CASH 4
CAR 4
SCAL 4
SCDEMAND4


0 1 0 0 0
0 0 0 0 0
0 6 0 0 0
0 50 0 0 0
0 0 0 0 0
0 -5000 0 0 0
0 0 0 0 0


0 0
0 1 0 0 0 50 6
0 0 0 0 0 600 50
0 6 0 0 0 -3300 0
0 50 0 0 0 0 -5000
0 0 0 0 0 0 0
0 -5000 0 0 0
0 0 0 0 0


<= 156
<= 2000
=0
=0
<= 3000

<= 1.5
<= 1
<= 156
<= 2000
= 0
=0
<= 3000

<= 1.5
<= 1
<= 156
<= 2000
= 0
=0
<= 2000


1 1 0 0 0 = 1.5


0 0 0 0.3 0.5 -1 0 0 = 1
0 0 0 150 100 0 0 0 <= 156
0 0 0 3200 2000 800 -3 -3 <= 2000
0 0 0 0 0 0 1 0 =0
0 0 0 0 -2500 0 0 1 = 0
0 0 0 0 0 0 0 1 <= 1500


0 1 0 0 0 1 1 0 0 0
0 0 0 0 0 0.3 0.5 -1 0 0
50 6 0 0 0 150 100 0 0 0
600 50 0 0 0 3200 1700 800 -1.5 -3
-3300 0 0 0 0 0 0 0 1 0
0 -4000 0 0 0 0 -2000 0 0 1
0 0 0 0 0 0 0 0 0 1 1 1 0 0 0
0.3 0.5 -1 0 0
0 1 0 0 0 0 1 0 0 0 150 100 0 0 0
0 0 0 0 0 0 0 0 0 0 3200 1700 1000 -3 -2
0 6 0 0 0 50 6 0 0 0 0 0 0 1 0
0 50 0 0 0 600 50 0 0 0 0 -2000 0 0 1
0 0 0 0 0 -3300 0 0 0 0 0 0 0 0 1
0 -4000 0 0 0 0 -4000 0 0 0
0 0 0 0 0 0 0 0 0 0 0 1 0 0 0











Table 2: OPTIMAL LP MODEL SOLUTION


VARIABLE VALUE RESOURCE SLACK SHADOW PRICE
C1 0 LAND 1 1.2 .00
Si .3 GRASS 1 .85 .00
BG1 0 LABOR 1 126 .00
SC1 0 CASH 1 5090 .00
SS1 600 ESCAL DEMAND 1 2400 .00

C2 1.02 LAND 2 .17 .00
S2 0 GRASS 2 .69 .00
BG2 0 LABOR 2 0 27.96
SC2 0 CASH 2 2295 .00
SS2 1200 ESCAL DEMAND 2 1800 .00

C3 .68 LAND 3 .51 .00
S3 0 GRASS 3 .79 .00
BG3 0 LABOR 3 0 38.11
SC3 3392 CASH 3 11752 .00
SS3 1200 ESCAL DEMAND 3 800 .00

C4 .79 LAND 4 .40 .00
S4 0 GRASS 4 .76 .00
BG4 0 LABOR 4 0 7.66
SC4 2261 CASH 4 10300 .00
SS4 1500 ESCAL DEMAND 4 0 11.71

C5 0 LAND 5 1.2 .00
S5 0 GRASS 5 1 .00
BG5 0 LABOR 5 114 .00
SC5 2638 CASH 5 12663 .00
SS5 1200 ESCAL DEMAND 5 1800 .00

C6 1 LAND 6 .17 .00
S6 0 GRASS 6 .69 .00
BG6 0 LABOR 6 0 27.11
SC6 0 CASH 6 2295 .00
SS6 1200 ESCAL DEMAND 6 1800 .00

C7 .68 LAND 7 .51 .00
87 0 GRASS 7 .79 .00
BG7 0 LABOR 7 0 40.66
SC7 3392 CASH 7 11752 .00
SS7 1200 ESCAL DEMAND 7 800 .00

C8 0 LAND 8 1.2 .00
S8 0 GRASS 8 1 .00
BG8 0 LABOR 8 120 .00
SC8 2261 CASH 8 12858 .00
SS8 1500 ESCAL DEMAND 8 0 8.75











Table 3: Parametric Analysis of Labor in Period 7

Value of the objective function = $55,921

VARIABLE VALUE


C7
S7
BG7
SC7
SS7


1.2
.0
.0
3392.4
1200.0


C8 .0
S8 .0
BG8 .0
SC8 3960.0
SS8 1500.0

RESOURCE SLACK
LAND 7 .0
GRASS 7 .64
LABOR 7 22.80
CASH 7 10105.40
ESCAL DEM 7 800.00

LAND 8 1.20
GRASS 8 1.00
LABOR 8 94.20
CASH 8 17645.00
ESCAL DEM 8 .00


SHADOW
PRICE
6100.00
.00
.00
.00
.00

.00
.00
.00
.00
7.57


Table 3: Days of labor available in period 7 was increased frcui 156 to 256.
On doing this, land in period 7 becomes constraining, and labor is no longer
constraining. The objective function value increases by $3139 due to increased
carrot production in period 7.

LIMITATIONS OF THE PRELIMINARY MODEL
This preliminary analysis is based on data from one farmer. The results
are fairly consistent with this farmer's actual decisions. The final model will
be extended over a longer time period, will include a more comprehensive array
of production choices and constraints, and will be based on data compiled from
a representative sample of farmers. Options for producing tomato, thyme, sweet
pepper, and melon will be included, and an option to hire labor, thus enabling
farmers to overcome the labor constraint. The solution will likely result in
many combinations of activities, all of which are equally profitable, reflecting
the actual diversity of production patterns in the study area.






Figure 2 OBSERVED PLANTING PATTERNS
JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC

.06 acre SWEET PEPPER :.:.

nursery
TOMATO


CARROT
.12 acres



RED PEA
.17 acre RED.PEA........'.... /.T...O..


MELON Melon crop failed, _\\ _\\\_\
most seed did rot germinate. i


CARROT
.36 acre
MELON



.37 acres CARROT



.25 acres CARROT


.10acre ESCAUION . .. ....








Matrix of Input/Output Coefficients I


PERIOD 1 OPTIONS


8


w
Q)


z




.j
-i
w
U)


PERIOD 2 OPTIONS


a.


I
I
I


C,
U4


-j
-J


z




.j
d
0
-J



-J
uJ
U)


PERIOD 3 OPTIONS


5





a.


z
Q


a
o


m
C,

U


-I
8


ij
w
(A


z


0

-j
to


RESOURCES

AVAILABLE


LAND 1 1 <= 1.SACRES
......................... ..... .............................. ................
GRA........... .3 .6 -1 <= 1 ACRE

LABOR z0 1W <= 1BDAYS


ESCAL STORAGE -2000 1 = 0
DEMAND CONSTR. 1 < 3000 LBS


LAND
GRA89
LABOR
CASH
CARROT STORAGE
ESCAL STORAGE
DEMAND CONSTR.


LAND
GRABS
LABOR
CASH

CARROT STORAGE
ESCAL STORAGE
DEMAND CONSTR.


60
$600
3300


1


6
$60


-4000


1
.3

150

-- ,,


1
.5

100



-2000


4*800


1


14

1


1-4 -4 4 4 4 4 .4- I- 4 4 -


1


6
*e *


50

-3300


1


60



-4000
..,..o


1

.3
150
e320C
,=,


1
.6
100
$1700


-1


$100,


43
I- ---


4 -


42


1
I


<= 1.6 ACRES
<= 1 ACRE
<= 166 DAYS
<= $2,000
= 0
= 0
<= 3000 LBS


<= 1.6ACRES
<= 1 ACRE
<= 166 DAYS
<= $2,000
= 0
= 0
<= 2000 Ib.


MAX NET REVENUE = -3800 -2800 -800 +1.6 +6


Figure 4


u
0



ma
UJ a 3


- M


-4000 .


-3800 -2200 -800


+1.6 +3 -3800 -2200 -1000 +3 +2





Figure 5 LP MODEL SOLUTION AND SENSITIVITY ANALYSIS
OBJECTIVE FUNCTION INCREASE OR DECREASE THAT
ACTIVITY VALUE COEFFICIENT WILL CHANGE THE SOLUTION
plant carrot 0 $3800 -- $250 decrease
Q plant escallion 3 acres in cost of growing carrot
0 buy grass 0
IU sell carrot 0
0
sell sicalllon O0 Ilbe.
S plant carrot 1 acre
0 plant escallion 0
0 buy grass 0
SIUJ sell carrot 0 $1.50 $.07 increase
sell scallion 1200 Ilb. in price of carrot
Plant carrot .68 acres
Cr plant escallion 0
20 buy grass 0
MC
Wl sell carrot 3392 Ibs $3.00 --- $.22 decrease
ell escallion 1200 Ibs. in price of carrot
plant carrot .79 acres
o plant escallion 0
0 buy grass 0
Ll sell carrot 2261 Ibs.
C sell escallion 1500 Ibs.
plant carrot 0 -$3800 --- $206 decrease
S plant escallion in cost of growing carrot
0 buy grass 0
wU sell carrot 2638 Ibs.
sell escalllon 1200 Ibs.
plant carrot 1 acre
to plant scallion
t 0
0 buy grass 0
J y sell carrot 0 $1.50 --- $.06 increase
O sell escalllon 1200 Ib. in price of carrot
Z plant carrot .68 acre
8( plant escallion 0
SQ buy gras 0
S sell carrot 3392 Ib $300 $.18 decrease
C sell escalllon 1200 Ibs. In price of carrot
plant carrot 0
plant escallion 0
0
0 buy grass 0
S -sell carrot 2261 Ibs.
L sell escallion 1500 Ibs.





Figure 6 ANALYSIS OF RESOURCE CONSTRAINTS
SHADOW RESOURCE
ACTIVITY VALUE RESOURCE SLACK PRICE AVAILABLE
plant carrot O land 1.2 0 1.5 acres
Plant escallion .3 acres grass .85 0 1 acre
O
Sbuy grass 0 labor 126 0 156 days
L sell carrot 0 cash 5090 0 $2000
sell escalllon 600 Ibs. escal demand 2400 0 3000 Ibs.
C plant carrot 1 acre land .17 0 1.5 acres
a plant escallion 0 grass .69 0 binding 1 acre
binding
Sbuy grass 0 labor 0 27.96 --- 156 days
Ul sell carrot 0 cash 2295 0 $2000
sell escallion 1200 Ibs. escal demand 1800 0 3000 Ibs.
Plant carrot .68 acres land .51 0 1.5 acres
0 plant escallion 0 grass .79 0 1 acre
L buy grass 0 labor 0 38.11 binding 156 days
U sell carrot 3392 Ibs. cash 11752 0 $2000
sell escalllon 1200 Ibs. escal demand 800 0 2000 Ibs.
plant carrot .79 acres land .40 0 1.5 acres
Q plant escallion 0 grass .76 0 binding 1 acre
0 buy grass 0 labor 0 $7.66 ----- 156 days
ME $2000
W seII carrot 2261 Iba. cash 10300 0
Sell escalllon 1500 SIb. cal demand 0 $11.71 binding 1500 lbs.
plant carrot 0 land 1.2 0 1.5 acres
1o
Q plant escallion 0 grass 1 0 1 acre
0 buy grass 0 labor 114 0 156 days
tu sell carrot 2638 Ibs. cash 12663 0
S sll escalllon 1200 Ibs. escal demand 1800 0 3000lbs.
plant carrot 1 acre land .17 0 1.5 acres
r plant escallion 0 grass .69 0 1 acre
0 buy grass 0 labor 0 $27.11 binding 156 days
U- sell carrot 0 cash 2295 0 $2000
g- sell escalllon 1200 Ibs. escal demand 1800 0 3000 Ibs.

) plant carrot .68 acres land .51 0 1.5 acres
1 plant escallion 0 grass .79 0 1 acre
i0 buy grass 0 labor 0 $40.66 binding 156 days
lu sell carrot 3392 Ibs. cash 11752 0 $2000
a. sell escalllon 1200 Ibs. escal demand 800 0 2000 lbs.
plant carrot 0 land 1.2 0 1.5 acres
o plant escallion 0 grass 1 0 1 acre
0 buy grass 0 labor 120 0 156 days
uL sell carrot 2261 Ibs. cash 12858 0 $2000
a- sell escalllon 1500 Ibs. Iscal demand 0 8.7 binding 1500 bs.




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