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Economics Report 7
Economic
Implications of
Water Hyacinth Control
Food and Resource Economics Department
Agricultural Experiment Stations
Institute of Food and Agricultural Sciences
University of Florida, Gainesville 32611
Michael Justin Ma
ay 1975
ABSTRACT
The purpose of this report is to furnish information useful to
state agencies and others concerned with water hyacinth control in
Florida.
This study was concerned with the least cost method of mechani-
cally controlling water hyacinths in Florida. A cost minimizing linear
programming model was developed and applied to a hypothetical lake to
determine the least cost method and seasonal pattern of removal to
attain specified levels of control.
The annual costs of controlling water hyacinths for a 400 acre lake
under specified conditions were estimated to be $13,500 or $33.75 per
acre. The total annual cost remained rather invariant to changes in the
level of control desired, but was greatly affected by changes in the
initial infestation on the lake. The least cost type of harvester de-
pends on the size of the lake. The smaller capacity of the fixed point
harvester makes it more suitable for small lakes; whereas, the mobile
harvester is more suitable on large lakes.
Three water hyacinths by-products (compost potting blend, soil
amendment, and feed ingredient in beef cattle diets) were examined in an
attempt to estimate the demand for by-products made from water hyacinths.
There was evidence that hyacinths had some value as a blend in potting
soil. However, the quantity demanded in this use would be quite limited.
The value of hyacinths as a soil amendment was estimated to be less than
hauling and spreading costs. The results indicate that hyacinths have
little value as a feed. The value of water hyacinths as an animal feed
ingredient was estimated using a least cost diet formulation for two
beef cattle diets.
For hyacinth control purposes, mechanical methods are repetitive
and costly. A combination of chemical-mechanical control has been recom-
mended in other research studies as an optimal method of control. The
results of this study lend support for such a strategy.
Key words: Water hyacinth, by-products, mechanical harvesting.
I
ACKNOWLEDGMENTS
I deeply appreciate the assistance of Dr. Max R. Langham in this
research. His help in defining the model and his patience in preparing
the report were invaluable. I also appreciate the help and comments of
Drs. J. F. Hentges, Jr., L. O. Bagnall, R. L. Scheaffer, and W. W.
McPherson. Finally, I want to thank Richard Levins for the inspiration
he gave me in writing the report.
All computer work was done at the facilities of Northeast Regional
Data Center.
Mrs. LeAnne van Elburg typed the thesis manuscript on which this
report is based. Mrs. Janet Eldred prepared this report for final
publication. Lastly, I want to thank my wife, Julie, for her support
during this study.
TABLE OF CONTENTS
Page
ACKNOWLEDGMENTS . . . .. . i
LIST OF TABLES . . . . . . v
LIST OF FIGURES . . . . vi
CHAPTER I: INTRODUCTION ......... . . 1
Review of Literature ........ ........ .. 4
Mechanical Harvesting ................. ... 4
Harvesting Concepts . . .. . . 4
Type of Disposal System . . . .. .. 5
CHAPTER II: THE MODEL . . . . . 7
Objective Function . . . ... .. .. 7
Model Constraints . . . .... .. .. 9
Biological Constraints . . . . 9
Harvesting Constraints . . . .. 12
Non-negativity Constraints . . . .. 14
General Comments Concerning the Model . . .. 14
Summary of Model . . . . . 15
CHAPTER III: ANALYSIS. .... . . . 17
Estimation of Model Parameters . . . .. 17
Objective Function . . . . .. 17
Biological . . . . . 19
Harvesting . . . . . 20
Results . . . . .. 22
A Possible Strategy for Control . . . 30
CHAPTER IV: BY-PRODUCTS . . . . .. 33
Demand for Selected Water Hyacinth By-products . .. 33
As Potting Compost . . . . ... 33
As Soil Amendment . . . . .. 34
As a Feed TI'gredierit in Beef Cattle Diets . .. 35
The Results . .. . . . 36
Brood Cow .................. . 36
Finishing Steer Calf . . ...... 39
Summary . . . . . . 39
TABLE OF CONTENTS (Continued)
Page
CHAPTER V: SUMMARY AND CONCLUSIONS. .. . . .. 45
Summary . . . . . ....... . 45
Conclusions . . . .. .... 46
For Mechanical Control . .... ..... 46
For By-products . . . .. . 47
Implications for Hyacinth Control . . . 47
Limitations and Need for Future Research .... 48
APPENDIX . ... .... . . . . 49
REFERENCES . .... ...... . .. .. 61
LIST OF TABLES
Table Pag
1 Average daily temperature, daily growth factors (D,),
and constant monthly growth coefficients (c.) by
months, April through October ... .. . .... 21
2 Estimated minimum control costs and quantities of
water hyacinths harvested from a 400 acre lake for
different combinations of harvesters, initial infesta-
tion, and levels of control. . . . 23
3 Estimated quantity of hyacinths on a 400 acre lake,
quantity harvested, and percent harvested by months,
April through October . . . . 25
4 Estimated minimum control costs for different size
lakes for different combinations of harvesters, initial
infestation, and levels of control .. . ... .. .. 27
5 Estimated quantity of hyacinths on various size lakes,
quantity harvested, and percent harvested by months,
April through October . . . . 28
6 Effects of changes in level of control desired and ini-
tial infestation of water hyacinths on the number of
harvesters required, control cost, and total quantity
of water hyacinths harvested . . . 29
7 Quantities of chopped or ensiled water hyacinths in
least cost daily diets for brook cows (400 kilograms)
ni:sirj. calves at various r 'ices of other feed ingredi-
ents and of water hyacinths . . . 37
8 Quantities of chopped or ensiled water hyacinths in
least cost daily diets for finishing steer calves (300
kilograms) at various prices of other feed ingredients
and of water hyacinths . .. . ... 40
A-1 Prices used in beef cattle rations . .. 51
A-2 Simple. t.ibj.u f.r least cost diet problem . . 52
LIST OF TABLES (Continued)
Table
A-3 Daily diet requirements per head for finishing steer
calves (300 kilograms) and cows (400 kilograms)
nursing calves .... .. .......
A-4 Detailed description of the feed ingredients .....
A-5 Simplex tableau for harvesting cost model . . .
LIST OF FIGURES
Figure
1 Hypothetical marginal cost of harvesting water
hyacinths . . . .
2 Graph of assumption of constant growth during the
month with harvesting at the end of the month ..
3 The demands for ensiled (SIL) and chopped (FW)
water hyacinths in a cow (400 kilograms) nursing
calf diet for three time periods . .. .
4 The demand for ensiled (SIL) and chopped (FW)
water hyacinths in a finishing steer calf (300
kilograms) diet for three time periods . ...
Page
56
57
58
8
ECONOMIC IMPLICATIONS OF WATER HYACINTH CONTROL
Michael Justin Mara
CHAPTER I: INTRODUCTION
Within the boundaries of the State of Florida there are approxi-
mately 3.7 million surface acres of inland water [4, p. 3].1 This acre-
age includes farm ponds, lakes, rivers, canals, etc. Approximately 2.96
million acres [4, p. 3] are classified as fresh water. Conservatively,
200,000 to 300,000 acres are infested with noxious aquatic plants [16,
p. 2], thus hindering the usefulness of many of the water bodies.
The infestation of waterways and lakes by aquatic weeds is a prob-
lem that directly or indirectly affects all people living near or using
an area infested by weeds. Water hyacinths have exhibited the most ex-
plosive infestation of all the harmful aquatic weeds, and are the focus
2
of this study. They are a floating weed; any wind or current assists
in spreading them. It has been estimated that water hyacinths today in-
fest over 100,000 surface acres of water in Florida [2, p. 1].
There is no reliable source of information which mentions the water
hyacinth (Eichornia crassipes) in Florida prior to 1890. According to
Numbers in brackets refer to references cited at the end of this
report.
2Water hyacinths are not the only aquatic weed infesting Florida
waters; numerous other harmful aquatic weed species exist, e.g., water
lettuce (Pistia stratiotes), Hydrilla species, waterfern (Azolla
species), alligator weed (Alternanthera philoxeroides), and sedges
(Carex species) [13, p. 10].
MICHAEL JUSTIN MARA was formerly a graduate research assistant in
the Food and Resource Economics Department at the University of Florida;
he is now an economic analyst in the Agricultural Economics Department
at the University of Georgia at Athens.
eyewitness accounts, the plant was Imported into a pond on private
grounds near Palatka on the St. John's River in 1890. The hyacinths were
removed from this pond and introduced into the St. John's River in that
year [9, p. 18]. With the warm sunshine and long growing season typical
of Florida, they have spread until today they are an important environ-
mental nuisance in Florida waters.
Water hyacinths have several effects on the environment. They choke
off growth of other aquatic plants. As the water hyacinths are moved
about on the water by wind or current they disturb the eggs of fish with
their roots. Decaying water hyacinths compete with fish for oxygen. The
ecological food chain of aquatic life is interrupted through retardation
of plankton growth due to shading from water hyacinths. They increase
the loss of water from the surface by transpiration which is three to
four times the rate of loss by evaporation. This water loss is important
with the water shortages that South Florida has and will continue to ex-
perience as human population grows. They decrease waterfront property
values [26, p. 25]. Also, mosquitoes and other insects breed and hide in
these plants. Besides being a nuisance, there is some danger of diseases
(e.g., malaria) from these insects [26, p. 24].
Water current flow velocity can be reduced significantly by weed
colonies. Since water control may be seriously hampered by the choking
of drains and diversionary canals and the clogging of flood control gates,
floating mats may increase the likelihood of flooding. The water, in-
stead of being properly diverted into run-off basins or ponds, backs up
and increases the flood danger that the canal system was designed to avert.
Weed interference with municipal or industrial water supply plants
is an actual and potential hazard. The floating weeds may clog the in-
takes and cause additional operating and maintenance expenses. Also, the
clogging of sewage lines and other interference with sewage disposal and
drainage systems can be damaging.
Barge, water traffic, and fishing are seriously restricted by aquatic
weeds. These restrictions result in substantial economic loss. The weeds
not only contribute to the physical obstruction of navigation, but where
infestation is not so severe as to limit fish populations, the weeds may
obstruct the use of boats [13, p. 16].
The total expenditure to control water hyacinths by public agencies
in the State of Florida has been estimated to be between ten and fifteen
million dollars per year [21,p. 1]. Benefits of control in excess of
$100,000,000 per year have been estimated [17, p. 17].
There are three means of control available: biological, chemical,
and mechanical. Of these, mechanical harvesting of water hyacinths
seems to have the most potential for the following environmental reasons:
first, mechanical harvesting does not harm the fish; second, mechanical
harvesting leaves no environmental residues;' and third, since water hya-
cinths remove nutrients from the water [22, p. 27], mechanical harvesting
improves water quality. Mechanical harvesting also makes water hya-
cinths available for possible conversion to such uses as soil amendment,
paper, and feed. If a market can be developed, products processed from
water hyacinths may help defray the cost of mechanical control.
A mathematical programming model which incorporates the biological
growth patterns of hyacinths was developed in this study to investigate
the cost of mechanical control. The cost for mechanical harvesting
estimated in this study will give policy makers an indication of the
level of funding necessary to usemechanical harvesting as a means of
controlling water hyacinths. The model developed was illustrated with
an application to a hypothetical lake under specified conditions.
Potential demand for products from water hyacinths was also inves-
tigated to the extent possible with available data. It is possible that
revenues from such by-products will someday be used to help defray
control cost.
The specific objective of this study in analyzing the cost of me-
chanical harvesting of water hyacinths was to provide insight into the
following questions:
1) What are the required inputs to mechanical harvesting and
their costs, and how do costs vary with factors influencing
hyacinths control?
2) What is the demand for the by-products that can be derived
from water hyacinths that are harvested?
3) What will be the minimum cost of mechanical harvesting as
a means of controlling water hyacinths under specified
conditions?
Review of Literature
Although this researcher found no previous studies of the economics
of aquatic weed control, there are publications which provide some infor-
mation for an economic analysis. References [20; 21; 23; and 24] are
concerned with the experimental costs of mechanical harvesting on several
lakes and canals in Florida. The different techniques of mechanical
harvesting were set forth by Curtis [10]. Bates and Hentges [4] have a
summary of the water hyacinth problem and literature available on this
topic. Also, the Hyacinth Control Journal, published by the Hyacinth
Control Society, includes articles about hyacinth control. A short
history of mechanical harvesting can be found in Van Dyke [24] and
Curtis [10]. An up-to-date reference on literature available on water
hyacinths is provided by Boyd [7].
Mechanical Harvesting
At present the use of machinery to remove aquatic weeds from bodies
of water is the most effective and nonpolluting control method, but it
requires a recurring effort involving machine and labor inputs.
Since the harvesting schemes developed have been contingent upon
such factors as weed type, waterway topography, and infestation, an all-
purpose harvester seems unlikely [28, p. 22]. This study looks at two
types of harvesters that have been used in hyacinth control.
Harvesting Concepts
Many different types of equipment are utilized for removing aquatic
vegetation. This equipment varies from commercially available devices
such as draglines and cranes to equipment designed especially for har-
vesting aquatic vegetation. The design for this equipment can be divided
into two types--fixed point and mobil units [10, p. 5].
Themobile harvester involves covering the infested areas of a water
body in a systematic manner with the machine. "Such a harvester normally
must have a storage capacity as well as a means for transporting and
unloading at a shore location. In Florida such systems have presented
problems because of the weight and bulk of harvested plants" [10, p. 5].
5
The fixed point harvester involves operating a harvester from a
shore location. "This system is normally used for removal of floating
aquatics such as water hyacinth and for removal of rooted aquatics in
canals and has the advantage 9f eliminating the need for onboard storage
or transport craft. With this system support craft may be needed to
break or cut plants free and to push plants to the harvester site" [10,
p. 5].
Type of Disposal System
Since the plants cannot be left on shore once they have been
harvested, a disposal system is required. At the present time the bulk
of the harvested vegetation is hauled by truck to a convenient dumping
site.
"There are several possible alternatives for disposal. The most
attractive solution for disposal would be the development of a commer-
cial product from the plants. This would allow processing equipment to
be installed on site and then the product could be moved into commercial
channels" [10, p. 6], Two such products and their potential values in
helping to defray costs are discussed in Chapter IV.
CHAPTER II: THE MODEL
In this section a linear programming model is developed which may be
used to analyze the costs involved in mechanically harvesting hyacinths.
The model allows one to investigate these costs under different levels of
hyacinth infestation, different levels of control, and with different
types of harvesting equipment. Linear programming and the related tech-
nique of parametric programming, used in this analysis, are explained in
Gass [14] and in Hadley [15].
Objective Function
The objective function is a mathematical statement of mechanical
harvesting costs. Harvesting costs are part of control costs and have
variable and fixed components. The cost of disposing of hyacinths, once
they are harvested, is not included in the model. The variable harvest-
ing costs are those associated with the variable inputs of harvesting
(chiefly labor and equipment operating costs). Fixed costs include in-
surance, depreciation, taxes, interest on the undepreciated investment
balance, some repairs, and housing.
Water hyacinths have a natural tendency to cluster. This is in
large part due to the fact that they are a floating plant and are blown
together by the wind. Clustering is also influenced by vegetative re-
production and consequent connecting stoloms. Because of these phenomena,
the marginal cost of harvesting water hyacinths remains approximately
constant as long as there remains a sizeable area of hyacinths to be
harvested. This situation may be depicted as in Figure 1 by a marginal
1Initially, it was planned to include disposal cost in the model.
However, the information on the demand for water hyacinths in by-product
uses was not adequate for one to determine a meaningful net cost of dis-
posal. Treating water hyacinths as a valueless waste currently seems to
be the only viable alternative for their disposal on a large scale basis.
Therefore, disposal costs would include such costs as those for hauling
and dumping the hyacinths.
cost curve that remains fairly constant from some effective minimum,
A m, up to point a and then begins to rise sharply as the area of hya-
cinths on the water becomes nearly depleted. If one assumes that the
maximum amount of water hyacinths that can be harvested is less.than a
(or a ax in the model) constant marginal costs and hence average varia-
J 2
ble cost can be used without undue misrepresentation of the real world
situation. A 100 percent water hyacinth density is assumed to be ap-
proximately 200 tons per acre. The tendency of hyacinths to bunch due
to prevailing winds supports the use of both this constant density as
well as a constant average variable harvesting cost.
Marginal cost
of harvesting
(dollars)
Total amount
of hyacinths
on the lake
Amin a
A
Quantity of hyacinths harvested
Figure l.--Hypothetical marginal cost of harvesting water hyacinths
Ain becomes the effective origin for measuring the quantity of
hyacinths harvested and a constant marginal cost up to the point a
implies a constant average cost when measured from Amin.
I _
The harvesting costs for J months and K types of harvesters can be
represented as follows:
(1.0) rjk xjk + fzk 1, ..'., J 12, and k = 1, ..., K
jk k
where: rk is the average variable cost of a type k harvester in month
jk 4
xjk is the amount of hyacinths harvested in month j by type k
harvesters,
fk is the annual fixed cost of a type k harvester, and
k
zk is the number of harvesters of type k.
Notice that the total variable cost (Q E rjk xjk) depends on the
5 j k
amount harvested (xjk), but the fixed costs are an annual expenditure
and are independent of the number of hons harvested.
Model Constraints
The constraints for the model are of three types: biological,
harvesting, and non-negativity.
Biological Constraints
The levels of infestation of water hyacinths for a given month de-
pends on many factors. Among these are the initial infestation of water
hyacinths, air and water temperature, salinity, hardness, pH, nutrient
3If the period of analysis is more than one year, i.e., J > 12,
then the model presented in this report would have to be modified to in-
sure that annual fixed cost were incurred for each year or part thereof
covered by the model, e.g., if J = 15 = 1 years, fixed costs must be
incurred for 2 years.
4If average disposal costs were constant and known for a particular
water body, the rjk could be modified to include these costs.
5The model as specified includes no discounting of variable costs
incurred in the second through jth month. The rk, j = 2, ..., J, could
be appropriately modified to reflect a cost of money if greater accuracy
is desired.
level, humidity, cloud cover, water currents, density of plants, natural
loss of hyacinths on the water body, and area of the water body.6
Temperature is among the most important factors affecting hyacinths
growth. The warmer the temperature--air or water--the faster water hya-
cinths grow. A temperature of 280 F will kill the tops of the plants
and temperatures below 280 F for several days will kill the entire plant.
Therefore, April through October are the principle breeding months in
Florida although both growth and propagation continue to some extent
throughout the winter if temperatures are sufficiently moderate. For
all practical purposes, however, the months of November, December,
January, and February may be regarded as a season of no growth, or in
the case of a moderately cold winter, retrogression. Marked shrinkage
and almost total disappearance is observed in unusually cold seasons
[9, p. 4].
Although sufficient data to include many of these factors in the
model have not yet been collected, some general observations can be made.
Salinity above 15 percent that of sea level kills water hyacinths [9,
p. 11]. Some suggestions have been made to tow the water hyacinths to
salt water and let it kill them but equipment to move the bulky masses
is not available and distances in many cases make it too costly.
The effects of pH, hardness, humidity, and cloud cover have not
been researched. Those working in the field indicate that water hya-
cinths do not grow well in soft water. In waters where tannic acid is
in heavy concentration there has been little growth observed. This
phenomenon can be observed in the Okeefenokee Swamp and some of the
lakes along the high ridge in Central Florida. Not much can be concluded
from humidity and cloud cover as to their effects.
High nutrient (nitrates, nitrites, and other organic and inorganic
substances) levels in the water stimulate growth. Consequently, the
higher the nutrient level the higher the control cost. Nutrient-laden
pollutants, therefore, add to the control problem.
Water currents and density of plants are related factors affecting
control costs and can help or aggravate the problem sometimes. Water
currents and wind assist in spreading the water hyacinths--thus reducing
their density and increasing the control cost. At other times winds and
currents may assist in concentrating water hyacinths and make them
easier to harvest. Winds and currents have been important factors in
spreading infestation of hyacinths.
The area of a water body dictates the upper limit on the amount of
water hyacinths it can support. As the area of the water body increases
the marginal cost of control decreases. The cost of moving and setting
up equipment for mechanical control may make the cost of control prohibi-
tive on smaller water bodies.
Wind and wave action in throwing water hyacinths upon shore repre-
sent some of the natural loss of the water hyacinths to the water body.
Natural losses, of course, lower control costs.
In a study by Bock [6], air and water temperatures were chosen as
the environmental parameters for determining the amount of hyacinth
growth to indicate the rate of vegetative reproduction. A "daily incre-
ment factor to produce the next count" was derived. "Theoretically, the
plants increased daily by this factor. The daily increment factor to
predict the next weight was obtained to show at what rate a plant must
grow between two dates in order to increase to the weight found at the
later date. This calculation assumes the plants are increasing in
weight at a geometric (and constant) rate between measurements. Although
it is true that plants usually do not grow at a constant rate, field mea-
surements were made frequently enough by Bock so that the 'index' fur-
nishes an accurate picture of growth rate fluctuation over a growing
season [6, p. 461]." In Bock's study, the increase in grams of wet
weight (net productivity) was considered [6, p. 462].
Once the daily increment factor is known, the amount of water hya-
cinths growth in t days can be estimated in Wt = Wo Dt where W is the
total weight of the plants at the end of t days, Wo is the initial weight
of the plants and D is the daily increment factor for weight [6, p. 461,
463].
Therefore, aax, the maximum number of water hyacinths that can be
harvested in month j can be calculated as follows:
max t
aj "N Dj
where: N. is the initial amount of hyacinths in month j
D. is the daily increment factor for month j, and
t is the number of days in month j.
To simplify notation, set D. = c. to get
max
a. =N. c..
3 3 3
If a value for N1, the initial infestation in the first month, is
max
assumed, knowledge of the cj's and x.k's allows a. to be calculated for
all months as follows:
max
(l.la) ama c N
1Cl N1
max
(l.lb) a N, j = 2, ..., J.
If no harvesting occurs in the month prior to month j (i.e., E x. 0),
k 3-l,k
then N. = a. However, harvesting in month j-1 will obviously reduce
j j-1
the initial infestation in month j .by whatever amount is harvested in
month j-1. The model accounts for this as follows:
max
(1.2) N a + j, k 0 j = 2, ..., J.
J j-1 Jk j-,k
After the hyacinths achieve some growth level, say M, which is deter-
mined by maximum density and the amount of area available for growth on
a water body, no further growth is possible.' Thus, the following con-
straint is included:
max
(1.3) a. < M, j 1, ..., J.
Harvesting Constraints
Even though the limitations of available data forced the assumption
that hk, the harvesting capacity of a machine of type k is constant, it
may be well to point out some of the factors not accounted for in this
model that can cause hk to vary. The size of the conveyor belt used to
lift water hyacinths out of the water is an important factor affecting
the amount harvested [23, p. 10]. High temperatures, wind, noise from
the conveyor belts, and engine reduce the crew's efficiency [21, p. 7].
Debris or foreign matter encountered in harvesting (e.g., logs, turtles
and alligators) can result in breakdown time and increased need for
maintenance and repair.
The nature of the water body can affect the amount harvested in
many ways. In a river, the streamflow may be used to aid harvesting. A
jagged shoreline increases the amount of maneuvering necessary for har-
vesting and is costly in time required to harvest. Also the shape of
the water body is important because of the distances involved in gather-
ing weeds for harvest and getting them to the shore conveyor no matter
which technique is used. The depth of the water is another factor af-
fecting the harvester's ability to maneuver.
Plant density affects the amount harvested. Generally, the denser
the plants, the more one can harvest per unit of time.
The wind is an important factor in determining the amount harvested.
Fixed point harvesters should be located downwind and in the direction
of the prevailing winds. If not, more time and expense are required to
bring the water hyacinths to the harvester. If no other factors preclude
it, perhaps mobile harvester shoulA be considered for an area with
shifting winds. Excessive winds as well as rains hinder the operations
of both types of harvesters.
Lastly, tides can also affect both fixed point and mobile harvesting.
Whether they aid or hinder the operation depends upon the direction of
the currents.
The first harvesting constraint is simply that the amount of water
hyacinths harvested in the jth month must be no greater than the maximum
amount of water hyacinths available for harvesting:
(1.4) E x. < a. j = 1, ..., J.
max
The next constraint concerns A"., a policy-set quantity of hyacinth
present that is the maximum tolerable level after the hyacinths have been
harvested each month:
max max
(1.5) aax x < A ..., J.
j k j ,
Parametric programming can vary these maxima policy variables to deter-
mine the implications of changing control levels.
A constraint on the quantity of water hyacinths that can be left be-
hind was incorporated into the model since it is not possible for all
water hyacinths on the lake to be harvested. Thus, the initial quantity
of water hyacinth in the next time period must be greater than zero.
min
This constraint is specified by equation (1.6) where A is the minimum
quantity of water hyacinths that can be left on the lake (or the maximum
level of control attainable):
min
(1,6) N > A j = 2, ..., J.
The model as specified requires that the number of harvesters, zk,
of each type be an interger (equation 1.7):
(1.7) zk e integers, k 1, ..., K.
This assumption could be relaxed if part-time use of harvesters was
available, i.e., they could be rented.
Finally, the product of the number of each type harvester and its
capacity must be equal to or greater than the amount harvested in the
jth month by that harvester type:
(1.8) hk Zk xjk 0, j = 1, ..., J and k = 1, ..., K.
Non-negativity Constraints
The non-negativity constraints (equation 1.9) are self-explanatory.
They are listed in the summary section of this chapter.
General Comments Concerning the Model
This model is dynamic in the sense that it looks at the growth
cycle over a period of time. The principal breeding months of April to
October provide the major focus of the study in the annual cycle. The
length of each time interval, j, was a month. Growth was assumed to
occur throughout the month and harvesting at the end of the month. Thus,
continuous time was approximated with discrete increments. Actually,
harvesting and growth were taking place simultaneously throughout the
month. A diagram of the assumption of growth and harvesting of water
hyacinths is shown in Figure 2. Greater accuracy of the real world
growth and harvesting phenomena could be attained by shortening the
length of time increment. The data available at this time does not, how-
ever, permit one to meaningfully work with intervals of less than a month
Quantity of
water hyacinths
max
a2
a -.----------
max
al
N10
20
April May June July
Month
Figure 2.--Graph of assumption of constant growth during the month with
harvesting at the end of the month
However, as indicated earlier, interseasonal discounting of costs
was not made a part of the model.
Summary pf Model
The model that was estimated empirically in this study can be written
as follows:
(1.0) Minimize
j,k
subject to
Biological
max
(l.la) a c N1
(l.lb) max = cj N.
max
(1.2) N. a +
j j-1
max
(1.3) aa < M
Harvesting
jk jk jk + k k
j k k
j = 2, ..., 7
Sx ,k
t
j = 2,
j = 1, ..., 7
(1.4) x < ax
k jk -
max max
(1.5) am -x E < A.
J k jk j
min
(1.6) N. > Ai
(1.7) zk E integers
(1.8) hk Zk Xk >0
Non-negativity
j = 1, ... 7
j = 1,
**., 7
j = 2, ..., 7
k = 1, 2
j = 1, ..., 7; k = 1, 2
(1.9) x.k, Zk 0 j 1, ..., 7; k = 1, 2
where: r.k is the average variable cost of harvesting a ton of water
jk
hyacinths in month j with harvester type k in dollars per ton,
xjk is the tons of water hyacinths harvested in month j by type
k harvester,
fk is the average fixed costs for type k harvester in dollars
per year,
Zk is the number of type k harvesters,
c is the constant growth coefficient of water hyacinths in
month j for each initial quantity of water hyacinths,
hk is the harvesting capacity in tons of each type k harvester,
N is the initial tons of water hyacinths in month j, N1 is
assumed to be known,
max
a. is the maximum quantity of water hyacinths in tons available
to be harvested in month j,
M is the maximum amount of water hyacinths in tons the lake
can support based on maximum water hyacinth density and area
on the lake,
max
A. is a policy variable representing the maximum tonnage of
water hyacinths remaining on the lake after harvesting in
month j, and
min
A is the minimum quantity of water hyacinths that can be left
on the lake (the maximum level of control attainable on this
water body) measured in tons.
.CHAPTER III: ANALYSIS
This chapter is divided into three parts--estimation of the empirical
model parameters, the results, and a possible strategy for control.
Estimation of Model Parameters
Objective Function
The coefficients to be estimated in the objective function are:
rjk, j = 1, ..., 7, k = 1, 2; and fk, k = 1, 2. They are, respectively,
the variable and the fixed cost of harvesting.
Due to insufficient information to differentiate the estimates over
time it was assumed that rjk = rk, j = 1, ..., 7, k = 1, 2.
Each of the coefficients and the method of estimating it will be
discussed in turn.
Fixed costs.--The average annual fixed cost of each type of harvester,
fk' was estimated using the annuity method in order to recover principal
and interest on the investment.
The annual flow, R, which would be required to recover the invest-
ment, C, at interest i over a period of n years is given by the formula
[25, p. 185]:
(4.0) R = (C L) 1 (i + Li
where: R is the annual flow in dollars required to recover capital and
interest,
C is the original investment in dollars,
L is the estimated salvage value in dollars,
i is the opportunity cost of capital in percent, and
n is the number of years over which the capital is to be recovered.
Here it is assumed that interest and capital recovery is a constant
each year.
18
The opportunity cost of money used for both types of harvesters was
10 percent. The harvesters were assumed to have a life of 10 years. With
these assumptions the formula for the kth harvester type becomes:
(4.1) R (Ck L) -10 + .l Lk = (Ck Lk) .163 + .1 Lk
1-(1.1)
Insurance costs were estimated to be $110 and $575 per year for
Types 1 and 2 harvesters, respectively. These costs plus taxes were added
to the annuity. Taxes were added under the assumption that the harvesters
2
were privately owned. These taxes were estimated to be $96 and $456 per
year for Types 1 and 2 harvesters, respectively.
The fixed point harvester (Type 1) used in this study was a modified
S-650 from Aquamarine Corporation as found in Phillippy and Perryman [21].
The S-650 cost $7,560 as of December 12, 1973. The modification to permit
direct pickup from the water was assumed to cost an additional $1,000.
Two airboats are used in conjunction with this type harvester to move the
weeds to the shore based harvester. These airboats were assumed to cost
$3,000 for a total cost of $11,560 for all equipment needed for the fixed
point harvester. The salvage value was assumed to be $200. Using equa-
tion (4.1) the annual flow required to recover capital and interest was
estimated to be $1,870 per year (rounded to the nearest $10). The sum
of the annuity costs, taxes and insurance gives an annual fixed cost for
the fixed point harvester of $2,070 per year (rounded to the nearest $10).
The mobile harvester (Type 2) was an AQUA-TRIO from Aquamarine Cor-
poration. It consisted of one H-650 harvester, one T-650 transport, and
one S-650 shore conveyor. The cost of the AQUA-TRIO was $56,760. The
salvage value was assumed to be $500. Using equation (4.1) the annual
flow required to cover the investment was estimated to be $9,220 per year
(rounded to the nearest $10). The sum of the annuity costs, taxes, and
insurance gives an annual fixed cost for the mobile harvester of $10,250
per year (rounded to the nearest $10).
1The Farm Bureau Insurance Company gave these estimates of insurance
costs.
2Taxes were estimated for Alachua County at a rate of approximately
$20 per thousand on 40 percent of the original cost.
3
As of December 12, 1973, per Aquamarine Corporation.
Variable costs.--The average variable cost of harvesting was assumed
to be composed of labor costs and operating and maintenance expenses.
Both types of harvesters require three operators. Assuming a wage
rate of $6 per hour (including fringe benefits) per operator and 160
hours per month gives a total labor cost of $2,880 per month. Operating
4
and maintenance costs have been estimated to be $365 per month. Thus
the average variable cost for both types of harvesters was estimated to
be $3,245 per month.5
Average variable costs must be put on a per ton basis to be placed
in the objective function. The average monthly harvesting capacities of
the fixed point and the mobile harvester were estimated to be 1,256 and
8,8006 tons per month, respectively. Thus, the average monthly variable
costs per ton for the fixed point and mobile harvesters, respectively,
were 2.58 and 0.37 dollars per ton.
Biological
max
The coefficients in the biological constraints are aj cj, N ,
and M for j = 1, ..., 7.
The aax's, the maximum quantity of water hyacinths available to be
J
harvested in month j, are determined by the model. They are assumed to
be some proportion of the initial infestation of the water hyacinths in
month j, N.. The N.'s are also determined by the model except for N1,
the initial infestation in the first month, which is assumed to be known.
The constant of monthly hyacinth growth in month j, cj, was estimated
by:
c. = D.
j J
Operating and maintenance costs for a mobile harvester were reported
to be $1,200 for 66 days (Aquamarine Corporation personal communication).
No information exists on the operating and maintenance costs for a
fixed point harvester. However, the cost of operating and maintaining
a fixed point harvester is believed to be less than for a mobile harvester.
Therefore, the $365 per month operating and maintenance cost which was
used in the model represents an upper bound.
See page 21 for method of estimating these coefficients.
where t is the number of days in monLh j. The D.'s represent the constant
daily growth factor in month j. Rock [6, p. 463] has estimated DJUN = 1.048.
For the other months there were no eOtimates. Since temperature is an im-
portant factor in the growth rate of water hyacinths average monthly temper-
atures were used to compute estimates of Dj for the other months.
Since the D 's are constant daily percentage increases it was neces-
sary to find the variation in the constant daily growth rate due to dif-
ferences in average monthly temperatures to compute D 's for the unestimated
months. The method used to accomplish this was to subtract one from DJUN
giving the percent increase for June since it is the only month for which
an estimate was available. The percent increase was multiplied by the
quotient of the average monthly temperature for the month to be estimated
and the average monthly temperature for June. The result gives the pro-
portional change in the growth rate, mj, between June and month j. To
determine the constant daily growth rate for month j, add the proportional
change, mj, to one. The D 's (jiJUI) were estimated by the formulas:
j = (DjN 1) and
JUN
D. = 1 + m. j = APR, MAY, JUL, AUG, SEP, OCT.
Table 1 contains the estimates of Dj, c and the average monthly
temperatures used to calculate the D 's.
The constant M in equation (1.3) was derived using the estimate of
200 tons per acre as the maximum density of water hyacinths [1, p. 2] and
the number of acres on the lake. The total amount of water hyacinths the
lake can support was considered to be the product of these two factors.
Since the lake used in this model had an area of 400 acres, then the maxi-
mum tonnage of water hyacinths this lake could support was estimated to
be 80,000 tons.
Harvesting
The coefficients to be estimated in the harvesting constraints are
Ain Aax, j ..., 7, and hk, k = 1, 2. They are the minimum quantity
of water hyacinths that can be left on the lake, the policy-set levels of
th
control in month j, and the harvesting capacity of the k type harvester,
respectively.
Table l.--Average daily temperature,a daily growth factors (Dj), and con-
stant monthly growth coefficients (cj) by months April through
October
Average daily Daily growth Estimated monthly growth
j Month temperature in F factor (Dj) coefficient (cj)
1 April 71.9 1.044 3.692
2 May 76.0 1.047 4.153
3 June 77.5 1.048 4.082
4 July 79.7 1.049 4.407
5 August 81.2 1.050 4.538
6 September 79.7 1.049 4.406
7 October 71.2 1.044 3.900
aThe average monthly temperatures for Gainesville were taken from
[18, p. 6].
It has been assumed for this study that the density of weeks in both
experiments whose results were used to estimate the harvesting coefficients
were the same. This allows a comparison to be made on the harvesters
operation on equidensity infested lakes since in the model both harvesters
are competing to do work on the same lake. Also it was assumed that the
harvesting capacity was constant for each type harvester.
The fixed point harvester harvested 1,633 tons in 208.0 hours [21,
p. 3]. To put this on a monthly basis (assumed to be 160 hours) it was
necessary to divide the actual number of tons, 1,633, by the actual num-
ber of hours operated, 208.0, and multiply this by the number of working
hours in a month (again, assumed to be 160 hours). This gives a harvesting
capacity of 1,256 tons per month for the fixed point harvester.
In the mobile harvester experiment an average of 5.5 tons per crew
hour [8, p. 39] was harvested. Based on a 160-hour month, an estimate
of 8,800 tons per month were harvested by the mobile harvester.
In the fixed point harvester experiment the weed concentration was-
1,633 tons of water hyacinths on 105 acres or 15.5 tons per acre [21, pp.
3 and 4]. The average weed concentration in the mobile harvester experi-
ment was 15.4 tons per surface acre [8, p. 38].
The actual experiment was run on harvesting Elodea, another aquatic
weed. It has been assumed that the same rate would apply in harvesting
water hyacinths.
The A ax's are the policy-set levels of control for month j. They
were estimated by determining what effect fringe widths of various choices
would have on the amount of hyacinths that would have to be harvested from
a water body of a given surface area. This study assumes the hyacinths
distribute themselves evenly around the circumference of the lake, i.e.,
the shoreline. The radial distance they cover, which would be uniform
anywhere on the lake, is called the fringe width. To convert a width into
an amount of water hyacinths the following procedure was followed. Assume
the width of the fringe allowed is f. Then the area this width represents
is found by wr2 w(r-f)2 assuming a circular lake. This determines the
surface area infested. The area of the lake is found to be the product
of the size of the lake (assumed to be 400 acres) and the fact that there
are 43,560 square feet per acre giving a total area of 17,424,00 square
feet for the specified lake. Solving for the radius of the lake using
radius equals the square root of the quotient of the area of the lake and
pi one gets a value of approximately 2,355 feet. Now solving for the area
represented by a fringe width f one gets:
Area of fringe width = r[r2 (r-f)2].
To determine the tonnage this area represents, multiply the percentage
of area infested by the total possible tonnage of water hyacinths the
lake can sustain (80,000 tons). Thus the formula used was:
max w[r2 (r-f)2] (80,000) 2rf )(80,000)
7rr r
where: r is the radius of the lake, and
f is the width of the fringe set by policy makers.
The quantity of water hyacinths left on the lake (or the maximum
min
level of control attainable), A was assumed to be a constant.
Results
Initial infestation and level of control were varied to determine
their impact on harvesting control costs and patterns (Table 2). For a
given initial infestation and minimum level of control, the model was
first solved with quantities of both harvesters being unconstrained (see
solutions with citation to footnote a, Table 2). A fractional value for
mobile harvesters was obtained. Then the model was run again holding
Table 2.--Escimated minimum control costs and quantities of water
harvesters, initial infestation, and levels of control
hyacinths harvested from a 400 acre lake for different combinations of
Number of harvesters Initial Minimum level Total annual Total quantity of Control cost
Run Mobil infestation, N1 of control, Amax cost of control, W water hyacinths
Fixed Mobile harvested Ton Acre
----Tons----- ----Tons---- ----Dollars----- ----Tons-- ------Dollars------
Ia 0,00 0.38 1,000 2,025 7,155 8,779 0.815 17.89
2b 0.00 1.00 13,489 1.538 33.75
3c 2.67 0.00 28,239 3.217 70.60
4d 3.00 0.00 28,925 3.295 72.31
5a 0.00 0.31 1,000 1,350 7,219 8,952 0.806 18.05
6b 0.00 1.00 13,562 1.515 33.91
7c 2.67 0.00 28,686 3.204 71.72
8d 3.00 0.00 29,372 3.281 73.43
9a 0.00 0.38 1,000 675 7,460 9,603 0.777 18.65
o1b 0.00 1.00 13,803 1.437 34.51
11c 2.67 0.00 30,369 3.162 75.92
12d 3.00 0.00 31,055 3.234 77.64
13a 0.00 0.17 500 2,025 4,322 6,933 0.623 10.81
14b 0.00 1.00 12,815 1.848 32.04
15C 1.20 0.00 20,412 2.944 51.03
16 2.00 0.00 22,074 3.184 55.19
17a 0.00 2.06 5,000 2,025 29,820 23,547 1.266- 74.55
18 0.00 3.00 39,462 1.676 98.66
19C 14.43 0.00 90,856 3.858 227.14
20 15.00 0.00 92,045 3.909 230.11
Unconstrained solutions.
b
bNumber of mobile harvesters held at a positive integer level and number of fixed point harvesters held at zero level.
C Number of fixed point harvesters unconstrained and number of mobile harvesters held at zero level.
Number of fixed point harvesters held at positive integer level and number of mobile harvesters held at zero level.
the number of fixed point harvesters at the zero level and mobile har-
vesters at the smallest integer level larger than the fractional number
of mobile harvesters in the results 9f the unconstrained runs (see runs
with citation to footnote b, Table 2). Next the number of mobile har-
vesters in each run was held at the zero level and the number of fixed
point harvesters was unconstrained (see runs with citation to footnote c,
Table 2). Finally, a fourth run for each set of initial conditions held
the number of fixed point harvesters at the smallest integer larger than
the fractional number of fixed harvesters in the result of the uncon-
strained run and held the number of mobile harvesters at the zero level
(see runs with citation to footnote d, Table 2).
For an example of how to interpret the results in Table 2, consider
run 2. With one mobile harvester, an initial infestation of 1,000 tons,
and a control level of 2,025 tons (a 30 foot fringe) the estimated mini-
9
mum control cost was about $13,500 or $33.75 per acre. The total quan-
tity of water hyacinths harvested during the year was 8,779 tons.
The quantity of water hyacinths harvested in each month is contained
in Table 3 for each model run. The percentage of water hyacinths which
were harvested in each month and the maximum amount of water hyacinths
available to be harvested are also presented. An interesting observa-
tion on the harvesting patterns of the fixed point and mobile harvesters
is that they are the same. The harvesting patterns for runs 1 to 12 and.
17 to 20 differ only in the first and last months. The differences in
these months were due to a change in the level of control and an increase
in the initial level of infestation.
Excess harvesting capacity results for the 400 acre lake if the num-
ber of harvesters are required to take on integer values. If mobile and
fixed point harvesters were moved to other lakes then the excess capacity
could be used in controlling them and thus reducing the unused capacity
of the harvesters. With a strategy of moving harvesters among lakes, the
unconstrained solutions provide more accurate estimates of control cost.
Runs were also made to determine the impact of lake size on control
cost. The model was run for lakes of various sizes under the same rela-
tive initial conditions as runs 1 through 4 of Table 2. That is, the
9The estimate of $33.75 per acre is in the range of control cost
estimated by Wunderlich ($25-$45 per acre) [27, p. 29].
w b 0o. 0 C
rO.cO CCC4N 'JCO-
rI 4* 0 M C4 -O 00t- w'0 CMC w
d I0-1 0 >o m oo %D n %0o 'to& o
** so as M Mo
0 A A A I A i
0 1 0 0 Nm 0 0
&0 0 0 0 In 0 0
C! cl V1,0 mC o .
a oo M M o o o
I> CM -.1t N N p
0O -4
U 4 A A 44
(1) ao It o r- rl
1H 1 H H H H 0
S0
St-0 f0 -0 C 0 0
tj 4-I %0 0* 0,
S0-4 I 1 r 0 D
0 0H H mH mH H OH H 0H
0 H w0
ss mi- i mn
0o 0 ri 1
,o n rr o: -n -T D'
ko rl clol 0 r r, or ID 0Io I a
MO M M rr
F T0 0 T0 0 0 4a
t 0 un n In o n
0 04 a. 04.0 04 -T 0. co -H 0 .0
0j 'OH coo H -(nH -to O T
0
w M0 w M a 00 0 4
o r. 4J 9 4 g j 4
H- HH HH HH HH
O) 04 0- o 0a) 0
iMl w Wo t- o a -vO v 01o c ( o*1W *w 1
S> A A A > p
4- -4 to o -p M T-o
H ( H rH .1 oH H
0& & 0 H* 4
S3 *DC'3 (7 *Y0(14 (7 P4
4j H
o o
0 0 0 O 0
1) IJ 43 0Q) 0 04JO 0
!i 0 ) 000 0s) '1 0 00 0t
00 0.0 0.0 0.00 oa0 0.0 0) r
I* Hs H- M(
same percentage of water surface was initially infested on the lake and
the level of control was the same percentage of total lake area. A sum-
mary of results is contained in Table 4. The seasonal harvesting patterns
for these runs is presented in Table 5.
The results in Tables 4 and 5 were based on runs in which the number
of harvesters were constrained to take on integer values because harvesters
are relatively immobile between lakes [11, p. 15]. The fixed point type
harvester is more mobile between lakes than the mobile harvester.. This
factor as well as its smaller capacity makes the fixed point harvester
more suitable on small lakes. The mobile harvester, contrary to its name,
is more difficult to move among lakes because of the difficulty in moving
the barge required to haul hyacinths. This immobility makes it impractical
to put a mobile harvester on a small lake that uses only a small fraction
of its capacity.
If only fixed point harvesters are available at positive integer
levels the solution (run 4, Table 4) requires two of them and the con-
trol cost is 50 percent more than the cost of a single mobile harvester.
For a 10 acre lake the opposite is found. Here using one mobile har-
vester will increase the estimated cost of control four times over the
estimated control cost of using one fixed point harvester. This is due
to the fixed point harvester having less excess capacity for harvesting
under these conditions.
These results suggest that fixed point harvesters should be used on
small lakes. The point at which cost of control for the two harvesters
is equal (i.e., the point of indifference) is approximately 160 acres.
Since this estimate is based on the assumption that the cost of moving
harvesters among lakes is equal this estimate represents a lower bound.
The effects of change in the level of control desired and the ini-
tial infestation of water hyacinths in the first month on the number of
harvesters required, control cost, and the total quantity of water hya-
cinths harvested are contained in Table 6. For an example of how to in-
terpret the table reference is made to the first row. In this case runs
2 vs. 6 are considered. Changes are measured with run 2 as the base.
The level of control desired increased by 33 percent and the initial
infestation did not change. This resulted in no change in the number of
harvesters required to control the lake, an increase in the estimated
Table 4.--Estimated minimum control
and levels of control
costs for different size lakes for different combinations of harvesters, initial infestation,
Number or hMr. = 0 Lake Initial Minimum level of Total annual Total quantity of Control cost per
Run Fixed Mobile size infestation, N1 control, Amax Amin cost of water hyacinths
control, W harvested Acre Ton
Acres -----Tons----- -----Tons------ Tons ---Dollars-- ----Tons------ -----Dollars----
la 0.00 0.19 200 500 1,428 170 3,543 4,299 17.72 0.824
2b 0.00 1.00 11,841 59.21 2.754
3c 1.33 0.00 13,885 69.43 3.230
4d 2.00 0.00 15,270 -76.35 3.552
5a 0.00 0.10 100 250 1,066 85 1,744 2,083 17.44 0.837
6b 0.00 1.00 11,018 110.18 5.290
7 0.67 0.00 6,749 67.49 3.240
8d 1.00 0.00 7,441 74.41 3.572
9a 0.00 0.05 10 125 106 9 744 584 74.40 1.274
10b 0.00 1.00 10,466 104.66 17.920
11i 0.36 0.00 2,259 22.59 3.868
12d 1.00 0.00 3,589 35.89 6.146
Unconstrained solution.
Number of mobile harvesters held at a positive integer level and number of fixed point harvesters held at zero level.
C Number of fixed point harvesters unconstrained and number of mobile harvesters held at zero level.
d ber of field pot harvesters held at positive integer level and uber of mobile harvesters held at zero level.
Number of fixed point harvesters held at positive integer level and number of mobile harvesters held at zero level.
Table 5.-Estimated quantity of hyacinths on various size lakes, quantity harvested, and percent harvested
by months, April through October
Month
Run Item
April May June July August September October Totals
1 thru 4 Quantity on lake in tons 1,846 706 694 749 771 749 1,428 6,943
Quantity harvested in tons 1,676 536 579 579 601 38S 0 4,299
Percent harvested 90.79 75.92 75.50 77.31 77.96 51.12 0.00 61.9
5 thru 8 Quantity on lake in tons 923 353 347 375 386 375 1,006 3,756
Quantity harvested in tons 838 268 370 290 301 117 0 2,083
Percent harvested 90.79 75.92 77.81 77.31 77.96 31.12 0.00 55.3
9 thru 12 Quantity on lake in tons 462 37 37 40 41 40 106 763
Quantity harvested in tons 453 28 28 31 32 12 0 584
Percent harvested 98.05 75.90 75.50 77.31 77.96 31.48 0.00 76.5
SSee Table 4 for number of harvesters used, lake size, initial infestation of lake, and level of control.
Table 6.--Effects of changes in level of control desired and initial infestation of water
hyacinths on the number of harvesters required, control cost, and total quantity
of water hyacinths harvested
a level of A initial A number A quantity
Runsa A lel of infestation of of mobile A cost harvested of
control desired
Sd water hyacinths harvesters water hyacinths
---------------------------------Percent-----------------------------------
2 vs. 6 +33.00 0.00 0.00 +0.47 +1.98
2 vs. 10 +67.00 0.00 0.00 +2.24 +9.40
2 vs. 14 0.00 -50.00 0.00 -5.06 -21.03
2 vs. 18 0.00 +400.00 +200.00 +192.35 +168.22
aee Table 2 for daa on which percentage changes were based.
See Table 2 for data on which percentage changes were based.
minimum control cost of 0.47 percent, and an increase in the total quan-
tity of water hyacinths harvested of 1.98 percent. Control costs increased
as the level of control desired increased (i.e., the fringe width decreased)
because the total area to be cleared of water hyacinths increased. This
increased control effort can be seen in the total amount harvested in
Table 2. The results, as summarized in Table 6, suggest that the esti-
mated minimum control cost is not very responsive to changes in the level
of control desired. However, the initial amount of water hyacinths on
the lake in the first month exerts considerable effect on control costs.
Thus, for the policy maker, fixing the level of control will not seriously
affect control costs but the initial amount of infestation on the lake in
the first month will have a considerable impact on control costs. The
greater the initial infestation, the more it will cost to control a lake.
A Possible Strategy for Control
One might suspect that if the quantity of water hyacinths on the
lake were decreased to very low levels initially that control costs would
be less than if they were left at some critical mass which would permit
rapid reinfestation. To investigate this idea one run was made with no
restriction on the amount of water hyacinths left on the lake. Also, in
this run the number of harvesters were permitted to take on fractional
.values. Under the initial conditions of a 400 acre lake with an initial
infestation of 1,000 tons and with a 30 foot fringe control level the
estimated minimum control cost was $5,666 or $14.16 per acre. The num-
ber of mobile harvesters called for in the solution was 0.42 and the
number of fixed point harvesters was zero. The total quantity of water
hyacinths harvested was 3,692 tons which were all harvested in the first
month. This left 1 ton of water hyacinths on the lake in May, 6 tons in
June, 26 tons in July, 116 tons in August, 513 tons in September, and
200 tons in October. Thus most of the water hyacinths (99.99 percent)
were harvested in the first month and it required the rest of the grow-
ing season for the water hyacinths to grow to the control level so no
harvesting activity took place in the months of May through October.
With the use of mechanical harvesting alone, one might find it
surprising that the water hyacinths could be cut back to such a low
level of infestation (1 ton) wsth the present state of technology. A
strategy for hyacinth control frequently put forward in literature is
to combine harvesting operations with chemical spraying operations to
destroy any residual water hyacinths left behind. If chemical spraying
were used in conjunction with mechanical harvesting, the above results
of the model run is suggestive of what might happen with just one spray
application immediately following a month of strong mechanical control.
Control costs with chemical spraying have been estimated to be
$12.00 per acre per application for floating weeds [28, p. 29]. With
this estimate, a combination of mechanical harvesting and chemical con-
trol would cost an estimated $26.16 per acre--an amount less than the
estimated $33.75 for mechanical control alone. Whether this difference
in cost would be sufficient to offset the environmental cost from the
chemical pollution was beyond the scope of this study.
CHAPTER IV: BY-PRODUCTS
A factor not considered in the model analyzed in the last two
chapters is the value of the hyacinths once they are harvested. If they
are of no use, the control cost would need to be increased by costs in-
volved in disposing of the hyacinths. On the other hand, if economically
feasible uses for the hyacinths exist, the value of the hyacinths in
these uses could help defray control costs.
Buckman [9, p. 35] suggested the following uses for water hyacinths:
cattle or chicken feed, mulches or composts, nutrient media, paper pulp,
cigar wrappers, and fuel. Many other marketable products made of water
hyacinths have been found. As noted in [5, p. 52], "Most of these pro-
ducts, including upholstery stuffing, rope, bags, paper, plastics, timber
substitutes, and ice chests, are of inferior quality."
Demand for Selected Water Hyacinth By-products
Data on which to estimate the demand for by-products are essentially
nonexistent. In this section some selected uses (compost, soil amend-
ment, and cattle feed) of hyacinths are discussed and some information
on the demand for these uses is presented.
As Potting Compost
The demand for hyacinths as a compost would probably be elastic up
to the quantity that would satisfy the demand for potting compost and
then turn very inelastic, i.e., a consumer would be willing to buy all
of the poLting compost he wanted up to a certain quantity at a given
price. Beyond this quantity he would have no further desire for potting
compost. The 1973 production costs for the finished compost were esti-
mated at $1.31 per bushel for a Florida firm which uses a half and half
mixture of dry hyacinths and peat. This firm is selling the compost for
$1.75 per bushel. Thus, this firm could pay at most $0.44 for the water
hyacinths that are required to make a bushel of dry compost. This amount
converts to $98.20 per dry ton or at most $6.42 per wet ton.2 Again
this amount represents an upper limit on the value of water hyacinths for
composting, and it provides no information on the quantity that would be
demanded at this price. However, one would expect that a very limited
quantity would be demanded at such a price, because there is a finite de-
mand for potting compost. There is no data to determine what this demand
might be.
As Soil Amendment
Water hyacinths may have some compost value when used alone. If
hyacinths are used as a soil amendment, their price would have to cover
-the costs involved in transporting, spreading, and working them into the
soil. The fertilizer value of a dry ton of water hyacinths is approxi-
mately $0.30. Additionally, they would have some value in improving
the tilth of the soil.
A transportation cost was estimated at $0.27 per ton per mile [23].
The transportation cost alone suggests that water hyacinths would not be
demanded as a compost by farmers at distances of more than one mile from
the lake. If all costs were considered it is doubtful if any hyacinths
would be demanded as a soil amendment at even this relatively close
distance.
1Based on 21.7,bushels per cubic yard, 5.14 cubic yards per ton,
and $0.44 per one half bushel of water hyacinths. The estimate of cubic
yards per ton was determined from one of the mechanical harvesting ex-
periments by dividing 8,395 cubic yards [21, p. 4] of water hyacinths
harvested by 1,633 tons [21, p. 4] of water hyacinths harvested giving
5.14 cubic yards per ton harvested.
2Using a wet to dry ratio of 15.3, the wet to dry ratios were found
to remain constant throughout the growing season. This ratio averaged
15.3 with a standard deviation of 2.1 (i.e., 93.4 percent water) [6, p.
461].
3Using 600 tons of water hyacinths are equal to one ton of 8-8-8
fertilizer at 1974 fertilizer prices. ,
4This is based on 151.5 tonS being hauled 2.3 miles at a cost of
$92.80 [21, p. 8].
As a Feed Ingredient in Beef Cattle Diets
A third use for the harvested water hyacinths often discussed in
the literature, is as an ingredient in beef cattle diets. Chopped and/
or ensiled water hyacinths were considered in two least cost beef cattle
diets for finishing steer calves weighing 300 kilograms and for brook
cows weighing 400 kilograms and nursing calves. These rations, selected
with the assistance of Dr. James F. Hentges, Jr., an animal scientist at
the University of Florida, indicate the range of demand for water hya-
cinths as a feed ingredient for beef cattle. The minimum cost of the
diets was determined for prices of feed ingredients in three time
periods: (1) average of January to May, 1972; (2) May 1973; and,
(3) January 17, 1974, by using a least cost diet model.
A least cost diet model is a means of determining feed ingredients
that insure that the animal gets specified levels of nutrients at a
minimum cost. The nutrient content and prices of the ingredients are
assumed to be known.
The least cost diet model for a particular ration may be specified
as follows:6
n
(4.0) Minimize v = E pj yj
yj j=1
n
(4.1) subject to Z ai y. > b i 1, ...,m
j=l 3 -< <
y. > 0 j = 1, ..., n
where: v is the cost of the daily ration per head in dollars,
p is the price of the jth feed ingredient in dollars per
kilogram,
a i is kilograms of the ith nutrient in one kilogram of the jth
feed ingredient,
The prices for the three time periods are presented in Table A-1.
6The tableau for the least cost diet model is contained in Table
A-2.
yj is kilograms of the jtI ingredient in the diet per day for
this animal, and
b is the kilograms of nutrient i that is the minimum required
i 7
or maximum allowed in the diet per day.
The diets were estimated on a dry matter basis. The relevant prices
for such a model are those at the nearest location where a particular
ingredient is available at the specified price plus transportation costs.
Volume purchases as well as shipping costs can, of course, cause prices
to vary.
The Results
Brood Cow
In the brood cow diet with the average prices of other feed ingredi-
ents at levels experienced during the January to May 1972 time period,
there was no demand for water hyacinths at a zero price (Table 7 and
Figure 3).
When May 1973 prices were used for other feed ingredients, the least
cost cow nursing calf diet included 0.37 kilograms per head of chopped
water hyacinths when prices for chopped water hyacinths ranged from zero
to 4 cents per kilogram. At prices greater than 4 cents per kilogram
for chopped water hyacinths, no water hyacinths entered the diet. The
results did not vary when ensiled water hyacinths raher than chopped
water hyacinths were included in the matrix as a feed.
When the January 1974 prices were used for other feed ingredients,
0.2 kilograms of ensiled or chopped water hyacinths were included in the
least cost cow nursing calf diet when the price of water hyacinths was
zero.
7A table of these requirements (the right hand side elements) for
the two beef cattle diets is contained in Table A-3.
8The results in Tables 7 and 8 and Figures 3 and 4 for both animal
diets are based on parametric programming the prices of chopped and
ensiled water hyacinths in the least cost diet model from zero up to one
dollar per kilogram. No hyacinths were included in the diets at prices
of hyacinths above those shown. The IBM NPS/360 system was used to
obtain solutions.
Table 7.--Quantities of chopped or ensiled water hyacinths in least cost daily diets for brood cows
(400 kilograms) nursing calves at various prices of other feed ingredients and of water
hyacinths
Water Hyacinths
Base
periods for Chopped Ensiled
periods for
prices for all Price Kilograms Price Kilograms
other feed of water of water Total cost of water of water Total cost
ingredients hyacinths hyacinths of diet hyacinths hyacinths of diet
($/kilogram)b in daily diets ($/day/head) ($/kilogram)b in daily diets ($/day/head)
1972 0.00 0.00000 0.02747 0.00 0.00000 0.03747
0.01 0.00000 0.02747 0.01 0.00000 0.03747
0.02 0.00000 0.02747 0.02 0.00000 0.03747
0.03 0.00000 0.02747 0.03 0.00000 0.03747
0.04 0.00000 0.02747 0.04 0.00000 0.03747
1973 0.00 0.36468 0.12727 0.00 0.35803 0.13030
0.01 0.36468 0.13092 0.01 0.35803 0.13388
0.02 0.36468 0.13457 0.02 0.35803 0.13746
0.03 0.36468 0.13821 0.03 0.35803 0.14104
0.04 0.36468 0.14186 0.04 0.35803 0.14462
1974 0.00 0.20455 0.14033 0.00 0.19476 0.14056
0.01 0.00000 0.14233 0.01 0.00000 0.14233
0.02 0.00000 0.14233 0.02 0.00000 0.14233
0.03 0.00000 0.14233 0.03 0.00000 0.14233
0.04 0.00000 0.04233 0.04 0.00000 0.14233
aSee Table A-i for prices of other feed ingredients in these time periods.
bNo hyacinths were included in the
No hyacinths were included in the
diet at prices of hyacinths above those shown.
Quantity (SIL) (kilogram/head/day)
-"1
ti
.36
St
2
.19
t
0
.04 1.0
Price ($/kilogram)
Quantity (FW) (kilogram/head/day)
t\
.36
t
2
.20
t
0I
0 to I
.04 1.0
Price ($/kilogram)
Figure 3.--The demand for ensiled (SIL) and chopped (FW) water hyacinths
in a cow (400 kilograms) nursing calf diet for three time
periods a
a See Table A-l for prices of other feed ingredients in these time
periods,
Finishing Steer Calf
In the finishing steer calf diet with the average prices of other
feed ingredients at levels experienced during the January to May 1972
time period, there was no demand for water hyacinths in the diet at a
zero hyacinth price (Table 8 and Figure 4). t
The least cost diet for finishing steer calves included 0.45 kilo-
grams of chopped water hyacinths when chopped water hyacinths were free
and other feeds were available at their average May 1973 prices. For
prices from one to four cents per kilogram, 0.08 kilograms were demanded
and for prices four to six cents 0.05 kilograms were demanded. When
prices of chopped water hyacinths were over six cents per kilogram, none
were demanded in the diet for finishing steer calves. Again, the sub-
stitution of ensiled for chopped water hyacinths had little effect on
these results.
The diet for finishing steer calves, using the January 1974 prices
for other feed ingredients, included 0.23 kilograms of ensiled or chop-
ped water hyacinths when prices for hyacinths ranged from zero to five
cents per kilogram. For prices of five to eight cents per kilogram, 0.2
kilograms of chopped or ensiled water hyacinths entered the diet and for
prices greater than eight cents neither chopped nor ensiled water hya-
cinths were a part of the diets.
Summary
In summary, at the average prices which prevailed during January
through May 1972, the results suggest that water hyacinths were not an
economical feed ingredient. Feed price increases experienced in the
last year and one half have increased the relative value of water hya-
cinths as a feed. The most water hyacinths demanded in any of the diets
was 0.45 kilograms per finishing steer calf per day at the May 1973
price level. This estimate would translate into an estimated yearly de-
mand for water hyacinths for finishing a steer calf of 164.25 kilograms
9
or approximately 360 pounds per year. If water hyacinths were fed at
9This estimate assumes that a steer calf averaging 300 kilograms
in weight is kept in the feed lot 365 days a year.
Table 8.--Ou nciiries of chopped or ensiled water hyacinths in least cost daily diets for finishing
steer calves (300 kil.grams) at various prices of other feed ingredients and of water
hyacinths
Water Hyacinths
Base
periods for
prices of all
other feed
ingredientsa
Chopped
Price
of water
hyacinths
($/kilogram)b
Kilograms
of water
hyacinths
in daily diet
Total cost
of diet
(S/day/head)
Price
of water
hyacinths
($/kilogram)b
Ensiled
Kilograms
of water
hyacinths
in daily diet
Total cost
of diet
($/day/head)
0.00000
0.00000
0.00000
0.00000
0.00000
0.00000
0.00000
0.00000
0.000000
0,0851.7
0.08517
0.08517
0,08517
0.08517
0.08517
0,05517
0.08517
0.08517
0.08517
0.08270 0.20317
0.08270 0.20399
0.08270 0.20482
0.08270 0.20565
0.08270 0.20648S
0.05144 0.20700
0.05144 0.20751
0.00000 0.20786
0.00000 0.20786
1972
1973
0.00
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.00
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.00000
0.00000
0.00000
0.00000
0,000000
0.00000
0.00000
0.00000
0. 00000
0.45261
0.08416
0.08416
0.08416
0.08416
0.05385
0.05385
0.00000
0,000ro0
0.08517
0.08517
0.08517
0.08517
0.08517
0.08517
0.08517
0.08517
0,08517
0.20227
0.20368
0.20453
0.20537
0.20621
0.20685
0,20739
0.20786
0.20786
0.00
0.01
0,02
0.03
0.04
0,05
0.06
0.07
0.08
0.00
0.01
0.02
0.03
0.04
0,05
0.06
0.07
0,08
------------
Table 8.--Quantities of chopped or ensiled water hyacinths in least cost daily diets for finishing
steer calves (300 kilograms) at various prices of other feed ingredients and of water
hvacinths--Continued
.Water hyacinths
Base
Base f Chopped Ensiled
periods for
prices of all Price Kilograms Price Kilograms.
other feed Total cost Total cost
of water of water of water of water
ingredients" of diet of diet
ingredients hyacinths hyacinths di hyacinths hyacinths of diet
b .($/day/head) b ($/day/head)
($/kilogram) in daily diet /day/head) ($/kilogram) in daily diet /
1974 0.00 0.22724 0.21565 0.00 0.22818 0.21626
0.01 0.22724 0,21792 0.01 0.22818 0.21854
0.02 0.22724 0.22019 0,02 0,22818 0,22082
0.03 0.22724 0.22246 0,03. 0.22818 0.22311
0.04 0.22724 0.22474 0.04 0.22818 0.22539
0.05 0.22724 0.22701 0.05 0,22818 0.22767
0.06 0.21319 0.22919 0.06 0.21394 0.22982
0.07 0.21319 0,23132 0.07 0.21394 0.23196
0.08 0.21319 0.23345 0,08 0.00000 0,23351
aSee Table A-I for prices of other feed ingredients in these time periods.
bNo hyacinths were included in the diet at prices of hyacinths above those shown,
No hyacinths were included in the diet at prices of hyacinths above those shown,
42
Quantity (SIL) (kilogram/head/day)
/x
ti
0to
t
-I'^
I I
I i
I
.04 .05 .06 .07
Price ($/kilogram)
Quantity (FW)
(kilogram/head/day)
-"N
.45
.23
.21
.08
.05
0
ti
L1
"1
tI
r
to 1
0
t2
f
I
t
1
I
.01 .04 .05 .06 .08
Price ($/kilogram)
Figure 4.--The demand for ensiled (SIL) and chopped (FW) water hyacinths
in a finishing steer calf (300 kilograms) diet for three time
periods
aSee Table A-1 for prices of other feed ingredients in these time
periods.
%
|
this rate to all the cattle and calves in Florida (estimated to be
2,490,000 as of January 1, 1974) [12, p. 1] 449,880 tons would be used
during a year. This amount of water hyacinths would be available on
2250 acres of water with an assumed density of 200 tons per acre. This
area represents .076 percent of Florida's inland water or 2.25 percent
of the area estimated to be infested by water hyacinths. Thus feeding
of water hyacinths is at best only a very partial solution to the hya-
cinths disposal problem and then only if feed prices remain at the high
levels experienced in 1973-74.
The prices of chopped and ensiled water hyacinths in the animal
diets were costs at the point of harvest. The costs of processing and
hauling the hyacinths are not zero and must, of course, be covered by
their price if hyacinths are to be used. If these costs had to be
covered by the price of hyacinths in the least cost diet models, then
hyacinths would have been excluded from all rations.
10This amount is, of course, a gross upper bound because this many
hyacinths could not be profitably fed.
CHAPTER V: SUMMARY AND CONCLUSIONS
Summary
A dynamic linear programming model was developed and used to de-
lineate the important variables involved in mechanical harvesting and
their effect on control cost. Biological growth of hyacinths was of
particular importance.
The model was run to determine the estimated minimum control cost
for a 400 acre lake with an initial infestation of 1,000 tons of water
hyacinths and a 30 foot fringe width as the level of control. The least
cost of control for this situation was $33.75 per acre and required one
mobile harvester. Three fixed point harvesters at a control cost of
$72.31 per acre would be required to do the same job.
The initial infestation of water hyacinths in the first month was
varied to determine the effect on control cost. The results suggest
that the control cost is very responsive to changes in the initial in-
festation of water hyacinths. The model was also run to determine the
effects of level of control desired on the control cost. The results
suggest that control costs were not sensitive to changes in the level of
control desired.
Lastly, the model was run for different sized lakes. The results
suggest the control cost would be equal for the two types of harvesters--
mobile and fixed point--when the lake size is approximately 160 acres.
For smaller lakes the fixed point harvesters have a smaller per acre (or
per ton) estimated control cost. For larger lakes mobile harvesters
have lower costs.
By-products which can be made from water hyacinths as suggested by
the literature were considered and attempts were made to measure the
demand for selected by-products--compost, soil amendment, and feed ingre-
dient in beef cattle diets.
Using data from a Florida firm, an upper limit on the value of water
hyacinths was determined to be $6.42 per wet ton when used in a compost
blend. There was no basis for determining if the actual value was near
this bound or how many hyacinths would be demanded at this price.
However, one would suspect that only a very limited quantity could be
used in this way.
An estimate of the value of water hyacinths as a soil amendment was
made. It is doubtful that their value as a soil amendment would cover
the costs of transporting and spreading of hyacinths on the land and work-
ing them into the soil.
Chopped and ensiled water hyacinths were treated as different water
hyacinths feed ingredients for cows weighing 400 kilograms and nursing
calves and for finishing steer calves weighing 300 kilograms. A least
cost diet model was used to determine a value for water hyacinths in
these diets. The diets were run for three time periods to show how the
demand for water hyacinths as a feed ingredient has changed in the last
two years as other feed prices have increased. The results agree with
theoretical expectations that there has been an increased demand for
water hyacinths as a feed ingredient due to the increased price of other
feed ingredients. But even with the increased demand for water hyacinths
the quantity demanded is not very significant. For example, if all the
cattle in Florida were fed year around with a diet including water hya-
cinths at the highest rate estimated in the least cost diets, then all of
the demand could be supplied by 2.25 percent of the total infested area
in the state.
Conclusions
For Mechanical Control
The results indicate that mechanical harvesting costs an estimated
$33.75 per acre. These costs increase as the initial amount of infesta-
tion from which geometric growth of the biomass occurs and/or the size of
the water body increases.
For By-products
The results suggest that by-products from water hyacinths have very
little value and offer little help in defraying harvesting costs.
Mechanical harvesting will require a location to simply dump the bulk of
the water hyacinths harvested or a subsidized program that will make
more constructive uses of them more attractive. The site costs for
dumping will, of course, add to control cost.
Implications for Hyacinth Control
The high cost of mechanical harvesting in comparison with the cost
of chemical control suggest that a combination of mechanical and chemi-
cal methods may be optimal from society's point of view. Mechanical
methods could be used to rid the water body of most of the infestation.
Hyacinths remaining could then be spot sprayed with chemicals to further
cut the infestation. Such an approach could reduce the initial biomass
to a level that would prevent an unacceptable buildup during the remain-
der of the growing season. Admittedly this approach would result in
some potentially harmful chemicals and some decaying water hyacinths in
the water.
There are, of course, trade-offs between the amounts of pollutants
and additional mechanical harvesting effort. The optimal level of
trade-offs was not determined in this study.
Mechanical control costs were estimated to be $33.75 per acre.
Based on observed chemical control costs of $12.00 per acre for floating
weeds and an estimated mechanical control cost of $14.16 per acre for
early season (initial month harvested), the estimated control cost of
the suggested mechanical-chemical combination would be $26.16 per acre.
By mechanically harvesting the bulk of the water hyacinths the use
of environmentally harmful chemicals would be minimized. Only residual
plants, mostly in areas where the harvester could not gain access, would
be left behind after mechanical control, These plants could be spot
sprayed. The environmental damage associated with chemical control of
the residual hyacinths and their subsequent decay was not estimated in
this study.
Limitations and Needs for Further Research
The major limitations of this stqdy on the economic implications of
hyacinths control can be attributed tq the lack of information about the
biological and physical phenomena associated with hyacinth infestation
and their mechanical control. As a consequence, many simplifying assump-
tions were made in specifying the empirical model.
A rather serious simplification is associated with the biological
functions. For one thing they were estimated with a series of discrete
linear functions. A second and more serious limitation is that this
study only looked at hyacinth growth as a function of temperature. As
was indicated earlier, there are many other factors which affect bio-
logical growth. The nonexistence of data made it impossible to make any
kind of estimate of hyacinths growth based on these other factors.
Although the coefficients estimated were "rough," the general con-
clusions from the study were clear. Research efforts to obtain more pre-
cise estimates may not be justified by the knowledge gained.
For use in animal diets the prices of chopped and ensiled water
hyacinths were costs at the point of harvest. The costs of processing
and hauling the hyacinths are not zero and must, of course, be covered
by their price if hyacinths are to be used. If these costs had to be
covered by the price of hyacinths in the least cost diet models, then
hyacinths would have been excluded from all rations.
Hyacinths as a feed and as other by-products considered in this
study did not offer much promise in helping to defray control cost. This
is not to say that by-products research should be discontinued. A by-
product may exist which is an economically feasible solution to the ques-
tion of what to do with the water hyacinths once they have been harvested.
Mechanical control is expensive--perhaps too expensive for the State
to use as sole method of control. This fact plus the rather well accepted
hypothesis that chemical control is harmful to the environment suggest
that some monies should be used to research biological methods of control.
APPENDIX
Table A-l.--Prices used in beef cattle rations
Feed ingredients May 1973 Jan. 17, 1974 Jan.-May 1972 (ave.)
- - $/Kilogram - - -
Alfalfa .0342 .0591c .0140f
Bermuda hay .0149 .0256cd .0150g
Ground corn cobs .0226 .0354c .0110h
Corn silage .0082 .0159e .0027e
Citrus pulp .0252 .0239c .0108
Yellow dent corn .0331 .0325C .0190
Sugarcane molasses .0241 .0477 .0082h
Cotton seed hulls .0163 .0225c .0058
Cotton seed meal .0645 .0273c .0182h
Soybean soil meal .1018 .0682c .0199h
Urea .0249 .0500e .0177h
Salt .0113 .0120C .0125"
Calcium phosphate .0272 .0296e .0205
Limestone .0068 .0046e .0027g
Mineral mix .0227 .1700e .10008
Vitamin mix .3721 .2050e .1210
Defluorinated
phosphate .0249 .1932e .0168
For a more complete explanation of the diet ingredients see Table
A-4.
Prices from one Gainesville feed firm for May 1973.
CAverage prices from two feed firms in Gainesville for January 17,
1974.
d$2.25/bale and using 50 bales = 1 ton, thus $112.50/ton = $0.0563/
pound $0.0256/kilogram.
prices obtained from Dr. J. F. Hentges, Jr., Department of Animal
Science, University of Florida.
Atlanta prices for January 24, 1972.
-P = 1974 1974
base (l+r) 1. 6948 For some prices in January through May
1972, no estimate existed. Therefore, .an estimate was derived based on
the average change in price of all other feeds from January through May
1972, to January 1974. The price in the base period, Pbase' i.e.,
January through May 1972, is some percentage of the price in 1974. The
percentage used, r, is an average change in prices for all other feeds
in the diet from January through May 1972 to January 1974.
Based on prices for Atlanta obtained from Feedstuffs. Mr. E. H.
Finlav.son, Department of Food and Resource Economics, University of Florida,
averaged the prices for the period January through May 1972.
a
Table A-2.--Simplex tableau for least cost diet problem
Feed ingredient
Nutrient
Ensiled water Fresh water Alfalfa Bermuda Corn ground Corn Citrus
hyacinths hyacinths hay cobs silage pulp
Cost ($/kg.) 0.0342 0.0149 0.0226 0.0082 0.0252
Dry matter weight
(kgs.) 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000
Net energy for main-
tenance (Meal.) 1.3100 1.0800 1.0600 1.5700 1.9700
Net energy for gain
(Meal.) 0.6900 0.2600 0.2500 1.0000 1.3200
Total digestible nu-
trients (kgs.) 0.3271 0.3271 0.6100 0.4400 0.4700 0.7100 0.7700
Crude protein (kgs.) 0.1360 0.1130 0.1630 0.0950 0.0280 0.0780 0.0730
Calcium (kgs.)b 0.0250 0.0250 0.0132 0.0046 0.0012 0.0027 0.0218
Phosphorus (kgs.) 0.0040d 0.0077 0.0024 0.0018 0.0004 0.0019 0.0013
Manganese (kgs.)b 0.0054 0.0051 0.0031 0.0017 0.0007 0.0018
Potassium (kgs.)b 0.0703 0.0703d 0.0084 0.0069
Sulfur (kgs.) 0.0250 0.0047
Cobalt (kgs.)b 0.1900 0.1300
Vitamin mix (kgs.)
Trace mineral mix
(kgs.)
Salt (kgs.)
Molasses (kgs.)
Roughage (kgs.) 1.0000e 1.0000 1.0000e 1.0000e 1.0000e 1.0000 1.0000e
Continued
See footnotes on page 55.
Table A-2.--Simplex tableau for least cost diet problem--Continueda
Feed ingredient
Nutrient
Yellow Sugarcane Cotton Cotton Soybean Calcium
dent corn molasses meal hulls seed meal oil meal phosphate
Cost ($/kg.) 0.0331 0.0241 0.0163 0.0645 0.1018 0.0249 0.0113 0.0172
Dry matter weight
(kgs.) 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000
Net energy for main-
tenance (Mcal.) 1.2800 2.2700 1.0300 1.6900 1.9300
Net energy for gain
(Mcal.) 1.4800 1.4800 0.1900 1.1100 1.2900
Total digestible nu-
trients (kgs.) 0.9100 0.9100 0.4100 0.7500 0.8100
Crude protein (kgs.) 0.1010 0.0430 0.0430 0.4480 0.5150 2.8100
Calcium (kgs.)b 0.0002 0.0119 0.0016 0.0017 0.0036 0.2313
Phosphorus (kgs. 0.0029 0.0011 0.0010 0.0131 0.0075 0.1865
Manganese (kgs.) 0.0047 0.0014 0.0061 0.0030
Potassium (kgs.)b 0.0317 0.0084 0.0153 0.0221
Sulfur (kgs.)
Cobalt (kgs.) 0.0200 0.1640 0.1000
Vitamin mix (kgs.)
Trace mineral mix
(kgs.)
Salt (kgs.) 1.0000
Molasses (kgs.) 1.0000
Roughage (kgs.) 1.0000e
See footnotes on page 55.Continued
Table A-2.--Simplex tableau for least cost diet problem--Continueda
Feed ingredient
Type of Finishing Cow
Nutrilent Trace Vitamin Defluorinated constraint steer nursing
Limestone phosphate calf calf
mineral mix mix phosphate
Cost ($/kg.) 0.0068 0.0227 0.3721 0.0249
Dry matter weight
(kgs.) 1.0000 1.0000 1.0000 1.0000 < 7.1000 9.3000
Net energy for main-
tenance (Mcal.) > 5.5500
Net energy for gain
(Mcal.) > 4.7800
Total digestible nu-
trients (kgs.) > 5.2500 5.3000
Crude protein (kgs.) > 0.8660 0.8556.
Calcium (kgs.)b 0.3384 0.3307 > 0.0260 0.0260
Phosphorus (kgs.) 0.0002 0.1804 > 0.0190 0.0214
Manganese (kgs.)6 0.0092 > 0.0028
Potassium (kgs.)b >0.0426
Sulfur (kgs.) > 0.0071 0.0093
Cobalt (kgs.) 0.3550
Vitamin mix (kgs.) 1.0000 = 0.0020 0.0020
Trace mineral mix
(kgs.) 1.0000 = 0.0025 0.0025
Salt (kgs.) < 0.0475 0.0475
Molasses (kgs.) < 0.7100 0.9300
Roughage (kgs.) > 1.4200 1.8600
Continued
See footnotes on page 55.
Footnotes for Table A-2:
a .th
Numers in the table represent the amount of the i nutrient
in the j feed ingredient. These values are from [19] unless other-
wise referenced. For a more complete description of the diet ingre-
dients see Table A-4.
The following ranges were used for these nutrients: calcium
+ .01; potassium + .01438; manganese + .00432; and cobalt + .36.
CEstimates obtained from personal communication with Bernard
Kiflewahid, Graduate Assistant in the Animal Science Department.
Estimates obtained from [3, p. 40].
eAll ingredients with value as a roughage were given a value of one
in this constraint. The total amount of the roughage in the diet must
exceed twenty percent of the total dry matter weight of the diet.
Table A-3.--Daily diet requirements per head for finishing steer calves
(300 kilograms) anj cows (400 kilograms) nursing calvesa
Requirements per head
Nutrient
Finishing steer Cow nursing
calves (300 kgs.) calves (400 kgs.)
Dry matter weight (kgs.) 7.1000 9.3000
Net energy-maintenance (Mcal.) 5.5500 --
Net energy-gain (Mcal.) 4.7800 -
Total digestible nutrients (kgs.) 5.2540 5.3000
Crude protein (kgs.) 0.8660 0.8556
Digestible protein (kgs.) 0.5750 0.5022
Calcium (kgs.) 0,0260 0.0260
Phosphorus (kgs.) 0.0190 0.0214
Manganese (kgs.) 0.0028
Sulfur (kgs.) 0.0071 0.0093
Potassium (kgs.) 0.0426 0.0558
Cobalt (kgs.) 0.3550 --
Vitamin mix (kgs.) 0.0020 0.0020
True mineral mix (kgs.) 0.0025 0.0025
Salt (kgs.) 0.0475 0.0475
Molasses (kgs.) 0.7100 0.9300
Roughage (kgs.) 1.4200 1.8600
aAnimal weights are average for the feeding period.
Table A-4.--Detailed description of the feed ingredients
Ingredient name used
in Tables A-1 and A-3
Alfalfa
Bermuda hay
Ground corn cobs
Citrus pulp
Yellow dent corn
Corn silage
Limestone
Defluorinated
phosphate
Soybean oil meal
Cotton seed hulls
Cotton seed meal
Calcium phosphate
Sugarcane molasses
Detailed description
Alfalfa, aerial part, dehydrated and ground, minimum 15% protein
Bermuda grass, coastal, hay
Corn, cobs, ground
Citrus pulp, without fines, shredded dehydrated
Corn, dent yellow, grain, grade 3 U.S. minimum weight 52 pounds per bushel
Corn, aerial part, ensiled, mature, well-eared minimum 50% dry matter
Limestone, ground, minimum 33% calcium
Phosphate rock, defluorinated and ground, mix 1 part flourine per 100 parts
phosphorus
Soybean, seeds, solvent-extracted and ground, maximum 7% fiber
Cotton, seed hulls
Cotton, seeds, with some hulls, solvent-extracted and ground, minimum 41%
protein, maximum 14% fiber, minimum 0.5% fat
Calcium phosphate, dibasic, commercial
Sugarcane, molasses, minimum 48% invest sugar, minimum 79.5 degrees brix
_ __
Table A-5,-Siplex tableau for harvesting cost model
Activity
Constraint A t t
a _________ 'm "1 N 12 '1 'I2 '2 31 "a1 41 '42 51 x52 x61 x62 71 x72
Number of Number of
Numbera Description fixed point mobile a Tons harvested in the jth month by the type k harvester
harvesters harvesters
0i O) O )ctive
Function 2,070 10,250 2.584 0.31 2.584 0.37 2.584 O.J1 2.584 0.37 2.584 0.31 2.584 0.37 2.564 0,3
1.1.1 Biological
1.1.2 growth in
1.1.3 jth aonth
.1.14 in tons
1.1.5
1.1.4
1.1.7
1.2.2 Initial in- 1.0 1.0
1.2.3 festation 1.0 1.0
1.2.4 in j-1 1.0 1.0
1.2.S month in 1.0 1.0'
1.2.6 tons 1.0 1.0
1.2.7 1.0 1.0.
1.3.1 Biological
1.3.2 capacity of
1.3.3 lake for
1.3.4 hyacinth
1.3.5 growth in
1.3.6 tons
1.3.7
1.6.1 Total 3.0 1,0
1.4.2 quantity 1.0 1.0
1.4.3 in tons 1.0 1.0
1.4.4 harvested 1.0 1.0
1.4.5 in 3th 1,0 1.0
1.4.6 month 1.0 1.0
1.4.7 1.0 1.
1.5.1 Quantlty -1.0 -1.0
1.5.2 In tons -*l0 1.0
1.5.3 remaining -1.0 -1,0
1.5.4 on lake with -1.0 -1.0
1.5-5 control -.0 -1.0
'1.5.6 desired -1.0 -1.0
1.5.7 -1.0 -1
1.6.1 Quantity
1.6.2 in tons
1.6.3 Tr=iining
1.6.4 cn .I.e wlth
1.6.5 ri)lmui
1.6.6 control
1.6.7
1...1 Quantity 1,256 -1.0
1.8.1 in tons 8.800 -1.0
1.8.2 harvested 1,256 -1.0
1.8.2 by type k 8,800 -1.0
1.8.3 harvester 1,256 -1.0
1.8.3 in month j 8,800 -1.0
1.8.4 1,256 -1.0
1.8.4 8,800 -1.0
1.8.5 1,256 *-.0
1,8.5 8,800 -1.0
1.8.6 1,256 -1.0
1.8.6 8.00 -1.0
1.8.7 1,256 -1.0
1.8.7 8.800 -1
.. .. Contlnu
59
Table A-5.-Simplex tableau for harvesting cost model--Continued
Activity
Constraint--------------
Constraint mx max max max ma x max
aI a2 83 a 5 a6 a NH2 H3 '4 N5 H6 I Type of Right hand
a356 constraint sidcb
Number! Description Maximum quantity of hyacinths available Initial Infestation of
to be harvested in the jth modth hyacinths in the jth month
(1.0) Objective
Function
1.1.1 Biological 1.0 3.692
1.1.2 growth in -1.0 4.153 0
1.1.3 jth month -1.0 4.082 0
1.1.4 in tons -1.0 4.407 o
1.1.5 -1.0 4.538 0
1.1.6 .1.0 .406 0
1.1.7 -1.0 3.900 0
1.2.2 Inltal in- -1.0. 1.0 0
1.2.3 festation -1.0 1.0 0
1.2.4 in J-1 -1.0 1.0 0
1.2.5 month in -1.0 1.0 0
1.2.6 tons -1.0 1.0 0
1.2.7 -1,0 1.0 0
1.3.1 Biological < 80,000
1.,.2 capacity of 1.0 < 80.000
1.3.3 lake for 1.0 80,000
1.3.4 hyacinth 1.0 $ 80,000
1.3.5 growth in 1.0 ? 80.000
1.3.6 tons 1.0 80000
1.3.7 1.0 1.0 < 80,000
1.4.1 Total <
1.4.2 quantity -1.0 0
1.4.3 in tons -1.0 0
1.4.4 harvested -1.0 0
1.4.5 in jth -1.0 0
1.4.6 month -1.0 0
i.4.7 -1.0 -1.0 | 0
1.5.1 Quantity 2.025
1.5.2 in tons 1.0 2<025
1.5.3 remaining 3.0 2,025
1.5.4 on lake with 1. 2,025
1.5.5 control 1.0 2.025
1.5.6 desired 1.0 2,025
1.5.7 1.0 1.0 2025
1.6.1 Quantity .0 338
1.6.2 in tons 1.0 3 38
1.6.3 remaining 1.0 338
1.6.4 on lake with 1.0 38
1.6.5 maximum 1.0 338
1.6.6 control .0 338
1.6.7 338
1.8.1 Quantity 0
1.8.1 in tons
1.8.2 harvested 0
1.8.2 by type k 0
1.8.3 harvester 0
1.8.3 in month j 0
1.8.4 > 0
1,8.4 0
L.8.5 0
1.8.5 0
1.8.6 0
i.8.6 0
1.8.7 > 0
1.8.7 0
a Digit following second decimal In each number refers to month vhile the two digits around the first decimal refers to
equation numbers in the text.
b The right hand side (RIS) rns por.a..tric prrnrir.ned fnr various levels of initial infestation, RHS 1.1,I; lake sizes
RIIS's 1.4.1 through 1.4.7; and, levels of control, 3HS's 1,5.1 through ,.5.7.
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