Bontoc Campus,San Ramon, Bontoc, Southern Leyte

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Faculty in Aquatic and Applied Life Sciences

1st Semester 2024-2025
POMOLOGY AND ORCHARD MANAGEMENT
Laboratory

A CASE STUDY OF OPTIMIZATION OF THE

PRODUCTIONS OF WATERMELON AND
MELON IN CANDABA,PAMPANGA

Submitted by

Rhea Layola

Submitted to
Ms.Shikinah Tommy G. Engcoy
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Abstract

The study develop saline programming model that enables to maximize the profit of small–scale
farmer in Gulap, Candaba, Pampanga in the production of different varieties of watermelon and
melon. Three types of watermelon were considered in this study such asseminis, takis, stripes while
four types of melon were considered such as brilliant, sweet flavor, jade and Ilocos gold. Each crop has
a maximum period of 90days and the environmental conditions in1. 5hectares of planting ground
areas summed to be normal. The cropping seasons from October to December. In the development of
the model, several constraints were considered such as budgets for seeds, plant operating expenses,
delivery requirements or demands in the market and the area of planting field. It is also assumed
based on the farmers that each seed will only have one watermelon fruit of each type. There searchers
were able to produce 120linear programming models for each combination of the seven varieties of
watermelon. Using Microsoft Excel Solver, the solution for each model obtained and the best
combination was identified. Profit analysis was also done by comparing the profit earned by the
traditional way of planting against the developed combination of seeds using linear programming, and
it was proved that the developed model produces a higher profit

I.INTRODUCTION

Agricultural sector plays an important role in the economic progress of anation. The materials needed and the
economic activities come from this. First, the agricultural sector provides food. The Philippines oilis best suited
for root crops such as rice, corn, sugar cane, potatoes and many others. Mangoes, pineapples, coconuts, and
bananas also abound. Second,it provides raw materials needed to create other products. Natural materials
from forests, fields, and seas can be made into a different variety of handicraft products. The agricultural sector
also contributes to the economic progress through export. Agricultural products that are exported to other
countries include sugar, flowers, fruits, seafood and many others. An important source of income for the
governments the exportation of agricultural products. It provides employment to a large number of Filipinos.
Those on the country side depend on agriculture for their livelihood such as farming, fishing, raising livestock.
Last, a progressive agricultural sector can support other sectors of the economy like manufacturing, trade and
services by supplying the needed raw materials. That is why when a country dreams of industrialization, it
needs to expand and improve its agricultural production. (Pulse 101, 2013) The tropical and subtropical fruit
industry is an important sector in many countries in generating income and employment, providing foreign
exchange earnings and as an important source of nutrition and dietary requirements for a healthy population.
It is avibrantsector with progressive expansion in production, international trade and consumption. (Izham &
Chua, 2006)Watermelon (Citrulluslanatus )Is widespread in all tropical and subtropical regions of the world.
Mostly grown for fresh consumption of the juicy and sweet flesh of mature fruits. Locally known in the country
as pakwan, it is one of the most popularly grown fruits in the country today during summer. (DA-BPI, 2011)The
researchers consider only the following varieties of watermelon and melon like takis, stripes, seminis, jade,
brilliant, Ilocos gold and sweet flavour, which are used by small-scale farmers in Candaba,
Pampanga.Mathematical programming is a method for solving a problem where one function or objective is
maximized or minimized while other functions or constraints are satisfied. As an example, mathematical
programming can be used to maximize profit given constraints on available capital and labor. Mathematical
programming models developed by agricultural economists can be divided into two main categories: farm
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models and sector models (Hazell & Norton, 1986). Since the 1960’s mathematical programming techniques
have been widely used to model farm-level management decisions and to model agricultural sectors. Linear
Programming (LP) isperhapsthe most important and best-studied optimization problem. It was used in
representingtheagroforestrymodel. The model considered the government sector, production sector, market
sector andhouseholdsectorascomponentsof the system. Participatory rapid rural appraisal was used in
gathering dataand standard methods for financial analyses.Theoptimalsolutiongenerated a maximum value of
₱373,689.80 which includes ginger, banana and nangka with 122,857 plants, 32 plants and 247 trees
respectively. The optimal land allocation of21,611.57squaremeter(70.82%)and8,906.04 (29.18%) are for
agricultural crop production and fruit tree production respectively. The optimal area is 3.0571 hectares. All
constraints are non-binding except for maintenance/protection labor. Increasing the area to be planted with
trees reduces the objective functionvalue and favours the planting of mango.
Increaseinobjectivefunctionandincome were observed in varying the farm size from 1 hectare to 3.5 hectares.
Limiting the capital requirements resulted to planting oflowinputcrops.Forcingaspeciestobe included in the
optimal solution reduces the objective function. Adding erosion constraint drastically reduces the objective
function and species composition solution.(Hernandez,1998)LinearProgrammingtechniqueisrelevant
inoptimizationofresourceallocation and achieving efficiency in production planning particularly in achieving
increased agricultural productivity. Igwe, Onyenweaku and Nwaru applied a linear
programmingtechniquetodeterminethe optimum enterprise combination.The recommended optimum plan by
the LP model achieved a gross income of
N342,763.30fromN188,736.29,a44.6percentageincrease.Riddler,Rendeland Baker applied LPto a sheep and cow
farm. This led to a new system of how feed is grown and utilized and a refined system to make use of it with
breeding cows and ewes. Since the start of the use of the linear programming model, farm income has increased
for the past ten years. Mohring and Zimmermann constructed and applied linear programming farm model
with an integrated Life Cycle Assessment for the determination of sustainable milk production systems.
Linearprogrammingwasalsoapplied by Salimonu, et al. to model the efficient resourceallocationpatternsforfood
cropfarmersinNigeria.AreturnofN31,959.81 per hectare was the actual
levelofthefarmers’incomecomparedwithth returnofN98,861.24.Ifthefarmerswere to apply profit maximization
objective,this will be achieved by applying linear programming. LinearProgrammingtechniqueisrelevant
inoptimizationofcropmixforafinite-time planning horizon. Given limited available resources such as budget and
land acreage, the crop-mix planning model was formulated and transformed into a multi-
periodlinearprogrammingproblem. The objective was the maximization
ofthetotalreturnsattheendoftheplanning horizon. The problem was solved for selected vegetable crops using
LINDO. The results indicated promising returns evenforarelativelyshortplanninghorizon
of12monthsandifproperlyimplemented will enhance farm income and provide beneficial contribution to the
farming societies. (Mohamad and Said, 2011).

II.RESULTS AND DISCUSSIONS

The main objective of this study is to develop a Linear Programming

model/s.Itdeterminesthebestcombinationofwatermelonandmelonproductionof small–scale farmers in
Candaba, Pampanga so as to maximize their profit. In a 1.5 hectare land, the three varieties
ofwatermelon(seminis,takisandstripes) and 4 varieties of melon (brilliant, Ilocos
gold,jadeandsweetflavor)wereplanted. Each crop has a maximum grooming period of 90 days, and the
environmental conditions are assumed to be normal. A totalof120linearprogrammingmodelsof
differentcombinationsofwatermelonand melon were developed.
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FormulationofLinearConstraints

Let c1 to c4 be the constraints. Supposec1 is the budget for seeds. It is the sumof the cost per seed of
each crop which should not exceed to the total budget for seeds. The coefficient was achieved by
dividingthepriceperpackofeachcropto the number of seeds per pack as shown in Table 2.

Let c2 as an operating expense per seed. Operatingexpensesincludemachineries, fertilizers,

pesticides, herbicides and vitamins which are required to get the maximumgrowthofeachplant.
Table1.
Revenue Contribution of EachWatermelonandMelon

Table 2 :Budget for each crops and delivery requirements

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The coefficient was computed by dividing the allottedbudgetforoperatingexpenses to the total

number of planting holes that was 17,152. The allotted budget for the seeds was PhP 120,000.00.
Thus, each seed cost an operation of approximately PhP 7.00.

Let c3 be the delivery requirement. The minimum demand of all buyers was at least 10,000 kilos. If it
was not achieved, the buyer would no longer continue the transaction.Inthiscase,thefarmerwould
have a problem in selling their products.

Let c4 as the number of planting holes for cultivation. The number of planting holes limits the number
of seeds to be planted. Twoplantingholeswereprovidedforeach seedofwatermelonandoneplantinghole
per seed of melon. If the number of the plantingholesexceededinthegivenlimit, it might affect the
growing process of the crops because the area will be crowded.

TheLinearProgrammingModelsanditsOptimalSolution

The researcher presented only the maximumprofitforeachpossiblenumber

combinationsofcrops;thatis,fromtwoto seven combinations. Out of 120 possible combinations, there
were six best combinations:

1. CombinationofTakisandBrilliant(x2,x4)Objectivefunction
MaxZ=75x2+60x4

Subjectto
0.58x2+4.17x4≤ 15,000
7(x2+x4)≤120,000
7.5x2+2x4≥1,0000
2x2+x4≤ 17,152
x2,x4≥ 0

OptimalSolution:
x2=7,284,x4=2,584
andZ=Php701,340
Thereare21possiblecombinationsoftwo varieties of watermelon and melon. And based on these possible
combinations, the farmer should plant 7,284 seeds of takisand2,584seedsofbrillianttoamass maximum
profit of Php 701,340.

2. CombinationofSeminis,TakisandBrilliant(x1,x2,x4)

Objectivefunction
MaxZ=27x1+75x2+60x4

Subjectto
0.89x1+0.58x2+4.17x4≤15000
7(x1+x2+x4)≤120,000
2.25x1+7.5x2+2x4≥10,000
2x1+2x2+x4≤17,152
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x1,x2,x4≥0

OptimalSolution:
x1=0,x2=7,284,x4=2584,Z=Php701,340

Thereare35possiblecombinationsof three varieties of watermelon and melon. And based on these possible
combinations, the farmer should plant 7,284 seeds of takis and 2,584 seeds of brilliant only to have a
maximum profit of PhP 701,340.

3. Combinationof Seminis,Takis,StripesandBrilliant(x1,x2,x3,x4)

ObjectiveFunction
MaxZ=27x1+75x2+27x3+60x4

Subjectto
0.89x1+0.58x2+0.63x3+4.17x4≤15,000
7(x1+x2+x3+x4)≤120,000
2.25x1+7.5x2+2.25x3+2x4≥10,000
2x1+2x2+2x3+x4≤17,152
x1,x2,x3,x4≥0
OptimalSolution:
x1=0,x2=7,284,x3=0,x4=2,584Z=Php701,340

There are 35 possible combinations of four varieties of watermelon and melon. And
basedonthesepossiblecombinations,
the farmer should plant 7,284 seeds of takis and 2,584 seeds of brilliant only to have a maximum profit of PhP
701,340.

4. CombinationofSeminis,Takis,Stripes,BrilliantandJade(x1,x2,x3,x4,x5)

ObjectiveFunction
MaxZ=27x1+75x2+27x3+60x4
+50x5

Subjectto
0.89x1+0.58x2+0.63x3+4.17x4
+3.28x5≤15,000
7(x1+x2+x3+x4+x5)≤120,000
2.25x1+7.5x2+2.25x3+2x4
+2x5≥10,000
2x1+2x2+2x3+x4+x5≤17,152
x1,x2,x3,x4,x5≥0

OptimalSolution:
x1=0,x2=7,284,x3=0,
x4=2584,x5=0,Z=Php701,340
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There are 21 possible combinations of five varieties of watermelon and melon. And based on these possible
combinations, the farmer should plant 7,284 seeds of Takis and 2,584 seeds of Brilliant only to have a
maximum profit of Php 701,340.

5. CombinationofSeminis,Takis,Stripes,Brilliant,JadeandSweetFlavor(x1,x2,x3,x4,x5,x6)

Objectivefunction
MaxZ=27x1+75x2+27x3+60x4+50x5+40x6

Subjectto0.89x1+0.58x2+0.63x3+4.17x4+3.28x5+2.0
5x6≤15000
7(x1+x2+x3+x4+x5+x6)≤120,000
2.25x1+7.5x2+2.25x3+2x4+2x5+2x6≥10000
2x1+2x2+2x3+x4+x5+x6≤17152
x1,x2,x3,x4,x5,x6≥0
OptimalSolution:x1=0,x2=7,284,x3=0,x4=2,584,x5=0,x6=0,Z=Php701,340

Therearesevenpossiblecombinationsof six varieties of watermelon and melon.And

basedonthesepossiblecombinations,
the farmer should plant 7,284 seeds of Takis and 2,584 seeds of Brilliant only to have a maximum
profit of Php 701,340.

5.CombinationofSeminis,Takis,Stripes,Brilliant,Jade,SweetFlavorandIlocosGold(x1,x2,x3,x4,x5,x6,x7)

Objectivefunction
MaxZ=27x1+75x2+27x3
+60x4+50x5+40x6+60x7

Subjectto
0.89x1+0.58x2+0.63x3+4.17x4+
3.28x5+2.05x6+7x7≤15,000
7(x1+x2+x3+x4+x5+x6+x7) ≤
120,000
2.25x1+7.5x2+2.25x3+2x4+2x5
+2x6+2x7≥ 10,000
2x1+2x2+2x3+x4+x5+x6+x7
≤ 17,152
x1+x2+x3+x4+x5+x6+x7≥ 0

OptimalSolution:
x1=0,x2=7,284,x3=0,
x4=2,584,x5=0,
x6=0,x7=0,
Z=Php701,340
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Whenitcomestothesevencombinations ofdifferentvarietiesofwatermelonand melon, there is only one

possible combination. And based on this combination, the farmer should plant 7,284 seeds of takis
and 2,584 seeds of brilliant only to have a maximum profit of PhP 701,340.

Results show that for each different possible combinations of different varieties of watermelon and
melon, they producedthesamemaximumrevenue of PhP 701,340 by planting 7,284 seeds of takis
(watermelon) and 2,584 seeds of brilliant (melon).

Table3showacomparisonofprofit inthetraditionalplantingmethodand the solution using linear

programming. Basedonthistable,budgetallocation
Table3.
ComparisonofLPSolutionand Traditional Planting Method

IV.CONCLUSION

Based on the developed linear programmingmodel,itwasshowedthat planting a combination oftakis

(watermelon) and brilliant (melon) will maximizetherevenueandprofitofthe small-scale farmers in Candava,
Pampanga. The profit from traditional planting method has increased by as muchas113.82%fortheplantthebest
combination obtained using linear programming.Ontheotherhand,the combination of other varieties of
watermelon and melon such as stripes, seminisandothersgivesthelowestprofit among the other combinations.
Linear programming model is a quantitative technique used when it comes todecision making. It is a systematic
wayof determining our goal that is profit maximization given different constraints or restrictions.

IV.RECOMMENDATION

The researchers suggest that the small- scale farmers in Candava, Pampanga should plant 7,284 seeds of
takis and 2,584 seeds of brilliant to achieve a maximumprofitofPhP701,340.Wealso recommend the use of
other constraints such as factors that affect the growth of watermelons and melons.Environment conditions
in planting should also be consideredinfuturestudies.Usinglinear programming model is highly endorsedto
determine the optimal solution when it comestoprofitmaximizationgivencertain constraints.
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REFERENCES

Department of Agriculture, Bureau of Plant Industry, 2011. “Watermelon, Production Guide,” http://www.
bpi.da.gov.ph/ bpioldsite1/guide_ pakwan.php

Hernandez, Aristeo A. Linear ProgrammingModelforAgroforestry ManagementSystematDUEG,San

Clemente, Tarlac, 1998.

Hazell, P. B. R. & Norton, R. D. 1986. Mathematical Programming for Economic Analysis in Agriculture.
Macmillan Publishing Company. New York.

Igwe,K.C.,Onyenweaku,C.E.,& Nwaru, S. (2011). Application of Linear Programming to Semi- Commercial

Arable and Fishery Enterprises inArabia State, Nigeria. International Journal of Economics and
Management Sciences. Vol. 1, pp.75-81.

Izham, Ahmad and Chua, Piak Chwee 2006. “Increasing Consumption of Tropical and Subtropical Fruits,”
FruitandVegetablesforHealth

SUMMARY
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Agriculture is a critical sector for the Philippine economy, providing both employment and sustenance to a
large portion of the population, especially in rural areas. In particular, the cultivation of fruits like watermelon
and melon plays a significant role in generating income for small-scale farmers. In Candaba, Pampanga, a region
known for its agricultural activities, the optimization of fruit production is crucial for improving farm
profitability. The study titled “Optimization of the Production of Watermelon and Melon in Candaba,
Pampanga” employs linear programming (LP) to identify the best combination of watermelon and melon
varieties to maximize profit for small-scale farmers. The study’s primary objective is to develop a linear
programming model to help maximize the profit of small-scale farmers in Candaba by optimizing the
production of watermelon and melon varieties. This optimization process involves selecting the best
combination of watermelon and melon varieties to plant, given several constraints like budget, available
planting area, and market demand. The study focuses on three varieties of watermelon (Seminis, Takis, and
Stripes) and four types of melon (Brilliant, Sweet Flavor, Jade, and Ilocos Gold). These crops were selected
because they are commonly
A key aspect’of the study is the formulation of constraints that must be considered in the optimization process.
These constraints include seed costs, operating expenses, planting area limitations, and market demand
requirements. The constraints ensure that the optimal solution is both feasible and practical for the farmers. By
solving the linear programming models, the researchers aim to determine the crop combinations that yield the
highest profit, while also meeting all these constraints.Widely used mathematical optimization technique that
helps in making decisions to maximize or minimize an objective function under given constraints. In this case,
the objective was to maximize profit. LP was chosen for its ability to handle multiple variables and constraints
in a structured manner, providing an optimal solution based on the available data. The researchers developed
120 different linear programming models corresponding to different combinations of watermelon and melon
varieties. The key variables in the model represent the number of seeds to be planted for each variety. For
example, the variable denotes the number of Seminis watermelon seeds to be planted, represents Taki
watermelon seeds, and so on. The objective function in each model calculates the total revenue generated from
planting a particular combination of these crops. The total cost of seeds for each crop combination should not
exceed the total budget allocated for seed purchase. This includes the costs of fertilizers, pesticides, labor, and
other farming expenses. The total operating expense for each combination should be within the allocated
budget.To ensure market demand is met, the total weight of the crops harvested must meet the minimum
market requirement of 10,000 kilos.The number of planting holes is limited to 17,152, which restricts the total
number of seeds that can be planted. This constraint ensures that the crops are not overcrowded, which could
affect their growth.Each model was solved using Microsoft Excel’s Solver tool, which helped determine the
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optimal number of seeds to plant for each crop combination. After solving the models, the best combinations
were selected based on the highest revenue generated.The results showed that, regardless of the number of
varieties planted, the optimal solution for maximizing profit consistently involved planting 7,284 seeds of Takis
watermelon and 2,584 seeds of Brilliant melon. This combination yielded a maximum profit of Php 701,340.
The researchers tested various combinations of crops, ranging from two varieties to seven varieties, but in all
cases, the maximum profit remained the same. This suggests that the combination of Takis watermelon and
Brilliant melon is the most profitable for farmers in the study area.The optimal solution for this combination
resulted in planting 7,284 seeds of Takis watermelon and 2,584 seeds of Brilliant melon, which led to a profit of
Php 701,340. This result was consistent across all combinations tested.When additional varieties were
introduced, such as Stripes watermelon, Jade melon, Sweet Flavor melon, and Ilocos Gold melon, the optimal
planting solution remained unchanged, with the same seed numbers for Takis and Brilliant. This indicates that
adding other varieties did not significantly increase profit, suggesting that Takis and Brilliant were the most
efficient crops to grow under the given constraints.The study also compared the results obtained from linear
programming with the traditional planting methods employed by farmers in the region. In the traditional
method, farmers would plant a combination of various crops based on their experience and judgment, without
considering the optimal allocation of resources.The comparison revealed a substantial increase in profit when
using the LP model. Traditional planting yielded a profit of Php 323,000, while the linear programming solution
resulted in Php 701,340, a 113.82% increase in profit. Additionally, the operating expenses for planting using
the linear programming solution were significantly lower (Php 50,924 less) than the traditional method. This
indicates that the LP model not only maximizes profit but also helps reduce unnecessary costs.The study
concludes that using linear programming to optimize the production of watermelon and melon in Candaba,
Pampanga, can significantly increase farm profits. By planting a combination of 7,284 Takis watermelon seeds
and 2,584 Brilliant melon seeds, farmers can maximize their revenue under the given constraints. The LP
solution outperforms traditional farming practices, both in terms of profit and cost-efficiency.The researchers
recommend that small-scale farmers in Candaba adopt the linear programming model to improve their crop
selection and resource allocation. They also suggest further research to incorporate other factors that affect
crop growth, such as environmental conditions, pest control, and weather patterns, into the optimization
models. By expanding the scope of the study, future research can provide even more precise recommendations
for farmers, helping them achieve sustainable and profitable farming practices.Ultimately, the use of linear
programming in agricultural production can provide a data-driven approach to decision-making, enabling
farmers to maximize their profits while minimizing resource wastage. This approach could be applied to other
crops and regions, further enhancing the productivity and profitability of the agricultural sector in the
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Philippines.