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Linear Programming Approach: Optimization of Profit and Land Resource

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Indian Journal of Natural Sciences www.tnsroindia.org.in ©IJONS

Vol.15 / Issue 84 / Jun / 2024 International Bimonthly (Print) – Open Access ISSN: 0976 – 0997
RESEARCH ARTICLE

Linear Programming Approach: Optimization of Profit and Land

Resource

Prachi1, Sangeeta Gupta2*and Sweta Srivastav1

Department of Mathematics, Sharda University, Greater Noida, Uttar Pradesh, India.

1

The A.H. Siddiqi Centre for Advanced Research in Applied Mathematics and Physics, Sharda
2

University, Greater Noida, Uttar Pradesh, India.

Received: 29 Apr 2024 Revised: 05 May 2024 Accepted: 08 May 2024

*Address for Correspondence

Sangeeta Gupta
The A.H. Siddiqi Centre for Advanced Research in Applied Mathematics and Physics,
Sharda University, Greater Noida,
Uttar Pradesh, India.
Email: sangeeta.gupta@sharda.ac.in

This is an Open Access Journal / article distributed under the terms of the Creative Commons Attribution License
(CC BY-NC-ND 3.0) which permits unrestricted use, distribution, and reproduction in any medium, provided the
original work is properly cited. All rights reserved.

ABSTRACT

Allocating resources like land, fertilizer, crops, water, etc. requires a detailed farm plan. In this study, the
LINEAR PROGRAMMING MODEL is used to identify crop combinations for a farmer in the Gurugram
district of Haryana. This work provides a Linear Programming Model for RABI crops (Wheat, Mustard,
and Barley (Joo)) and for KHARIF crops (Millet(bajra), radish, and rice). The optimal allocation of land is
obtained with the use of MATLAB, which improves the quality of decisions. It was found that the profit
can be increased by 24% for the RABI crop and 6.7% can be increased for the KHARIF crop. Also, a graph
showing the comparison of the current situation and the optimal solution is shown (Fig. no.2 &3). To
create the perfect model, some farm attributes—such as climate and market fluctuations—are kept
constant.

Keywords: Linear programming, current situation, Optimal solution, Attributes, Market fluctuations, etc

INTRODUCTION

The agriculture sector plays a significant role in the social and economic development of India. Meeting the growing
demands for food, feed, and fibre presents ever-greater challenges for agriculture, the foundation of our global
economy. This vital industry that provides the majority of the world's food, faces the difficult task of balancing
productivity and resource use in the face of changing social, economic, and environmental factors. As the study done
by Joshi, A., Das, S., & VA seem, Mohd. [2] States that India's agricultural industry has numerous obstacles resulting
from variables relating to markets, policies, the environment, and structure. The modern period of changing climatic
circumstances and population expansion has made it essential to allocate resources optimally and maximize output.

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Vol.15 / Issue 84 / Jun / 2024 International Bimonthly (Print) – Open Access ISSN: 0976 – 0997

Prachi et al.,

The optimal use of land and water resources is necessary for agricultural production. This means that a farm's
resources must be distributed effectively. Choosing what to grow, when to plant it, what agricultural techniques are
available, and how much is needed are tough decisions that farmers must make. The revolutionary potential of
decision support systems in promoting sustainable development in the digital era and modernizing agricultural
practices is highlighted by Zhai, Martínez, Beltran, and Martínez [10]. The financial and physical state of farms are
taken into consideration when making decisions, but there is still a lot of uncertainty over this industry's planning
horizon. Resources such as workers, seeds, manures, and fertilizers might have erratic production and pricing (Priya
Priyadarshi and Purushothaman [8].

In order to make better decisions, allocate resources optimally, and increase the resilience, sustainability, and
efficiency of agricultural systems, linear programming is essential. Its applications cover a wide range of
management, policy, and production elements of agriculture and improve sustainable agriculture and rural
development globally. This study sets out to investigate the use of linear programming, a mathematical method of
optimization, in the field of agriculture. The work presented by N. A. Sofi, Aquil Ahmed, Mudasir Ahmad, and Bilal
Ahmad Bhat [6]focuses on using linear programming (LP) as an approach to successfully handle these issues. Also,
in a study of Senthilnathan S. [9] they highlighted the potential of linear programming models with the use of the MS
Excel in optimizing crop selection and resource allocation in Central Greece. Based on mathematical modelling,
linear programming offers a methodical way to make decisions. Majeke, F., Mubvuma, M. T., and Makaza, K. [3,4,5]
worked to find the best crop combination for a rural farmer, a linear programming model was used for this study.
The credit restriction was integrated into the linear programming paradigm. To maximize revenue was the goal.
The objective of this work is to explore the various aspects of the linear programming approach in agriculture,
clarifying its past development, present uses, and prospective future developments. Moreover, linear programming
can assist in long-term planning and decision-making.

Long-term planning and decision-making can benefit from the use of linear programming. Farmers can predict
future prices and demand by analysing market patterns and historical data. Alanoud and Farrukh [1]farmers can
make proactive decisions on crop selection, planting schedules, and resource allocation by integrating these forecasts
into the linear programming model. This will help them stay ahead of market fluctuations. The study by Poonia,
Tonk, Bhatia, etc. all[7] provide a useful tool for improving farm profitability and sustainability in resource-
constrained contexts by utilizing the power of linear programming.

We find the optimal solution understanding and utilizing the power of linear programming becomes essential for
sustainable and effective agricultural practices in an era climate uncertainty and pressures from a growing global
population need careful resource management. Therefore, this study's goals go beyond merely outlining its methods;
they also include a sincere attempt to clarify the revolutionary role that linear programming can play in influencing
how agriculture develops in the future. We find the optimal solution Understanding and utilizing the power of
linear programming becomes essential for sustainable and effective agricultural practices in an era climate
uncertainty and pressures from a growing global population need careful resource management. Therefore, this
study's goals go beyond merely outlining its methods; they also include a sincere attempt to clarify the revolutionary
role that linear programming can play in influencing how agriculture develops in the future.

An LP model was developed in this study to ascertain the best crop combination for a farmer in Gurugram district of
Haryana, India. Wheat, Mustard and Barley (Joo) were the crops taken into account in Rabi season and Millet(bajra),
radish and rice were the crops taken into account in Kharif season. The optimal solution to the problem is obtained
using MATLAB. Our goal is to offer insightful information on the intricate dynamics involved in making agricultural
decisions. Hence a comparison has also been done of the current situation and optimal solution suggested using LP
Model with the help of MATLAB. This comparison is shown by the graph (Figure 2 and 3). The following diagram
shows Optimization technique:

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Indian Journal of Natural Sciences www.tnsroindia.org.in ©IJONS

Vol.15 / Issue 84 / Jun / 2024 International Bimonthly (Print) – Open Access ISSN: 0976 – 0997
Prachi et al.,

METHODOLOGY

A linear programming with ‘’n`` decision variables and ‘’m`` constraints can be mathematically modelled as:
= + + + ⋯……….
+ + + ⋯………. ≤
+ + + ⋯………. ≤
+ + + ⋯………. ≤
≥ 0 , = 1 ,2 … … … …
Data Collection
The data is collected from a small village farmer of the Gurugram district of Haryana for both the seasons, Kharif
and Rabi. The crops sown by the farmer in Rabi season the crops are Wheat, Mustard, and Barley (Joo) whereas in
the kharif season are Millet (Bajra), Rice, and Radish. Data regarding land allocation, man-days, costs, and the net
return of each crop required for each crop is based on recent methodology used by the farmer for both seasons. The
LP problem is solved by using "MATLAB", a computer programming platform.
The LP (linear programming) model is developed using exact data given by farmer to maximize the net return at the
end of the Kharif and Rabi seasons.

RESULTS AND DISCUSSION

The LP (linear programming) model is developed using exact data given by farmer to maximize the net return at the
end of the Rabi and Kharif seasons.

RABI SEASON
Table 1 shows the farmer's cropping pattern (allocation of land, man-days, and operating capital required for the
preparation of the crops). As the table shows the farmer uses a total of 40 acres of land for Wheat, Mustard, and
Barley (Joo) with 500 total man-days and operating capital of rupees 550000 in the Rabi season which gives the net
returns of 1666000 rupees. Also, as per the farmer's requirements, he needs at least 3 acres of land for wheat, at least 2
acres for mustard, and 2 acres of land for Barley.

In this scenario, the output of different crops serves as the objective function, while the land, man-days, and
operating capitalrepresent the inequalities and the total requirement. Finding the ideal area for crops is now our
goal.

LP model
= 50000 + 52000 + 48000
S.to. + + ≤ 40
18000 + 14000 + 15000 ≤ 750000
11 + 4 + 11 ≤ 500
≥ 3, ≥ 2, ≥ 2
≥ 0 , = 1 ,2,3
where x1= acres of land allocated to Wheat
x2 = acres of land allocated to Mustard
x3= acres of land allocated to Barley

The LP model's recommended cropping pattern (Table 2) demonstrates that returns can be increased by allocating 3
acres of land to Wheat,35 acres to Mustard, and 2 acres of land to Barley. Hence according to the cropping pattern
recommended by the LP model planting more Mustard on available land can increase returns. Since the land
allocation in the LP model is different from land allocation by the farmer, so Man-days and Costs will also vary
accordingly.

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Indian Journal of Natural Sciences www.tnsroindia.org.in ©IJONS

Vol.15 / Issue 84 / Jun / 2024 International Bimonthly (Print) – Open Access ISSN: 0976 – 0997

Prachi et al.,

Thus, it is evident from the comparison graph and table that the cropping pattern suggested by the LP model can
raise the net return by 24%.

KHARIF SEASON
The farmer planted Millet (Bajra), rice, and Radish as their crops. Table 3 shows that the average amount of resources
available was 32 acres of land. The farmer leaves 8 acres of vacant land as fallow land,800 man-days, and 300000
rupees in operating capital during the Kharif season. Planning an appropriate farming pattern was intended to
increase yields relative to the current net average return of farmers, which was rupees 1867800.Also, the farmer
requires at least 10 acres of land for Millet (Bajra), at least 5 acres of land for Rice, and at least 5 acres of land for
Radish.

LP Model
= 35000 + 70400 + 85000
S.to. + + ≤ 32
15000 + 28000 + 33400 ≤ 950000
15 + 25 + 40 ≤ 800
≥ 10, ≥ 5, ≥ 5
≥ 0 , = 1 ,2,3
where x1=acres of land allocated to Millet (Bajra)
x2=acres of land allocated to Rice
x3=acres of land allocated to Radish

The LP model's recommended cropping pattern (Table 5) demonstrates that returns can be increased by allocating 10
acres of land to Millet (Bajra) ,15.34 acres to Rice and 6.67acres of land to Radish. Since the land allocation in LP
model is different from land allocation by farmer, so Man-days and Costs will also vary accordingly. Thus, it is
evident from the comparison graph and table that the cropping pattern suggested by the LP model can raise the net
return by 6.7%.

CONCLUSIONS

An LP model that establishes the ideal crop combination for the Rabi and Kharif seasons for a small farmer in the
Gurugram district of Haryana is created in this study. Crops considered in the Rabi season are Wheat, Mustard, and
Barley (Joo) whereas Crops considered in the Kharif season are Millet (Bajra), Rice, and Radish. For Rabi Season
planting the LP model suggests planting more Mustard will increase the net returns by up to 24% and for the Kharif
season planting more Rice on available land can increase net returns by up to 6.7%.

REFERENCES

1. Alotaibi, A., & Nadeem, F. (2021). A review of applications of linear programming to optimize agricultural
solutions. International Journal of Information Engineering and Electronic Business, 13(2), 11–21.
https://doi.org/10.5815/ijieeb.2021.02.02
2. Joshi, A., Das, S., & VA seem, Mohd. (2021). An analysis of challenges of the Agriculture Economy in India. South
Asian Journal of Marketing & Management Research, 11(10), 27–34. https://doi.org/10.5958/2249-
877x.2021.00065.5
3. Majeke, F., Mubvuma, M. T., Makaza, K., & Mutambara, J. (2013). Optimum combination of crop farm activities:
Application of a linear programming model to a rural farmer in Zimbabwe. Greener Journal of Economics and
Accountancy, 2(2), 058–061. https://doi.org/10.15580/gjea.2013.2.052213634

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Vol.15 / Issue 84 / Jun / 2024 International Bimonthly (Print) – Open Access ISSN: 0976 – 0997
Prachi et al.,

4. Majeke, F., Mubvuma, M. T., & Makaza, K. (2013a). Incorporating the credit constraint in a linear programming
model: A case study of a rural farmer in Zimbabwe. Journal of Management and Science, 1(2), 245–250.
https://doi.org/10.26524/jms.2013.30
5. Majeke, F., Mubvuma, M. T., Makaza, K., & Mutambara, J. (2013a). Optimum combination of crop farm activities:
Application of a linear programming model to a rural farmer in Zimbabwe. Greener Journal of Economics and
Accountancy, 2(2), 058–061. https://doi.org/10.15580/gjea.2013.2.052213634
6. NA Sofi, An Ahmed, M Ahmad, and BA Bhat (2015). Decision making in agriculture: A linear programming
approach.Internationaljournalofmodern mathematical sciences
7. Poonia, H., Tonk, M. S., Bhatia, J. K., Rekha, & Rani, N. (2020). Linear programming-based crop land allocation to
maximize profit of marginal/small farmers. Agricultural Research Journal, 57(2), 245. https://doi.org/10.5958/2395-
146x.2020.00037.x
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agriculture in India. Land Use Policy, 96, 104718. https://doi.org/10.1016/j.landusepol.2020.104718
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Journal. https://doi.org/10.2139/ssrn.2479777
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Survey and challenges. Computers and Electronics in Agriculture, 170, 105256.
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Table 1: Farmer’s methodology

Operating Capital (rupees/ Output (rupees/
Crops Land(acres) Man-days (days/acres)
acres) acres)
Wheat 22 11 18000 50000
Mustard 13 4 14000 52000
Barley 5 11 15000 48000
Total 40 500 750000
The net return = 1666000

Table 2: The Cropping Schedule as recommended by the LP Model

Crops Land(acre)
Wheat 3
Mustard 35
Barley 2
Total 40
The net return = 2066000

Table 3: Comparison of Farmer’s allocation and LP model allocation

Crops Land(acres) allocation by Farmer Land(acres) allocation by LP model
Wheat 22 3
Mustard 13 35
Barley 5 2
Total 40 40

Table 4:Farmer’s methodology

Output (rupees/
Crops Land(acres) Man-days (days/acres) Operating capital (rupees/ acres)
acres)
Millet (Bajra) 15 15 15000 35000
Rice 7 25 28000 70400

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 Indian Journal of Natural Sciences www.tnsroindia.org.in ©IJONS

Vol.15 / Issue 84 / Jun / 2024 International Bimonthly (Print) – Open Access ISSN: 0976 – 0997

Prachi et al.,

Radish 10 40 33400 85000

Total 32 800 950000
The net return = 1867000

Table 5: The cropping schedule as recommended by the LP model

Crops Land(acres)
Millet 10
Rice 15.34
Radish 6.67
Total 32
The Net Return =1996000

Table 6: Comparison of Farmer's allocation and LP model allocation

Crops Land (acres) allocation by Farmer Land (acres) allocation by LP Model
Millet (Bajra) 15 10
Rice 7 15.34
Radish 10 6.67
Total 32 32

Figure 1: Optimization Model Figure 2: Comparison of Land allocation

Figure 3: Comparison of land allocation

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