Application of optimization in various mathematical models
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Date
2023-06-16
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Department of Mathematics, OUAT, Bhubaneswar
Abstract
Today, it is quite difficult to meet everyone's food needs. The cultivation of crops faces several real obstacles, which are quite significant. One of the elements is a soil analysis. Studies of soil based tests for various crops, primarily paddy crop tests, and testing stoichiometric tests on soil and for the specialized area of impact, balanced fertilizers and organic matter amelioration were advised to obtain targeted yield of paddy crop. It supports crop plant’s abundant and dynamic growth using the appropriate soil texture under different agro climatologies. Studying the need for certain nutrients (N and P) to increase the production of paddy crop through the use of specialized fertilizers that is structured as a mathematical model. Data pertaining to the percentage study of nutrients dictated the creation of a model through analysis algorithm, principles,methods, and quantification. The experimental design building blocks are supported by regression based investigations. Studies using experimental block casting and experiment findings produced an effective recommended fertiliser % to upgrade, fill the gap left by insufficient fertilisers for the paddy crop, and achieve our desired yield by applying Quasi Newton method and Marquardt method. Mathematical conditions were applied to the effort to determine how much fertiliser is truly needed for crop growth based on analytical trends and comparison experimentation sheets. In a similar vein, another extremely difficult and important issue is the lack of harvesting fields for the production of various sorts of crops throughout the year. The ideal strategy for eradicating and resolving the problem of land scarcity is to harvest multiple crops at once. Harvesting multiple crops at once on a same piece of land increases yield and allows for the simultaneous cultivation of several distinct crops. The targeted multi-crop pattern in the study, control, and treatment blocks places an emphasis on various crops or an integrated farming system in the same field at a change in the cropping season's timing. To achieve the desired productivity, balanced
uptake fertilizers (N, P and K) are used in accordance with stoichiometric analysis. By implementing a successful agricultural Integrated Model and strategy for farming systems that place system intelligence, thought and technology at their core and emphasize simplicity. Multiple regression analysis and optimisation method (Approximated Solver method, Marquardt method,Quasi-Newton method) further give boost towards targeted yield productivity of integrated crops in contingency, feasibility and brisk growth, developmental choice models for thriving and succeeding in agriculture scenario continent. Many individuals depend on it to support their income. Most Asian nations have large fish eating populations. The main requirement in every food culture is both natural and artificial feed. It is a significant problem to meet market demand for fish in aquaculture (for both export and import) and to increase fish production to meet consumer demand and preferences in food. Today, technology is a key factor in improving cultural practises throughout most of the world. So, a massive amount of supplemental feed must be provided for fish species raised in aquaculture. The experimental design building blocks are supported by regression based investigations and nonlinear optimization with non-constraint equations. To meet our desired yield of fish production, studies using experimental design of blocks replication and experiment findings produced the most effective and efficient recommended nutrition dose to enrich and fill the gap of insufficient nutrition (crude protein and carbohydrate).Taking optimum nutrients in fish feed to find more production (Yield) of fish. Mathematical concepts are crucial and straightforward in solving these issues. Multiple regression models, the Gradient-Descent approach, and the Marquardt method have been used in certain circumstances.We also accomplished the grade of steel quality to locate better steel and increase the strength of steel using optimization techniques (Trust-Region and Marquardt) and mathematical models. Steel’s strength is the most crucial component when constructing steel parts since it determines how durable a component will be. The strength of a substance determines its durability. Therefore, the yield of strength of steel grades is expressed here to determine the material's maximum load. The yield strength of various steel grades was precisely predicted by our intended model, which was based on the various chemical compositions (C, Si, and Fe) of steel. By understanding the chemical compositions present in various steel grades and enhancing them by applying mathematical models based on algorithms and optimization techniques, developed multiple regression formulae are applied to meet our prediction of the strength of various steel grades.