DEPARTMENT OF MATHEMATICS

Linear programming is one of the most effective techniques used in decision-making and optimization problems, especially in business and industrial applications. This project focuses on the use of a linear programming to determine the most efficient way of maximizing profit and minimizing cost. Mouka Foam Company, Benin City, was used as a case study to demonstrate how mathematical models can support better production and resource allocation decisions The simplex method was applied to the formulated linear programming problem derived from the assumed but realistic data of Mouka Foam Company. The process involved defining the objective function, identifying the constraints, introducing slack variables, and systematically applying the simplex algorithm to reach an optimal solution. The entire computation was manually solved and verified to ensure the accuracy of results The result of the analysis shows that the simplex method provided an optimal solution that maximizes profit while minimizing production cost under the given constraints. The findings prove that linear programming is a reliable and efficient mathematical tool for managerial decision-making, especially in production planning and cost optimization.

This project work provides an overview on the application of linear algebra to artificial intelligence including natural language processing and machine learning. We discuss how linear algebra operations such as matrices, linear transformations, eigen values and eigen vectors, are used to optimize AI models, analyze complex data structures and enable efficient computation. Beginning with an overview of fundamental concepts in linear algebra, such as vectors, matrices, and linear transformations, the study delves into specific applications of these concepts in AI. One key area of focus is machine learning, where linear algebra forms the backbone of algorithms for tasks such as regression analysis, and principal component analysis for dimensionality reduction. This work also showcases the versatility of linear algebra by delving deep into the various reaches of linear algebra into many other fields and areas of study such as economics, physics and engineering.

Inventory control plays a critical role in optimizing operations, reducing costs, and ensuring efficiency in the manufacturing industry. This study explores the application of inventory control strategies in the manufacturing sector, using Guinness as a case study. It examines how effective inventory management techniques—such as Economic Order Quantity (EOQ), Just-in-Time (JIT), and Material Requirements Planning (MRP)—impact production efficiency, cost reduction, and overall supply chain performance. The research highlights the challenges Guinness faces in inventory control, including demand variability, stockouts, and holding costs, while also identifying solutions such as automation, real-time tracking, and data-driven forecasting. Findings suggest that implementing advanced inventory control mechanisms leads to improved operational efficiency, minimized waste, and enhanced profitability. This study provides valuable insights for manufacturers seeking to optimize inventory practices and maintain a competitive edge in the industry.

The Dynamics of infectious diseases are vital in the disease control in populations. The mathematical methods that describe these diseases models often are insoluble hence, the need for numerical approximations. Stage two Runge-Kutta methods are used to integrate the system of differential equations that evolves in the model formulation of the infectious diseases being studied.
The stability analysis of Runge-Kutta method is done using boundary bars plot. The solution and plots are carried out using MATHEMATICA program.

Second-order partial differential equations (PDEs) are fundamental in mathematical physics, engineering, and applied sciences. These equations involve second-order derivatives of an unknown function with respect to multiple independent variables. They are broadly classified into three types: elliptic, parabolic, and hyperbolic, based on their characteristic behaviour. Notable examples include the Laplace equation, the heat equation, and the wave equation, each governing essential physical phenomena such as steady-state distributions, diffusion processes, and wave propagation, respectively. Solutions to second-order PDEs often require analytical or numerical techniques, including separation of variables, Green’s functions, Fourier and Laplace transforms, and finite difference methods. Boundary and initial conditions play a crucial role in determining well-posed solutions. Recent advancements in computational methods, such as finite element analysis and deep learning-based PDE solvers, have significantly improved the ability to model complex systems.

Linearized water wave theory is a fundamental concept in fluid dynamics that has been extensively used to study wave propagation in various aquatic environments. Water waves play a crucial role in many engineering and scientific applications, including ocean and coastal engineering, ship hydrodynamics, and offshore engineering. However, the complexity of nonlinear wave dynamics has limited the accuracy of traditional numerical models, emphasizing the need for a simplified yet robust approach. Linearized water wave theory offers a promising solution by assuming small-amplitude waves, enabling the simplification of the governing equations and providing an efficient tool for wave analysis. This project explores the mathematical and physical principles underlying linearized water wave theory and its application in various fields such as oceanography, coastal engineering and naval architecture. The study begins with an overview of the basic equations governing water wave motion including the linearized Euler equation and boundary conditions. The dispersion equation which relates the wave frequency to its wavenumber is derived and analysed to properly understand wave propagation characteristics. In this study, we developed and applied linearized water wave theory to investigate wave propagation in a simplified fluid domain. We also discretized the linearized Navier-Stokes equations and then introduced a wave-like solution to represent the small-amplitude waves. By substituting this solution into the linearized equations, we obtained a set of ordinary differential equations that describe the wave propagation characteristics. Through mathematical analysis and numerical simulations, this study aims to provide a comprehensive understanding of linearized water wave theory and its applications in fluid dynamics. The applications of this study are diverse and far-reaching. Our results can be used to improve the design and optimization of various aquatic structures, such as seawalls, breakwaters, and offshore platforms, by providing a better understanding of wave-structure interactions. Additionally, our findings can be applied to enhance the accuracy of wave forecasting models, which are crucial for coastal erosion prediction, ship navigation, and offshore operations. Furthermore, the linearized water wave theory can be extended to study more complex wave phenomena, such as wave-current interactions and wave-induced sediment transport, offering a promising avenue for future research.

This project investigates improving pathfinding algorithms in Geographic Information Systems (GIS) by optimizing the calculation of geodesics. Geodesics refer to the shortest paths along the curved surface of the Earth, as opposed to straight lines drawn on a flat map. This is crucial for accurate navigation, especially over long distances. Traditional GIS pathfinding algorithms often rely on simpler Euclidean distance calculations, which can lead to significant errors.The objective of this study is to develop or improve upon existing methods for finding optimal geodesics paths within a GIS environment. This will enable more accurate and efficient navigation for various applications, such as: route planning for vehicles, pedestrians, and drones, search and rescue operations, ecological studies analyzing animal movement patterns. The study will explore different algorithms for calculating geodesics on a geoid (Earth's mathematical representation). This could involve techniques like Dijkstra's algorithm adapted for curved surfaces or A* search with appropriate heuristics for geodesic distances. The study might explore methods to optimize the pathfinding process. This could involve strategies like pre-computing geodesics for frequently used routes or implementing techniques to reduce computational complexity. This study by optimizing geodesics paths for navigation has the potential to significantly enhance the capabilities of GIS for various applications requiring accurate and efficientpathfinding.

This study examines the essence of effective inventories control and management to manufacturing companies with particular emphasis on Ama Greenfield Breweries plc. The aim of this study is to investigate and ascertain areas of lapses by the company and offer effective ways and solutions in which the manufacturing company can explore the services of inventory management to affect its objectives. In carrying out this study, various research instruments such as questionnaires and oral interview were used to collect data from respondents and a research design was adopted with a sample size of 52. The statistical tool used for this work is Chi square. Based on the analysis, it was discovered that inventory management plays a vital role in the manufacturing company. A well functional inventory management following the recommendations can bring about proper management thereby enhancing proper and effective production and it will equally ensure the effective, efficient and adequate use of materials and resources in the manufacturing company.

In conventional data envelopment analysis, decision making units are considered as a whole, that is, internal stages are generally ignored. In real life, most systems are composed of many divisions operating interdependently via the intermediate products that are created by some divisions and consumed by some others within the system. The aim of the study was to develop a formalized network mix efficiency model that can deal with both controllable and uncontrollable inputs as well as desirable and undesirable outputs by considering the internal structures of systems. A linear programming approach of data envelopment analysis was used by taking the ratio of slack based measure and directional distance function to measure the eco-efficiency of 54 African countries. The inputs into the system were classified as controllable and uncontrollable while the output as desirable and undesirable. Stage one captured agricultural production efficiency, while stage two evaluated the environmental impact of carrying out agricultural activities. The network efficiency model identified sources of inefficiencies from the components of a complex system rather than looking at the system as a black box. Controllable inputs and undesirable outputs were minimized while the desirable outputs were maximized. The approach provided policymakers with robust benchmarks for enhancing agricultural productivity while mitigating environmental degradation.

Itebukunmi is a riverine community in Ondo State Nigeria, known for its high traffic in fishing activities. The economic importance of fishing activities in Itebukunmi to the Nigerian economy necessitate the need to study the harvesting strategy of fishing in Itebukunmi waters and where necessary determine scientifically regulatory policy that will ensure sustained growth in population.
The Mathematical model of three species of fishes in Itebukunmi couple with human activites was derived using systems of ordinary differential equations. The qualitative analysis of the model such as the local, global, stability and bioeconomic analysis were done using linearization approach and bifurcation analysis. The result of the quantitative analysis showed that : as the control of the harvesting rate of cat fish increases, the population of cat fish and African knife fish, in Itebukunmi river increases, while the Ophiocephalus fish population decreases. Also, as the control of the harvesting rate of Ophiocephalus fish increases, the population of Ophiocephalus fish and African knife fish, in Itebukunmi river increases, while the cat fish population decreases. Furthermore, as the control of the harvesting rate of African knife fish increases, the population of African knife fish , in
Itebukunmi river increases, while the cat fish and Ophiocephalus fish population decreases