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Mathematical Modelling and Optimization of Inventory Control Through Linear Programming: A Case Study of Haske Modern Bakery in Bauchi State Aliyu, Umar Mujahid; Oyewola, David Opeoluwa; Taura, Joel John; Lukunti, Salisu
Mikailalsys Journal of Mathematics and Statistics Vol 4 No 1 (2026): Mikailalsys Journal of Mathematics and Statistics
Publisher : Darul Yasin Al Sys

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.58578/mjms.v4i1.7793

Abstract

This study investigates the application of linear programming optimization, complemented by primal and dual linear programming, to improve raw material allocation and maximize profitability for the Haske Modern Bakery in Bauchi, Nigeria. A mathematical model was developed to optimize raw material usage, increase production efficiency, and enhance company returns. Linear programming was employed to identify the most profitable production strategy. Additionally, the Economic Order Quantity (EOQ) model was utilized to effectively manage inventory. EOQ calculations determined the optimal order quantities for flour, sugar, butter, milk, and yeast to be approximately 59 bags, 22 bags, 11 cartons, 12 bags, and 56 cartons, respectively. The total costs of ordering flour, sugar, butter, milk, and yeast are N19,349, N11,171, N5,586, N6,119, and N27,928, respectively. Reorder points were established with stock levels triggering reorders in 20 bags of flour, 4 bags of sugar, 2 cartons of butter, 2 bags of milk, and 30 cartons of yeast, assuming a constant lead time of seven days. The results showed that the optimal production strategy involved producing 319.8294 units of small-medium loaf (X₅) and 533.0490 units of another product (Y₃), with all other products (X₁, X₂, X₃, ..., X₁₃ and Y₁, Y₂, Y₃, ..., Y₉) being zeros units. This strategy is projected to yield a maximum profit of N15991.47. This study underscores the significance of utilizing linear programming and EOQ models to enhance operational efficiency and profitability in the bakery industry.
Hybrid Integral Transform Techniques for the Solution of Third-Order Nonlinear Ordinary Differential Equations Aliyu, Umar Mujahid; Oyewola, David Opeoluwa; Taura, Joel John; Lukunti, Salisu; Muhammad, Hassan; Adamu, Abubakar Yahya; Ibrahim, Abdulhalim Isah; Muhammad, Mubarak; Ibrahim, Imafidor Hassan; Kolo, Mohammed Abubakar; Adamu, Isah; Piapna'an, Wallen Juliet; Mansur, Mustapha Mohammed; Adamu, Ibrahim Abubakar; Marafa, Mohammed Yusuf; Umar, Abdulwasiu; Ahmad, Sulaiman; Hashim, Nura
Mikailalsys Journal of Advanced Engineering International Vol 3 No 2 (2026): Mikailalsys Journal of Advanced Engineering International
Publisher : Darul Yasin Al Sys

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.58578/mjaei.v3i2.9236

Abstract

Third-order nonlinear ordinary differential equations frequently arise in the mathematical modeling of complex engineering and physical phenomena; however, exact analytical solutions remain difficult to obtain because of strong nonlinearities and higher-order derivative effects. Classical integral transform techniques, including the Laplace and Fourier transforms, are widely used for solving differential equations but often have limitations when extended to nonlinear systems. Although modern integral transforms such as the Sumudu, Mahgoub, and Elzaki transforms offer computational advantages, their applicability is generally restricted to linear models. This study introduces a hybrid analytical approach that integrates the Mahgoub transform with the Variational Iteration Method (VIM) to solve third-order nonlinear ordinary differential equations more effectively. The proposed method converts the governing equation into the transform domain and applies an iterative correction functional to address nonlinear terms without linearization or discretization. The resulting solutions are expressed in rapidly convergent series form. Numerical validation demonstrates strong agreement with exact solutions, confirming the efficiency, accuracy, and stability of the hybrid Mahgoub–VIM approach. The study concludes that this hybrid semi-analytical method provides a reliable framework for solving higher-order nonlinear differential equations in applied mathematics and engineering analysis. These findings contribute to the development of transform-based analytical methods by extending the applicability of the Mahgoub transform to nonlinear differential equation models through variational iteration.