Mathematical Modelling and Analysis of Student Budget Allocation Using Linear Programming

Overview:
This project focuses on the mathematical modeling of student budget allocation using linear programming techniques. It provides a framework for distributing a fixed monthly income across multiple categories such as rent, food, transport, study, entertainment, and savings. By formulating the budgeting task as a linear optimization problem, the project ensures that essential needs are met while maximizing overall utility based on priority weights. The case study demonstrates income allocation with real-world parameters, including constraints on rent and savings, and highlights how optimization leads to efficient financial planning. Sensitivity analysis is also included to show how the model adapts to changes in income or priorities.

Suitable For:

• BS Economics/Finance – applications in financial decision-making and budget planning

• BS Mathematics – applied optimization, linear programming models

• BS Statistics – tabular analysis, interpretation of results, sensitivity analysis

• BS Computer Science – implementation of linear programming models in Python

Technologies Used:

• Programming Language: Python (for solving optimization problems)

• Libraries & Tools: PuLP / SciPy (for linear programming), Pandas (data handling), Matplotlib (visualization), LaTeX (documentation)

• Techniques: Linear optimization, constraint-based modeling, sensitivity analysis

• Visualization: Optimized allocation bar charts, pie charts, sensitivity analysis tables

Features:

• Development of a mathematical model for income allocation using linear programming

• Definition of constraints such as rent limits and minimum savings requirements

• Priority-weighted allocation to reflect student preferences

• Step-by-step case study with real-world values (e.g., income of 50,000 units)

• Sensitivity analysis to study the effect of changing income or priorities

• Clear visualizations for comparison across categories

Deliverables:

• Python source code for income allocation optimization

• Documentation: problem statement, mathematical model, methodology, and case study

• Presentation slides (PPT): objectives, model, results, and analysis

• Visual assets: optimized budget tables, bar charts, pie charts, sensitivity analysis results

Support:

• Guidance for understanding, modifying, or extending the budget model to new scenarios

• Assistance with implementing additional constraints or objectives (e.g., maximizing savings)

• Help in interpreting optimization results and visualizations

Benefits for Students:

• Hands-on experience in applying linear programming to real-life financial problems

• Understanding how optimization balances needs, preferences, and constraints

• Ability to compute and interpret results both manually and programmatically

• Strengthened skills in mathematical modeling, coding, and data visualization

• Excellent capstone project for demonstrating applied mathematics, economics, or computer science techniques