Math Modeling and Decision Analysis: Chain Store Optimization Project

This project focuses on a linear programming and optimization problem faced by a large chain store planning to open new locations. The assignment details the problem of determining the optimal number of three different store types (A, B, and C), considering construction costs, operational costs, employee requirements, and projected annual revenues. The student formulates the problem with variables, constraints, and an objective function to maximize profits. The solution utilizes Excel Solver to find the optimal solution, which suggests constructing 11 units of Store A and 4 units of Store B, resulting in a maximum profit of 27.8497 million dollars. The sensitivity analysis and limits report are also provided, highlighting the risks associated with not constructing the optimal number of units. The project emphasizes the practical application of mathematical modeling in business decision-making and risk assessment.