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In this paper, our objective is to investigate a mathematical formulation of solving the Bin Packing Problem (BPP). It has become one of the leading mathematical applications throughout the time. A BPP basically describes in three ways; One-Dimensional, Two-Dimensional and Three-Dimensional Bin Packing problems. In our approach, Modified Branch and Bound Algorithm (MBBA) is developed to generate all the feasible packing patterns of given boxes to required containers for One-Dimensional BPP. Further development of algorithms was made to ascertain the locations of each box within the container by using Cartesian coordinate system. Developed algorithms are coded and programmed in the Python programming environment to generate feasible packing patterns. &nbsp