This research paper focuses on shelf space optimization in supermarkets or retail stores. Mathematical techniques have been used in the context of operations research in order to arrive at a set of findings. Through this research paper, methods of product placement on rack and shelves used in stores has been explained. Optimization and linear programming methods have been used to find the optimal product placement. Binary integer programming has been used which uses only two decision variables to come to a conclusion whether to place a certain product in a certain rack/shelf or not. The literature review also highlights work done in the past by other researchers in this field. Consumer psychology has also been explored to a certain extent when it comes to purchasing a product. The logic behind product placement has also been highlighted. Through the findings of this paper, basic decision-making that goes behind product placement has been shown. Findings in the research paper are done on a small scale which is why several factors like shape, size, etc. of the product have been ignored.