In approaching the retail company case study, we are tasked with the central problem of optimizing the amount of shelf space a given product receives in order to maximize store profitability. With this statement it first appears that an optimization model would lead us to our desired outcome. However. as we evaluate the problem more generally, we first must understand the relationship (if any) between shelf space and product sales. As seen in the case detail the retailer lays out three hypotheses for understanding the relationship between product sales and shelf space. Hypotheses: 1) As shelf space for a given product increases the sales of a given product increase. 2) As sales of a given product increase, the sales of the given products respective complementary products will increase. 3) If a given product and its respective complementary product are adjacent to one another, the sales of the complementary product will increase relative to if they were non-adjacent. Although each of these hypotheses seem reasonable in order to conduct a thorough analysis, we must first test the validity of each to verify that these are in fact the primary drivers of the effects. Prior to analyzing each of these cases we must also layout some general constraints so that view evaluate the problem with realistic constraints. Constraints: 1) Each store has a total maximum shelf space available (overall budget) - E shelf-space]: N == shelf space budget 2) Each product has a given minimum shelf space that must be allocated to it - Shelf-space]. 2 Minimum Product shelf space 3) Each product has a given maximum shelf space that must be allocated to it - Shelf-space]. 5 Maximum Product shelf space Now that we understand our general constraints, we need to address our limitations of analysis given our current data availability