In the context of predicting customer purchases during a sale using logistic regression, describe a detailed approach encompassing the use of dummy variables to represent categorical explanatory variables, the application and interpretation of the interaction between a dummy variable and a numeric variable, and the estimation and interpretation of both the linear probability model and the logistic regression model. Provide a concrete example of how these elements could be employed in the model, emphasizing the practical significance for retailers aiming to optimize sales outcomes during promotional events.