The virtual profit efficiency model is sensitive with respect to units of measurement as is the related directional distance function. It is shown that the model can be made invariant with respect to changes in units of measurement in a similar vein as the directional distance function. The geometric interpretation of changes in units of measurement in input output space is uncovered and shown to be similar to the interpretation of the underlying base model. A weighted virtual profit efficiency model with focus on input contractions and output expansions in selected dimensions is developed, and differences and similarities between the working of the weighted versus the unweighted base model are uncovered. It is demonstrated how to incorporate Assurance Regions and Cone Ratios in the virtual profit efficiency model.