The Marginal Value Theorem (MVT) is a cornerstone of biological theory. It connects the quality and distribution of patches in a fragmented habitat to the optimal time an individual should spend exploiting them, and thus its optimal rate of movement. However, predictions regarding how habitat alterations should impact optimal strategies have remained elusive, with heavy reliance on graphical arguments. Here we derive the sensitivity of realized fitness and optimal residence times to general habitat attributes, for homogeneous and heterogeneous habitats, retaining the level of generality of the MVT. We provide new predictions on how altering travel times, patch qualities and/or relative abundances should affect optimal strategies, and study the consequences of habitat heterogeneity. We show that knowledge of average characteristics is in general not sufficient to predict the change in the average rate of movement. We apply our results to examine the conditions under which the optimal strategies are invariant to scaling. We prove a previously conjectured form of invariance in homogeneous habitats, but show that invariances to scaling are not generic in heterogeneous habitats. We also consider the relative exploitation of patches that differ in quality, clarifying the conditions under which it is adaptive to stay longer on poorer patches.