While aerobic glycolysis, or the Warburg effect, has for a long time been considered a hallmark of tumor metabolism, recent studies have revealed a far more complex picture. Tumor cells exhibit widespread metabolic heterogeneity, not only in their presentation of the Warburg effect but also in the nutrients and the metabolic pathways they are dependent on. Moreover, tumor cells can switch between different metabolic phenotypes in response to environmental cues and therapeutic interventions. A framework to analyze the observed metabolic heterogeneity and plasticity is, however, lacking. Using a mechanistic model that includes the key metabolic pathways active in tumor cells, we show that the inhibition of phosphofructokinase by excess ATP in the cytoplasm can drive a preference for aerobic glycolysis in fast-proliferating tumor cells. The differing rates of ATP utilization by tumor cells can therefore drive heterogeneity with respect to the presentation of the Warburg effect. Building upon this idea, we couple the metabolic phenotype of tumor cells to their migratory phenotype, and show that our model predictions are in agreement with previous experiments. Next, we report that the reliance of proliferating cells on different anaplerotic pathways depends on the relative availability of glucose and glutamine, and can further drive metabolic heterogeneity. Finally, using treatment of melanoma cells with a BRAF inhibitor as an example, we show that our model can be used to predict the metabolic and gene expression changes in cancer cells in response to drug treatment. By making predictions that are far more generalizable and interpretable as compared to previous tumor metabolism modeling approaches, our framework identifies key principles that govern tumor cell metabolism, and the reported heterogeneity and plasticity. These principles could be key to targeting the metabolic vulnerabilities of cancer.