While proliferating cells optimize their metabolism to produce biomass, the metabolic objectives of cells that perform non-proliferative tasks are unclear. The opposing requirements for optimizing each objective results in a trade-off that forces single cells to prioritize their metabolic needs and optimally allocate limited resources. To define metabolic objectives and tradeoffs in biological systems mathematically, we integrated bulk and single-cell omics data with a novel framework to infer cell objectives using metabolic modeling and machine learning. We validated this framework by identifying essential genes from CRISPR-Cas9 screens in embryonic stem cells, and by inferring the metabolic objectives of quiescent cells and during different cell-cycle phases. Applying this to embryonic cell states, we observed a decrease in metabolic entropy upon development. We further uncovered a trade-off between glutathione and biosynthetic precursors in 1-cell zygote, 2-cell embryo, and blastocyst cells, potentially representing a trade-off between pluripotency and proliferation.