Given the increasing importance of sustainability in product design, tools for designing products with low environmental impact are important for tackling problems in the future. One important measure of environmental impact is life cycle energy (LCE), which uses the cumulative amount of energy a product consumes over its’ lifetime as a proxy for environmental impact. In this work, the core topology and face sheet thickness of a sandwich beam are optimized for different material compositions with the goal to minimize the life cycle energy of the beam. A constraint on the mean compliance of the beam is used as a proxy for functional requirements. The problem is solved using a mixed-integer programming extension of the established Topology Optimization of Binary Structures (TOBS) method. Numerical examples indicate that the method is able to find feasible minimum LCE solutions with varying topologies and face sheet thicknesses.