Methods from genetics and genomics can be employed to help save endangered species. One potential use is to provide a rational strategy for selecting a population of founders for a captive breeding program. The hope is to capture most of the available genetic diversity that remains in the wild population, to provide a safe haven where representatives of the species can be bred, and eventually to release the progeny back into the wild. However, the founders are often selected based on a random-sampling strategy whose validity is based on unrealistic assumptions. Here we outline an approach that starts by using cutting-edge genome sequencing and genotyping technologies to objectively assess the available genetic diversity. We show how combinatorial optimization methods can be applied to these data to guide the selection of the founder population. In particular, we develop a mixed-integer linear programming technique that identifies a set of animals whose genetic profile is as close as possible to specified abundances of alleles (i.e., genetic variants), subject to constraints on the number of founders and their genders and ages.