Constraint active search is a promising sample-efficient multiobjective experimental design formulation that aims to aid scientists and engineers in searching for new materials. In this proposal, we extend this formulation to situations where one can obtain observations from multiple sources each with a given cost, such as when both computer simulations and a laboratory experiments can be used to calculate (or estimate) properties of a material of interest. We present a novel cost-efficient policy that balances the cost of obtaining observations with the benefit of evaluating a more expensive-to-compute source. Initial results on a synthetic problem show that our proposed methodology is more selective when searching for the most expensive source.