This article presents a new model to manage the provision of healthy food despite incomplete information about exposure of natural resources to a persistent pollutant (chlordecone). This toxic molecule has contaminated both terrestrial and aquatic resources for several decades in the French West Indies. As a consequence, the threat of exposing humans to contaminated food jeopardizes local agricultural and livestock activities. We address the problem that breeders face: producing healthy food with incomplete information on the animals' contamination. We examine the compatibility of respecting health-production constraints with the timing of animal management. We consider the dual set of constraints that breeders face: (1) they must achieve a target contamination rate that complies with the regulation on the Maximum Residue Limits (MRL) and (2) they must comply with a production calendar that tells them at what age the animals are to be sold. We also discuss the economic and biotechnical consequences that changes in the MRL impose on meat production. We compute the time required to decontaminate the animals and analyse the cost for farmers to adapt to (i) the regulation in place and to (ii) the more stringent health-related targets that are expected in the future. Our results are sensitive to the choice of species cattle, goats, sheep and pigs), the rearing practices, the information setting and the initial contamination rate. This paper opens strategic windows for breeders to guarantee their economic sustainability and their ability to produce healthy meat despite the incomplete information on pollution at their disposal.