For individual biological populations, examining the impacts of competition within the species and the presence of toxic substances in the environment can effectively facilitate control measures. However research in this area remains limited. This article introduces a toxicant-population model incorporating a hierarchical age-structured and examines the minimum deviation problem within this model. The aim is to explore effective control strategies that strike a balance between improving the environment and population benefits. Through a novel approach, we reformulate the problem as an abstract Cauchy problem on a non-dense domain and then apply integrated semigroup theory to establish the existence, uniqueness, and positivity of solutions to the model. The existence of optimal control is derived using Ekeland's variational principle in functional analysis. The expression for optimal control is given by the Pontryagin's minimum principle. Lastly, we conducted numerical experiments on the model, applied optimality conditions to delineate optimal control, and illustrated the comparison between crucial population parameters under optimal control and those without any control.