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In this article, we propose a non-selective harvesting of a predator-prey scheme, utilising a rational harvesting quota rather than an indiscriminate one. In this model, the prey populations adhere to the principle of logistic growth. The successful reaction of predator's to prey density has been structured in such a way that any predator's realistic reaction to prey density is almost invariable as the prey population grows. The boundedness of the proposed model is verified. Eigenvalue procedure is used to analyze the existence of the consistent states as well as their local and global stabilities. The presence of bionomic equilibrium has been represented. Pontryagin's optimum theorem is then used to address the issue of deciding the best harvesting strategy. To investigate the impact of environmental variability on the harvested structure, we expect white noise stochastic perturbations. The numerical simulation confirmed our findings.