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This paper focuses on the modified logistic differential equation model for population growth of organisms in an environment. The situation considered was that of a fish population that were stocked in an environment, with the fact that the environment has a particular carrying capacity and the organisms are increasing as the other factors for their survival are kept constant. We incorporated a condition where the farmer is constrained to stock the same environment with additional fishes and another environment. These constraints led to the modification of the logistic differential equation model whose solution is based on the calculus approach. The results of the modified model demonstrate superiority over its classical counterparts in terms of carrying capacity with increase in the interval and step sizes.