A new type of non-linear profit maximization replenishment policy is suggested in an entropy order quantity model for deteriorating items with stock dependent demand rate. This model represents an appropriate combination of two component demand with entropy cost, particularly over a finite time horizon. Its main aim lies in the need for an entropic cost of the cycle time is a key feature of specific perishable products like fruits, vegetables, food stuffs, fishes etc. To handle this multiplicity of objectives in a pragmatic approach, entropic ordering quantity model with two component demand of perishable items to optimize its payoff is proposed. Two non-linear profit-maximization models are formulated by considering the effects of entropy cost and without entropy cost. Finally to clearly illustrate the non-linear profit maximization EnOQ model a numerical example and the sensitivity analysis are also conducted in the optimal solutions when different parameters are changed. It is considered that if the entropy is allowed in the model, the profit is approximately less in comparison to the non entropic model but the order quantity is more in EnOQ model. In addition, a comparative analysis between the profit-maximization models is conducted.