The goal of this work is to demonstrate the optimal strategy of an inventory system for perishable goods with hybrid demand dependent on selling price and stock under the partial backlogging with a certain fixed ratio. In this system, the concept of pre-payment policy with a discount facility and fixed preservation investment are also introduced. Then, this inventory system is modelled mathematically by governing differential equations, and solving these equations, the corresponding average profit of the proposed model is obtained as a non-linear maximization problem. To check the optimality of the solution of the obtained non-linear maximization problem, some results are derived with the help of pseudo concavity and optimality conditions of the objective function of the non-linear maximization problem. Then to justify the model, three examples are taken and solved by Lingo software. Also, the concavity of the average profit is examined graphically. Finally, a post optimality analysis is performed to show the effects of known inventory parameters on the optimal policy.