In this study, an deterministic inventory model based on the concept of permissible delay in payments is discussed. Demand is assumed to be price dependent, and a constant price function represents it. Shortages are allowed and partially backlogged. In the realistic environment, it observed that there are several items like dry fruits, vegetables, grocery, and fruits, etc. which deteriorate after a time gap. So this model is also based on non-instantaneous deterioration. This study aims is to optimize the optimal order level and selling price to maximize the retailer`s total profit. Finally, numerical examples solved by using a proposed algorithm to show the validity of the model and sensitivity analysis done on parameters..