<p>This study introduces an inventory system based on a linear time-demand function. The model incorporates various costs essential for effective inventory management, including holding, purchasing, ordering, and deterioration costs. The mathematical model is designed to maximize profits for retailers and manufacturers operating in challenging scenarios. The model is predicated on the interaction among price, time, and the duration of the replenishment period. It operates by replenishing inventory at specific intervals, gradually decreasing until it is fully depleted. A concept of partial backlog shortage is introduced during periods of insufficient stock. The proposed study explores the significant impact of various factors through numerical examples, Hessian matrix analysis, and specific case studies, aiming to identify optimal solutions across different demand functions that enhance retailer profitability. Furthermore, we conduct a sensitivity analysis to examine how market risks affect profit, inventory levels, and backlog orders, equipping industrialists with insights for effective planning. This approach facilitates the determination of the optimal selling price and replenishment period for a linear demand function. It accounts for additional profit and aims to minimize wastage due to deterioration effects on deteriorating items such as fruits, vegetables, and dairy products. This study provides a framework for making informed inventory decisions during critical situations, such as determining when and how much to order. Additionally, we address risk scenarios through auxiliary case studies to facilitate decision-making and mitigate risks in these contexts.</p>