<p>This study develops an economic production quantity (EPQ) model with stochastic production characterized by a mixture of Weibull distribution. This mixture Weibull distribution represents the heterogeneous nature of the production process, and the model presumes that the product’s lifespan is stochastic and follows an exponential distribution. Additionally, the selling price—a crucial component of practical inventory systems—determines demand. The aim of the study is to determine the optimal production uptime, downtime, and selling price by maximizing the profit rate. Using differential calculus, the total cost and profit functions are developed and optimized based on the suitable cost considerations. With the help of numerical illustration and sensitivity analysis, we investigate how different parameters affect production decisions and profit. The results indicate that optimal production policies and profit are influenced by production and deterioration parameters. The proposed model is helpful for examining production that operates in two units and incorporates some existing models as special cases.</p>