The fundamental economic production lot size model assumes that every product is of perfect quality. However, the reality is that no manufacturing method can successfully create every item of perfect quality. The majority of the production system produces both perfect and imperfect quality things. The manufacturer may reject these non-conforming products, have them repaired, sell them at a discounted price, or provide consumers with a refund if they are delivered. The third-order equation in this work considers an imperfect manufacturing system for defective items with price, advertising, renewable energy, and green-sensitive demand. The two decision variables are production lot size and pricing. To my knowledge, this is novel in the existence of advertisements, price-renewable energy, and green-sensitive dependent demand for imperfect production systems with defective items in the thirdorder equation. The price breakeven point is established, the law of demand is verified, and the highest possible profit is considered. Introducing transport costs and carbon emission costs is intended to mitigate carbon emissions. This paper aims to determine the optimal pricing and the production batch size to maximize the overall profit. The applicability of this model is illustrated through numerical examples. A sensitivity analysis of the optimal solutions is conducted to assess the model's stability.