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This lecture covers the basics of optimization problems, focusing on algebraic concepts and trinomial equations. Starting with the definition of the base domain and exploring examples, it delves into finding the area of shapes with fixed perimeters. The lecture progresses through different scenarios where the goal is to maximize the area while keeping the perimeter constant. It discusses the relationship between different variables and the steps involved in solving optimization problems. The lecture also touches upon the research process and the significance of understanding the relation between various parameters in optimization scenarios.