The discussion focuses on optimizing the dimensions of a window, which consists of a rectangle topped by a semi-circle, to maximize light admission while adhering to a total perimeter of 10 meters. The area of the window, which is the sum of the rectangle's area and the semi-circle's area, is the key factor in determining light admission. The variables defined include the width of the rectangle (x) and its height (y), with the radius of the semi-circle derived from these dimensions. The conversation emphasizes the relationship between the perimeter constraint and the area calculation to achieve maximum light. Ultimately, the goal is to find the optimal dimensions that maximize the window's area.