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Area Optimization with Equality Constraint

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August 8, 2024
geometryoptimizationslope2022

Problem Statement

Two rays emanate from the origin OO and form a 45∘45^\circ angle in the first quadrant of the Cartesian coordinate plane. For some positive numbers XX, YY, and SS, the ray with the larger slope passes through point A=(X,S)A = (X, S), and the ray with the smaller slope passes through point B=(S,Y)B = (S, Y). If 6X+6Y+5S=6006X + 6Y + 5S = 600, then determine the maximum possible area of △OAB\triangle OAB.
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