A grass fire burns in an approximate circle. Firefighters, spraying the fire, can affect the area of the fire (in sq. meters) according to the model, A = 1/2r^2 − 3t^2 + 2t, with t in minutes and r in meters. It is also observed that the radius of the fire changed linearly, obeying the equation, r − 2t = 1. Find the maximum area the fire can achieve under these conditions

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