A firm has, for a certain product, the following profit function: π = PQ - wL - rKWhere P: Price, Q: Level of production, L: Labor , K: Capital w, r = Price of inputs for L and K, further assume that Q = LαKβ with α = β < 1/2 . Determine the optimal level (L∗,K∗) that maximizes the firm's profit. Please explain step by step and be specific.

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