Question: Suppose a firm earns revenue R(Q) = aQ - bQ2 and incurs cost C(Q) = αQ + βQ2 as functions of output Q ≥ 0, where a, b, α, and β are positive parameters. The firm maximizes profit π(Q) = R(Q) - C(Q) subject to the constraint Q ≥ 0. Solve this one-variable problem by the Kuhn-Tucker method, and find conditions for the constraint to bind at the optimum.