Abu-Omar and Kittaneh [Numerical radius inequalities for products of Hilbert space operators, J. Operator Theory 72(2) (2014), 521–527], wonder what is the smallest constant c such that w(AB) ≤ c∥A∥w(B) for all bounded linear operators A, B on a complex Hilbert space with A is positive. Here, w(·) stands for the numerical radius. In this paper, we prove that c = ̲3̲√̲3̲ ꜭ