We propose a Boolean Linear Programming model for the preemptive single machine scheduling problem with equal processing times, arbitrary release dates and weights(priorities) minimizing the total weighted completion time. Almost always an optimal solution of the Linear Programming relaxation is integral and can be straightforwardly converted into an optimal schedule. To deal with the fractional solutions we present two heuristics. Very often our heuristics find solutions with objective function values equal to the lower bound found by the Linear Programming relaxation. For the cases when upper bound returned by our heuristics differs from the lower bound we embed the bounds into a Branch and Bound algorithm, which solves the problem to optimality. Exhaustive computational study showed that the algorithm substantially surpasses state-of-the-art methods.