Posix 1003.1b compliant systems provide two well-specified scheduling policies, namely sched_rr (Round-Robin like) and sched_fifo (FPP like). Recently, an optimal priority and policy assignment algorithm for Posix 1003.1b has been proposed in the case where the quantum value is a system-wide constant. In this study, we extend this analysis to the case where quanta can be chosen on a task-per-task basis. The algorithm is shown to be optimal with regards to the power of the feasibility test (i.e. its ability to distinguish feasible and non feasible configurations). Though much less complex than an exhaustive exploration of the search space, the exponential complexity of the algorithm limits its applicability to small or medium-size problems. In this context, as it is shown in the experiments, our proposal allows achieving a significant gain in terms of feasibility over FPP and Posix with system-wide quanta, and therefore using the computational resources at their fullest potential.