Redundant mechanical systems like humanoid robots are designed to fulfill multiple tasks at a time. A task, in velocity-resolved inverse kinematics, is a desired value for a function of the robot configuration that can be regulated with an ordinary differential equation (ODE). When facing simultaneous tasks, the corresponding equations can be grouped in a single system or, better, sorted in priority and solved each in the solutions set of higher priority tasks. This elegant framework for hierarchical task regulation has been implemented as a sequence of least-squares problems. Its limitation lies in the handling of inequality constraints, which are usually transformed into more restrictive equality constraints through potential fields. In this paper, we propose a new prioritized task-regulation framework based on a sequence of quadratic programs (QP) that removes the limitation. At the basis of the proposed algorithm, there is a study of the optimal sets resulting from the sequence of QPs. The algorithm is implemented and illustrated in simulation on the humanoid robot HRP-2.