In this paper, a scheduling problem with continuous resource and energy constraints is addressed. Given a limited resource capacity and a set of tasks, the objective is to find a schedule such that each task is processed in its time window and uses a quantity of the resource between a minimum and a maximum value. In addition, each task requires an energy demand; this energy follows a function of the amount of resources allotted. For the cumulative scheduling problem a polynomial satisfiability test exists. Here, we adapt this test to the case of linear and piecewise linear functions.