In a multifunctional radar performing searching and tracking operations, the maximum number of targets that can be managed is an important measure of performance. One way a radar can maximize tracking performance is to optimize its dwell scheduling. The problem of designing efficient dwell scheduling algorithms for various tracking and searching scenarios with respect to various objective functions has been considered many times in the past and many solutions have been proposed. We consider the dwell scheduling problem for two different scenarios where the only objective is to maximize the number of dwells scheduled during a scheduling period. We formulate the problem as a distributed and a nondistributed bin packing problem and present optimal solutions using an integer programming formulation. Obtaining an optimal solution gives the limit of radar performance. We also present a more computationally friendly but less optimal solution using a greedy approach.