In this report the problem of broadcast scheduling in Push broadcast systems is studied. We introduce an optimization approach that leads to well justified policies for Push broadcast systems with generalized cost functions. In particular, we apply our results to a Push broadcast system with different deadlines associated to the files while allowing the files to have unequal demand rates and lengths. We will show that our proposed policy covers some of the previously investigated Push systems as special cases and is applicable to a wide range of cost functions assigned to the files. We also calculate the optimal average cost for our experimental settings and show, through extensive simulation studies, that our results closely match that value for each experiment.