This paper investigates a practical energy minimization problem for multiuser relay-assisted downlink cellular networks. The system adopts an hybrid-automatic-repeat-request of type I (HARQ-I) protocol and each user has an average delay constraint to be satisfied under a total power constraint for the system. The contribution of this paper lies in several folds: i) By introducing new constraints and new variables in the original problem, the solution is analytically obtained by the dual method. ii) An algorithm that jointly allocates for every user the optimal downlink power at base station (BS) and relay station (RS) and selects the RS (if cooperation is decided) is proposed. iii) Another binary integer programming algorithm that selects the optimal modulation and coding scheme (MCS) and optimizes the number of time-frequency resource blocks (RBs) between users is proposed. In order to corroborate our findings, simulation results in terms of energy-delay tradeoff, average starvation user rates and selected MCS statistics are presented. Our analyses show that relay-assisted strategy improves up to 30 % the energy consumption compared to non-relay-assisted one.