In the existing mobile ad hoc network (MANET) QoS routing and multicasting protocols, the methods of bandwidth calculation and allocation were proposed to determine routes with bandwidth guaranteed for QoS applications. As our observations, two bandwidth-violation problems will be incurred in the above protocols. First: When a new bandwidth-requirement flow starts, the existing methods determine a bandwidth-satisfied route and reserve the bandwidth for the flow accordingly by considering the nodes' status on the route and network configuration. However, the reservation might violate the bandwidth capacities of other ongoing bandwidth-consuming flows. Second: Another bandwidth-violation problem would mislead the bandwidth reservation for QoS multicast applications when the multiple routes from a server to all clients were determined concurrently. Our simulation results exhibit that the two problems have high possibilities to be incurred so as to cause serious performance declination while the network traffic is heavy. In this paper, the problem of determining a bandwidth-satisfied tree is formulated as a 0/1 integer linear programming (ILP) for the theoretical studies. We minimize the number of forwarders for reducing the number of hosts participating in packet forwarding so as to lower bandwidth and power consumption that are crucial to MANET performance.