We consider the design of optimal strategies for joint power adaptation, rate adaptation and scheduling in a multi-hop wireless network. Most existing strategies control either power and scheduling, or rates and scheduling, but not all three together as we do. We assume the underlying physical layer is in the linear regime (the rate of a link can be approximated by a linear function of the signal-to-interference-and-noise ratio), like in time hopping UWB (TH-UWB) and low gain CDMA systems, and that it allows fine-grained rate adaptation, like in 802.11a/g, HDR/CDMA, TH-UWB.