We consider the problem of stabilizing a network consisting of linear time-invariant plants, sensors, controllers, and relays, where the links can be rate-limited. A recent result shows how to characterize such networks for which stabilizing controllers exist, and then shows how to synthesize the coding and control laws to stabilize the network. This paper shows how that characterization can be expressed as an LP, and how that LP can then be extended to find coding/control laws which are optimal in a sense. It is further shown how to find such laws using a sparse portion of the network when possible.