In this paper we consider the discrete-time LQ-optimal control problem for the class of linear systems with Markovian jump parameters and additivel2-stochastic input. The state-space of the Markov chain is assumed to be a countably infinite set. The controller has access to both the state-variable and jump-variable. It is shown that the optimal control law is characterized by a feedback term plus a term defined by the:l2-stochastic input and Markov chain. An application to the optimal control of a failure prone manufacturing system subject to a random demand for a single type of item is presented.