This paper is concerned with the linear programming formulation of Markov control processes with Borel state and action spaces, and the average cost (AC) criterion. The one-stage cost function may be unbounded. A linear program EP and its dual, EP*, are introduced. Their values, inf EP and sup EP*, bound the value (say, inf AC) of the AC problem, i.e., sup EP* less-than-or-equal-to inf AC less-than-or-equal-to inf EP. Conditions are provided for the existence of no duality gap, vis., sup EP* = inf EP, and also for strong duality, so that both EP and EP* we solvable and their optimal values satisfy max EP* = min EP. The latter implies (i) the existence of and AC-optimal control policy and that (ii) the AC optimality equation holds almost everywhere. These results are applied to a general vector-valued, additive-noise system with quadratic costs.