We examine inhomogeneous primordial nucleosynthesis for arbitrary distributions f of the baryon-to-photon ratio η, in the limit where neither particle diffusion nor gravitational collapse is important. By discretizing f(η) and using linear programming, we show that for a set of m constraints on the primordial element abundances, the maximum and minimum possible values of η̅ (the final mean value of η) are given when f(η) is a sum of at most m+1 delta functions. Our linear programming results

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... icate that when f is taken to be an arbitrary function, there is no lower bound on η̅, while the upper bound is essentially the homogeneous upper bound.