This completes our study of the equilibrium thermodynamics of the Huang-Yang-Luttinger model of a boson gas with a hard-sphere repulsion. In an earlier paper we obtained a lower bound on the pressure, but our proof of an upper bound held only for a truncated version of the model. In this paper we establish an upper bound on the pressure in the full model; the upper and lower bounds coincide and provide a variational formula for the pressure. The proof relies on recent second-level large deviation results for the occupation measure of the free boson gas. © 1990 Springer-Verlag.