An optimization problem with volume constraint involving the Φ-Laplacian in Orlicz-Sobolev spaces is considered for the case where Φ does not satisfy the natural condition introduced by Lieberman. A minimizer uΦ having non- degeneracy at the free boundary is proved to exist and some important conse- quences are established like the Lipschitz regularity of uΦ along the free bound- ary, that the set {uΦ > 0} has uniform positive density, that the free boundary is porous with porosity δ > 0 and has finite (N −δ)-Hausdorff measure. Under a geometric compatibility condition set up by Rossi and Teixeira, it is established the behavior of a l-quasilinear optimal design problem with volume constraint for l small. As l → 0+, we obtain a limiting free boundary problem driven by the infinity-Laplacian operator and find the optimal shape for the limiting problem. The proof is based on a penalization technique and a truncated minimization problem in terms of the Taylor polynomial of Φ.