Let U be a bounded open connected set in R-n (n >= 1). We refer to the unique weak solution of the Poisson problem - Delta u = xA on U with Dirichlet boundary conditions as u (A) for any measurable set A in U. The function psi := u(U) is the torsion function of U. Let V be the measure V := psi L-n on U where L-n stands for n-dimensional Lebesgue measure. We study the variational problem I (U, p) := sup {J (A) - V(U) p(2)} with p is an element of (0, 1) where J (A) := J(A) u(A) dx and the supremum is taken over measurable sets A subset of U subject to the constraint V(A) = pV( U). We relate the above problem to an unstable two-phase membrane problem. We characterise optimsers in the case n = 1. The proof makes use of weighted isoperimetric and Polya-Szego inequalities.