  In the present work, we study the noncommutative version of a quantum
cosmology model. The model has a Friedmann-Robertson-Walker geometry, the
matter content is a radiative perfect fluid and the spatial sections have
positive constant curvatures. We work in the Schutz's variational formalism. We
quantize the model and obtain the appropriate Wheeler-DeWitt equation. In this
model the states are bounded. Therefore, we compute the discrete energy
spectrum and the corresponding eigenfunctions. The energies depend on a
noncommutative parameter ($\theta$). The solutions to the Wheeler-DeWitt
equation are function of the scale factor ($a$) and a time variable ($\tau$),
associated to the fluid. They also depend on an integer ($n$) and $\theta$. The
most general solution ($\Psi(a,\tau)$) to the Wheeler-DeWitt equation is a sum,
in the integer $n$, of the solutions mentioned above. We observe that, there is
no $\Psi(a,\tau)$ satisfying the appropriate boundary conditions. Therefore, we
conclude that it is not possible to obtain a wavefunction satisfying the
appropriate boundary conditions for the present model with the considered
noncommutativity.
