  We prove an existence result for the prescribed Ricci curvature equation for
certain doubly warped product metrics on $\mathbb{S}^{d_1+1}\times
\mathbb{S}^{d_2}$, where $d_i \geq 2$. If $T$ is a metric satisfying certain
curvature assumptions, we show that $T$ can be scaled independently on the two
factors so as to itself be the Ricci tensor of some metric.
