Abstract
Starting from a Laver-indestructible supercompact $\kappa$ and a weakly compact $\lambda$ above $\kappa$, we show there is a forcing extension where $\kappa$ is a strong limit singular cardinal with cofinality $\omega$, $2^\kappa = \kappa^{+3} = \lambda^+$, and the tree property holds at $\kappa^{++} = \lambda$. Next we generalize this result to an arbitrary cardinal $\mu$ such that $\kappa <\mathrm{cf}(\mu)$ and $\lambda^+ \le \mu$.
This result provides more information about possible relationships between the tree property and the continuum function.