Two machines, A and B, fill containers. Machine A produces $n_A = 40$ units with mean $\bar{x}_A = 100$ and variance $\sigma_A^2 = 25$. Machine B produces $n_B = 60$ units with mean $\bar{x}_B = 110$ and variance $\sigma_B^2 = 36$. What is the variance of the combined dataset of $100$ units?