A population is partitioned into two strata: $N_1 = 600$ and $N_2 = 400$. We aim to estimate the population mean with a total sample $n = 100$ using Neyman allocation. If the stratum standard deviations are $S_1 = 2$ and $S_2 = 8$, what is the optimal sample size $n_1$ for stratum 1?