Sampling and Experiments · Superchallenge problem

A population is split into two strata that make up $40\%$ and $60\%$ of it, with standard deviations 30 and 10. A stratified sample takes $n_1$ from stratum 1 and $n_2$ from stratum 2 with $n_1 + n_2 = 90$, and the variance of the stratified estimate of the mean is (ignoring finite-population corrections)

Over all positive integers $n_1, n_2$ with $n_1 + n_2 = 90$, what is the smallest possible value of $V$?