In a survey using a stratified multi-stage design, suppose the variance of the estimator $\hat{Y}$ is expressed as $V(\hat{Y}) = \sum_{h=1}^H \frac{N_h^2}{n_h} (1 - f_h) S_h^2$. If the cost function is $C = c_0 + \sum_{h=1}^H c_h n_h$, where $c_h$ is the cost per unit in stratum $h$, what allocation $n_h$ minimizes the variance for a fixed total cost $C_{total}$?