A researcher wants to estimate the total population $Y$ of a city using a ratio estimator $\hat{Y}_R = \frac{\bar{y}}{\bar{x}} X$. Given population size $N=10,000$, sample size $n=100$, sample mean $\bar{y}=40$, sample mean of auxiliary variable $\bar{x}=25$, and known population auxiliary mean $\bar{X}=30$, what is the estimated population total $\hat{Y}_R$?