A survey researcher wants to estimate the total population $Y$ of a city using a ratio estimator. They have a known auxiliary variable $X$ (total number of housing units) for the city, where $X = 50,000$. They draw a simple random sample of $n = 400$ blocks. The sample mean of the variable of interest is $\bar{y} = 120$ (average population per block) and the sample mean of the auxiliary variable is $\bar{x} = 100$ (average housing units per block). What is the estimated total population $\hat{Y}_R$ using the ratio estimator?