Suppose you have just inherited a sum of $50,000 and you are considering investing it in the stock market. You have identified two stocks, Stock A and Stock B, which have expected returns of 12% and 10%, respectively. The expected standard deviation of Stock A is 20%, while the expected standard deviation of Stock B is 15%. You are risk-averse and prefer a portfolio with lower risk. Assuming that the two stocks are not perfectly correlated, what is the optimal allocation of the $50,000 between the two stocks to minimize portfolio risk? Show all your calculations.