Consider the following three stocks Apple Inc (AAPL), Facebook (FA), Microsoft (MSFT). Suppose that at the end of the trading day on January 3, 2020, you have $1,000,000 and want to build a portfolio with these three stocks with the added constraint that the amount invested in Apple (AAPL) should twice the amount invested on Facebook (FA). The expected daily rates of return of these stocks are raapl =0.002750609, rfb=0.001881764, rmsft=0.00197445, their standard deviations are saapl=0.016514173, sfb=0.01748264, smsft=0.012528159, their covariances are cov(aapl,fb)=0.000138217, cov(aapl,msft) =0.000129166, cov(fb,msft) =0.000117024. On January 3, 2020, these are the approximated quotes AAPL =295.924713, FB=208.669998, MSFT=157.748581. Let waapl, wfb, and wmsft be the respective weights of AAPL, FB, and MSFT.