You are planning on investing $$200,000$ in Gentox, the S&P $500,$ and risk free T$-$bills. Gentox has expected returns of $22\%$ and a standard deviation of $32\%,$ the S&P $500$ has expected return of $13\%$ with a standard deviation of $15\%,$ and the risk free rate is $4\%.$ The correlation between the two risky assets is $0\mathrm{.}5.$

a$.$ What is the expected returns, standard deviation, and Sharpe Ratio of a portfolio with a $30\%$ weight in the S&P $500$ and a $70\%$ weight in Gentox?

b$.$ You are considering putting all of your money in Gentox because you want expected returns of $22\%.$ Is there a better way to construct a portfolio with $22\%$ expected returns by combining the S&P $500$ and T$-$bills? If so$,$ how would you create such a portfolio and how much larger is its Sharpe ratio than the Sharpe ratio of Gentox? If not, explain why there is no better way to generate $22\%$ expected returns.