There are three securities A$,$ B$,$ C with mean returns of $17\%,13\%,$ and $9\%,$ respectively. Furthermore, their standard deviations are $20\%,40\%,$ and $15\%,$ respectively. The correlation between A and B is $0\mathrm{.}50,$ between B and C is $0\mathrm{.}30,$ and between A and C is zero. The risk$-$free rate is $5\%.$

A$)$ Find the Minimum Variance Portfolio and Tangent portfolios of these three assets, and calculate each of the portfolio return means and standard deviations.

B$)$ Write the equation for the efficient frontier of these three assets.

C$)$ Find the portfolio of A$,$ B$,$ C that gives the lowest posible variance for a return of $13\%,$ and find the portfolio that gives the highest posible return for a standard deviation of $15\%.$ Calculate the Sharpe ratios of these two portfolios.