What is the maximum expected Sharpe ratio by combining two assets into a portfolio? Given two assets that have expected excess returns of 7 and 4.
Also, given their expected co-variance matrix 
$$
        \begin{bmatrix}
        2 & 1 \\
        1 & 1 \\
        \end{bmatrix}
$$
What is the maximum expected Sharpe ratio that you can achieve by combining two assets into a portfolio?
I appreciate the elaborated solution with the explanation. Thanks

Let A and B be the two assets. From the Covariance Matrix, you get
$\sigma_A^2 = 2$, $\sigma_B^2 = 2$ $Cov(A,B) = 1$
Expected Excess Returns, $R_A = 7$, $R_B = 4$
Let A and B be have weights $w_A$, $w_B$ in the portfolio.
Now
Variance of the Portfolio $Var(P) = w_A^2\sigma_A^2+w_B^2\sigma_B^2+2w_Aw_BCov(A,B)$
$\sigma_P = \sqrt{Var(P)}$
$R_P = w_{A}R_A + w_{B}R_B$
$$Sharpe Ratio= \frac{R_P}{\sigma_P}$$
USing the above information set up a solver to find $w_A$ and $w_B$.  The below image illustrates and find the optimal solution that will maximize sharpe ratio.

