You are considering an investment in the stock. In the stock market, there are two risky stocks (A and B) and a risk free claim, C (you can think of it as the t-bill). The covariances and returns of these three stocks are described in the following table:

Covariance	A	B	C
A	0.25	0.06	0
B	0.06	0.15	0
C	0	0	0
Return	12.50%	9.75%	4.00%

Assume that you have a mean-variance utility function with risk aversion A=5. That is, your utility function is: U = E(r) - 1/2 * 5 * ²

1. Let P be the risky portfolio that consists of stocks A and B. Let w_PA be the weight of stock A in portfolio P and let w_PB = 1 - w_PA be the weight of stock B in the portfolio P. Write down the Sharpe ratio of portfolio P as a function of w_PA
2. Compute the weight of the optimal risky portfolio, w_PA, that maximizes the Sharpe ratio.