You manage a risky portfolio with an expected rate of return of $10\%$ and a standard deviation of $34\%.$ The T$-$bill rate is $4\%.$

Suppose that your client prefers to invest in your fund a proportion y that maximizes the expected return on the complete portfolio

subject to the constraint that the complete portfolio's standard deviation will not exceed $10\%.$

Required:

a$.$ What is the investment proportion, $y?$

b$.$ What is the expected rate of return on the complete portfolio?