You manage a risky fund with an expected rate of return of $15\%$ and a SD of $30\%.$ T bills rate is $4\%.$ Question: $1$a$.$Suppose your client prefers to invest in your funds a proportion of y that maximizes the expected return on the complete portfolio subject to the constraint that the maximum SD of the complete portfolio will not exceed $18\%$: What is the investment proportion of y$?$

$1$b$.$What is the expected return of your client's complete portfolio?