Suppose that there are two risky assets, A and B$,$ with expected returns

equal to $2\mathrm{.}3\%$ and $4\mathrm{.}5\%,$ respectively. Suppose that the standard devi$-$

ations of the returns are $\sqrt[\phantom{2}]{6}\%$ and $\sqrt[\phantom{2}]{11}\%$ and that the returns on the

assets have a correlation of $0\mathrm{.}17.$

$($a$)$ What portfolio of A and $B$ achieves a $3\%$ rate of expected return?

$($b$)$ What portfolios of A and B achieve a $\sqrt[\phantom{2}]{5\mathrm{.}5}\%$ standard deviation of

return? Among these, which has the largest expected return?