QUESTION $20$

"You are considering investing $$1,000$ in a T$-$bill that pays $0\mathrm{.}06$ and a risky portfolio, $P,$ constructed with two risky securities$,x$ and $Y.$ The weights of $x$ and $Y$ in $P$ are $0\mathrm{.}30$ and $0\mathrm{.}70,$ respectively. $x$ has an expected rate of return of $0\mathrm{.}04$ and variance of $0\mathrm{.}05,$ and $Y$ has an expected rate of return of $0\mathrm{.}10$ and a variance of $0\mathrm{.}23.$ What would be the dollar value of your positions in $x$ if you decide to hold a portfolio that has an expected return of $6\mathrm{.}4\%?"$

a$.$ $$127\mathrm{.}27$

b$.$ $$54\mathrm{.}55$

c$.$ $$300\mathrm{.}00$

d$.$ $$568\mathrm{.}00$