$4$ marks$)$ You are considering investing $1,000$ in a T$-$bill that pays $0\mathrm{.}05$ and a risky portfolio, P$,$ constructed with $2$ risky securities$,$ X and Y$.$ The weights of X and Y in P are $0\mathrm{.}60$ and $0\mathrm{.}40,$ respectively. X has an expected rate of return of $0\mathrm{.}14$ and variance of $0\mathrm{.}01,$ and Y has an expected rate of return of $0\mathrm{.}10$ and a variance of $0\mathrm{.}0081.$ If you want to form a portfolio with an expected rate of return of $0\mathrm{.}10,$ what percentages of your money must you invest in the T$-$bill, X$,$ and Y$,$ respectively if you keep X and Y in the same proportions to each other as in portfolio P$?$

$0\mathrm{.}25$; $0\mathrm{.}45$; $0\mathrm{.}30$

$0\mathrm{.}19$; $0\mathrm{.}49$; $0\mathrm{.}32$

$0\mathrm{.}32$; $0\mathrm{.}41$; $0\mathrm{.}27$

$0\mathrm{.}50$; $0\mathrm{.}30$; $0\mathrm{.}20$

None of the above