You are considering investing $$1,000$ in a complete portfolio. The complete portfolio is composed of Treasury bills that pay $4\%$ and a risky portfolio, $P,$ constructed with two risky securities$,$ A and B$.$ The optimal weights of A and B in $P$ are $60\%$ and $40\%$ respectively. Security A has an expected rate of return of $15\%,$ and Security $B$ has an expected rate of return of $12\mathrm{.}5\%.$ Compute the dollar amounts that you should invest in Security A and Security B$,$ so that your complete portfolio has an expected rate of return of $12\%.$