The Triad family of mutual funds allows investors to split their money between several

portfolios managed by Triad $($none of the portfolios can be shorted$).$

$$ Portfolio A consists entirely of risk$-$free securities and has a certain return of $4\%.$

$$ Portfolio B has an expected return of $19\%$ and a standard deviation of $25\%.$

$$ Portfolio C has an expected return of $10\%$ and a standard deviation of $15\%.$

Your client is leaning towards investing his money entirely in portfolio C since he is

unwilling to take the higher risk associated with portfolio B$,$ but wants a higher return than

offered by portfolio A$.$

$($a$)$ In your role as a Triad investment advisor, you suggest to him an alternative portfolio

$($consisting of a combination of A and B$)$ that has the same standard deviation as

portfolio C but a higher expected return. Assume he has $$200,000$ to invest.

$$ How much should he invest in A and how much in B$?$

$$ What is his expected return in this case?