Consider two stocks, A and B$.$ Expected returns on these stocks are:

$/bar(r{)}_A=10\mathrm{.}90\%\frac{,}{b}ar(r{)}_B=13\mathrm{.}68\%.$

Standard deviations of their returns are:

${}_A=23\mathrm{.}30\%,{}_B=34\mathrm{.}79\%.$

Returns on these two stocks are uncorrelated with each other. the risk$-$free interest rate is $4\mathrm{.}77\%.$

The lowest possible standard deviation you can achieve by forming a portfolio of A and B only is $19\mathrm{.}359\%($already calculated$)$

The highest Sharpe ratio you can achieve using a portfolio of A and B only is $36\mathrm{.}716\%($already calculated$)$

Alice is a mean$-$variance optimizer. Her objective is to maximize the following function $[$mean portfolio return $-2*$ portfolio variance$]$:

What fraction of her portfolio $($in $\%)$ should Alice invest in the risk$-$free asset?