Suppose there is a risk-free asset with $ r^0 = 5 $ and $2$ risky assets with $E r^1 = 8, \sigma^1 = 5, E r^2 = 20, \sigma^2 = 20, \text{corr}(r^1, r^2) = 0 $. What is the maximum average profit and in what proportions should one invest in the assets, if $ \sigma(r) < 15 $ (short sales are allowed).
[I am compiling a book of financial problems and would like to ask for help in solving a couple of problems I found from different sources for illustrative example, as the number of problems is too large, I can't solve them all by myself]