There are three independent random variables $X, Y, Z$.

The goal is to minimize the variance of $aX + bY + cZ$ where $a+b+c = 1$ and $0\le a,b,c \le1$.

$$\operatorname{var}(X) = 2\operatorname{var}(Y) = 3\operatorname{var}(Z)$$

I did $$K = aX + bY + cZ\quad,\quad \operatorname{var}(K) = a^2\operatorname{var}(X) + b^2\operatorname{var}(Y) + c^2\operatorname{var}(Z)\,,$$ but it looks like one more equation might be needed to solve the problem.

Is there anything I missed?