Given the function
$$ f(\alpha_{1},\ldots,\alpha_{k})=C\sum_{i=1}^k \alpha_i e^{-(b^2/d)\alpha_i}\text{ with } C>0,\ b>0,\ d>0,\ \forall i\in\{1,\ldots,k\}:\alpha_{i}\ge 0 $$
with the constraint
$$\sum_{i=1}^k \alpha_i=1$$
I have to maximize $f$. How do I do this? I tried working with the partial derivative but that only leads me to $\alpha_i=d/b^2$ which violates the constraint because $kd/b^2>1$.