I have an optimisation probem given below
$$argmax_{x_i \ \ \forall x_i=1,2...n} \sum_{i} S_ie^{-\alpha x_i}$$
subject to
$$\sum x_i = 1$$ $$\sum C_i x_i \leq B $$ $$\forall i \ \ x_i \geq 0 $$ where $\alpha >1$ , $B >0$ and $ \forall i \ \ C_{i}>0,S_{i} >0 $ are constants.
I have to calculate a solution for this problem computationally, given all the constants $\alpha,B, C_{i},S_{i} \ \ \forall i$ . I tried Lagrange multipliers method , but I am not able to get a closed solution, but i do have the a set of linear equations . Is there a way to solve this problem computationally ?