Binary integer programming problem of a very specific form The specificity of the problem lies in the fact that the objective function coincides with the left side of the only constraint. In other words:
$$
\sum\limits_{i=0}^n a_i x_i \to \max,
$$
$$
\sum\limits_{i=0}^n a_i x_i \leq C,
$$
$$
a_i\in\mathbb{R}, x_i\in\{0,1\}, C\in\mathbb{R}.
$$
Note that $a_i$ are real. Could you recommend the best method to solve this type of problem?
Thank you.

This is the knapsack problem for the case when profits and weights coincide.
