I have the following constrained maximization problem $$ \max_{X_1,X_2,...,X_i,...,X_N} \sum_{i=1}^{N}X_i f_i(X_1,...,X_N) \hspace{0.2 cm} \text{subject to} \sum_{i=1}^{N}X_i-B\leq 0 \text{ and } X_i\geq 0 \text{ } \forall i=1,...,N $$ where $f_i(X_1,...,X_N)$ is a function of $X_1,...,X_N$ different across $i$ such that the unconstrained maximum of the objective function always exists and $B>0$ .
Do you know whether there is a way to transform it in an unconstrained maximization problem?