Given a $3 \times 6$ coefficient matrix $A$, I want to find vector $X \in R^{3}$ to maximize the following function:
$$ \prod_{i,j,k \in [1, 6]} (1 + A_{1i}X_{1} + A_{2j}X_{2} + A_{3k}X_{3}),$$
$$ \text{with constraints:}\;\;\; X_{i} \ge 0, \sum X_{i} \le 1.$$
Basically, given $6$ coefficients for each of the $3$ variables, I want to maximize the product of the $216$ linear equations formed by taking any combination of the coefficients.
Note that there are no constraints on the matrix $A$.
It would be equally helpful if you could provide a MATLAB/Python code using which I could find the maximum.