Variable as subscript in Linear Programming

Question

I have to maximize this function

$max \sum_{i=0}^{n}x_{i}$ , $\bar{x}\in \mathbb{Z}, \bar{x}\geq 0$

is to possible to define this as a constraint ?

$\sum_{t=0}^{T_{i}}M_{i,x_{i+t}}= T_{i}$

(I'm using a variable as subscript,M is a matrix of variables, and Ti is given)

Answer 1

Add a constraint $x_i = \sum_{k=1}^p k y_k$ with $y_i \in \{0,1\}$, so that $y_k=1$ if $x_i=k$. Then $M_{i,x_{i+t}} = \sum_{j=1}^{n} M_{i,j} y_{i+t}$.