# How to optimize linear programming subproblems with respect to global constraints?

I have an optimization problem where I have several categories and for each category $$j$$ I have entries $$i = 1....m$$, I wish to assign some value $$x_{ij}$$ for each entry of each category but:

1. I need to assign it in a way that maximizes the sum $$\sum_{j} w_i x_i$$ for each category $$j$$
2. I need to respect some constraints, some are local to each category and some global for the whole problem

2.1 I need that for each category $$j$$: $$\sum_i x_{ij} < M$$ (local for each category)

2.2 I also need that $$\sum_{j}\sum_{i} x_{ij} < N,$$ (global category)

N and M are constants that I have for the problem, the main thing I want is that I need to maximize for each category and not across all categories.

I would really appreciate some help on how to do this using python mainly for example scipy or others.

• Your notation is very unclear. For example, you have $x_{ij}$ in one place and later $x_{i}$. You also have $\sum_{j} w_{i}x_{i}$, where the index of summation doesn't appear inside the sum. – Brian Borchers May 23 at 22:47