How we can get sets from elements of different groups?

This task may be present as LP problem.

So, let n(i) - count of elements in group i, m(j) - volume of cell number j. Our goal is to fill all calls with condition: there are elements from different groups in each cell.

Let X(i,j) - count of element that from group  i and put into cell j.

Our main goal is maximize sum(X(i,j)) for all j with follow constraints:

1)    upper bound for elements count from each group:

sum_j(X(i,j))<=n(i) for all i;

2)    upper bound for volume of each cell:

sum_i(X(i,j))<=m(j) for all j;

3) there are elements from the same group no more than t in each cell :

X(i,j)<=t for all i и j.