How to know, which constraint is being violated in linear programming problem?

(* convert the constraints from && form to list form *)
constraintsList = constraints /. And -> List;

(* make some fake setting of the xij *)
SeedRandom[12345];
someSettingOfTheX = Flatten[
  Table[Subscript[x, i, j] -> RandomReal[30], {i, 3}, {j, 4}],
 1];

(* check which constraints it satisfies and violates *)
constraintsList /. someSettingOfTheX

(* result: {True, False, True, False} *)

---

A simpler example might be helpful:

objective = x^2;
constraints = {x > 0, x < 1, 3 x < 24};
{min, result} = Minimize[{objective, constraints}, x];

(** Minimize::wksol: Warning: there is no minimum in the region
    in which the objective function is defined and the constraints
    are satisfied; returning a result on the boundary. **)

constraints /. result
(* result: {False, True, True} *)

As you can tell, the result {x -> 0} does not satisfy the first constraint.

With this set of constraints there is a solution which is the trivial solution. My procedure

vars = Flatten[Table[Subscript[x, i, j], {i, 3}, {j, 4}]];
restrs1 = Thread[vars >= 0];
restrs2 = {Subscript[x, 1, 4] <= 50 && 
 0.2 Subscript[x, 1, 2] + 0.8 Subscript[x, 1, 3] + 
 0.7 Subscript[x, 1, 4] + 0.3 Subscript[x, 2, 1] + 
 0.3 Subscript[x, 2, 3] + 0.2 Subscript[x, 2, 4] + 
 0.5 Subscript[x, 3, 1] + 0.1 Subscript[x, 3, 3] <= 50 && 
 0.8 Subscript[x, 1, 2] + 0.2 Subscript[x, 1, 3] + 
 0.3 Subscript[x, 1, 4] + 0.8 Subscript[x, 2, 1] + 
 0.3 Subscript[x, 2, 3] + 0.2 Subscript[x, 2, 4] + 
 0.5 Subscript[x, 3, 1] + 0.1 Subscript[x, 3, 3] <= 50 && 
 Subscript[x, 2, 1] + Subscript[x, 2, 2] + Subscript[x, 2, 3] + 
 Subscript[x, 2, 4] <= 50};

restrs = Join[restrs1, restrs2];

sol = FindInstance[restrs, vars]

Perhaps with more constraints the result changes...

NOTE

This can be used as follows

restrs1 =
{Subscript[x, 1, 4] <= 50, 
 0.2 Subscript[x, 1, 2] + 0.8 Subscript[x, 1, 3] + 
 0.7 Subscript[x, 1, 4] + 0.3 Subscript[x, 2, 1] + 
 0.3 Subscript[x, 2, 3] + 0.2 Subscript[x, 2, 4] + 
 0.5 Subscript[x, 3, 1] + 0.1 Subscript[x, 3, 3] <= 50, 
 0.8 Subscript[x, 1, 2] + 0.2 Subscript[x, 1, 3] + 
 0.3 Subscript[x, 1, 4] + 0.8 Subscript[x, 2, 1] + 
 0.3 Subscript[x, 2, 3] + 0.2 Subscript[x, 2, 4] + 
 0.5 Subscript[x, 3, 1] + 0.1 Subscript[x, 3, 3] <= 50, 
 Subscript[x, 2, 1] + Subscript[x, 2, 2] + Subscript[x, 2, 3] + 
 Subscript[x, 2, 4] <= 50}
restrs2 = Thread[vars >= 0]
restrs = Join[restrs1, restrs2]

For[k = 1, k <= Length[restrs], k++,
   sol = FindInstance[Take[restrs, {1, k}], vars];
   If[sol == {}, Print[k]; Break[]]
]