```json
{
  "sym_variables": [
    ("x0", "water purification units"),
    ("x1", "airborne infantry companies"),
    ("x2", "medical platoons"),
    ("x3", "artillery batteries")
  ],
  "objective_function": "3*x0 + 4*x1 + 4*x2 + 5*x3",
  "constraints": [
    "2*x0 + 16*x3 >= 49",
    "3*x1 + 16*x3 >= 51",
    "2*x0 + 3*x1 + 16*x2 >= 71",
    "2*x0 + 16*x2 + 16*x3 >= 71",
    "3*x1 + 16*x2 + 16*x3 >= 71",
    "2*x0 + 3*x1 + 16*x3 >= 71",
    "2*x0 + 3*x1 + 16*x2 >= 58",
    "2*x0 + 16*x2 + 16*x3 >= 58",
    "3*x1 + 16*x2 + 16*x3 >= 58",
    "2*x0 + 3*x1 + 16*x3 >= 58",
    "2*x0 + 3*x1 + 16*x2 >= 46",
    "2*x0 + 16*x2 + 16*x3 >= 46",
    "3*x1 + 16*x2 + 16*x3 >= 46",
    "2*x0 + 3*x1 + 16*x3 >= 46",
    "2*x0 + 3*x1 + 16*x2 >= 41",
    "2*x0 + 16*x2 + 16*x3 >= 41",
    "3*x1 + 16*x2 + 16*x3 >= 41",
    "2*x0 + 3*x1 + 16*x3 >= 41",
    "2*x0 + 3*x1 + 16*x2 + 16*x3 >= 41",
    "16*x2 + 13*x3 >= 30",
    "5*x0 + 17*x1 >= 19",
    "5*x0 + 13*x3 >= 47",
    "17*x1 + 13*x3 >= 50",
    "17*x1 + 16*x2 >= 42",
    "5*x0 + 17*x1 + 16*x2 >= 46",
    "17*x1 + 16*x2 + 13*x3 >= 46",
    "5*x0 + 17*x1 + 16*x2 >= 47",
    "17*x1 + 16*x2 + 13*x3 >= 47",
    "5*x0 + 17*x1 + 16*x2 + 13*x3 >= 47",
    "9*x1 + 10*x3 >= 20",
    "7*x0 + 13*x2 >= 36",
    "7*x0 + 9*x1 + 13*x2 + 10*x3 >= 36",
    "9*x0 + 8*x1 >= 37",
    "9*x0 + 6*x2 >= 36",
    "8*x1 + 6*x2 + 15*x3 >= 49",
    "9*x0 + 8*x1 + 6*x2 + 15*x3 >= 49",
    "-1*x0 + 8*x3 >= 0",
    "-6*x2 + 3*x3 >= 0",
    "2*x0 + 16*x2 + 16*x3 <= 165",
    "5*x0 + 17*x1 <= 77",
    "16*x2 + 13*x3 <= 107",
    "7*x0 + 13*x2 <= 92",
    "9*x1 + 10*x3 <= 157",
    "8*x1 + 6*x2 <= 180",
    "8*x1 + 6*x2 + 15*x3 <= 190",
    "9*x0 + 8*x1 + 6*x2 <= 144",
    "x0, x1, x2, x3 are integers"


  ]
}
```

```python
import gurobipy as gp

# Create a new model
m = gp.Model("resource_allocation")

# Create variables
x0 = m.addVar(vtype=gp.GRB.INTEGER, name="water_purification_units")
x1 = m.addVar(vtype=gp.GRB.INTEGER, name="airborne_infantry_companies")
x2 = m.addVar(vtype=gp.GRB.INTEGER, name="medical_platoons")
x3 = m.addVar(vtype=gp.GRB.INTEGER, name="artillery_batteries")


# Set objective function
m.setObjective(3*x0 + 4*x1 + 4*x2 + 5*x3, gp.GRB.MINIMIZE)

# Add constraints
m.addConstr(2*x0 + 16*x3 >= 49)
m.addConstr(3*x1 + 16*x3 >= 51)
m.addConstr(2*x0 + 3*x1 + 16*x2 >= 71)
m.addConstr(2*x0 + 16*x2 + 16*x3 >= 71)
m.addConstr(3*x1 + 16*x2 + 16*x3 >= 71)
m.addConstr(2*x0 + 3*x1 + 16*x3 >= 71)
m.addConstr(2*x0 + 3*x1 + 16*x2 >= 58)
m.addConstr(2*x0 + 16*x2 + 16*x3 >= 58)
m.addConstr(3*x1 + 16*x2 + 16*x3 >= 58)
m.addConstr(2*x0 + 3*x1 + 16*x3 >= 58)
m.addConstr(2*x0 + 3*x1 + 16*x2 >= 46)
m.addConstr(2*x0 + 16*x2 + 16*x3 >= 46)
m.addConstr(3*x1 + 16*x2 + 16*x3 >= 46)
m.addConstr(2*x0 + 3*x1 + 16*x3 >= 46)
m.addConstr(2*x0 + 3*x1 + 16*x2 >= 41)
m.addConstr(2*x0 + 16*x2 + 16*x3 >= 41)
m.addConstr(3*x1 + 16*x2 + 16*x3 >= 41)
m.addConstr(2*x0 + 3*x1 + 16*x3 >= 41)
m.addConstr(2*x0 + 3*x1 + 16*x2 + 16*x3 >= 41)
m.addConstr(16*x2 + 13*x3 >= 30)
m.addConstr(5*x0 + 17*x1 >= 19)
m.addConstr(5*x0 + 13*x3 >= 47)
m.addConstr(17*x1 + 13*x3 >= 50)
m.addConstr(17*x1 + 16*x2 >= 42)
m.addConstr(5*x0 + 17*x1 + 16*x2 >= 46)
m.addConstr(17*x1 + 16*x2 + 13*x3 >= 46)
m.addConstr(5*x0 + 17*x1 + 16*x2 >= 47)
m.addConstr(17*x1 + 16*x2 + 13*x3 >= 47)
m.addConstr(5*x0 + 17*x1 + 16*x2 + 13*x3 >= 47)
m.addConstr(9*x1 + 10*x3 >= 20)
m.addConstr(7*x0 + 13*x2 >= 36)
m.addConstr(7*x0 + 9*x1 + 13*x2 + 10*x3 >= 36)
m.addConstr(9*x0 + 8*x1 >= 37)
m.addConstr(9*x0 + 6*x2 >= 36)
m.addConstr(8*x1 + 6*x2 + 15*x3 >= 49)
m.addConstr(9*x0 + 8*x1 + 6*x2 + 15*x3 >= 49)
m.addConstr(-1*x0 + 8*x3 >= 0)
m.addConstr(-6*x2 + 3*x3 >= 0)
m.addConstr(2*x0 + 16*x2 + 16*x3 <= 165)
m.addConstr(5*x0 + 17*x1 <= 77)
m.addConstr(16*x2 + 13*x3 <= 107)
m.addConstr(7*x0 + 13*x2 <= 92)
m.addConstr(9*x1 + 10*x3 <= 157)
m.addConstr(8*x1 + 6*x2 <= 180)
m.addConstr(8*x1 + 6*x2 + 15*x3 <= 190)
m.addConstr(9*x0 + 8*x1 + 6*x2 <= 144)


# Optimize model
m.optimize()

# Print results
if m.status == gp.GRB.OPTIMAL:
    print('Obj: %g' % m.objVal)
    for v in m.getVars():
        print('%s %g' % (v.varName, v.x))
elif m.status == gp.GRB.INFEASIBLE:
    print("The model is infeasible.")
else:
    print("Optimization ended with status:", m.status)

```