```json
{
  "sym_variables": [
    ("x0", "milligrams of vitamin A"),
    ("x1", "milligrams of vitamin B5"),
    ("x2", "milligrams of vitamin B3"),
    ("x3", "milligrams of iron")
  ],
  "objective_function": "9.87 * x0 + 2.03 * x1 + 7.26 * x2 + 4.87 * x3",
  "constraints": [
    "29 * x0 + 21 * x1 + 31 * x2 + 29 * x3 <= 303",
    "21 * x1 + 29 * x3 >= 26",
    "29 * x0 + 29 * x3 >= 41",
    "29 * x0 + 21 * x1 >= 27",
    "21 * x1 + 31 * x2 >= 71",
    "31 * x2 + 29 * x3 >= 31",
    "29 * x0 + 31 * x2 >= 39",
    "21 * x1 + 31 * x2 + 29 * x3 >= 56",
    "29 * x0 + 21 * x1 + 31 * x2 + 29 * x3 >= 56",
    "7 * x1 - 4 * x3 >= 0",
    "21 * x1 + 31 * x2 <= 293",
    "29 * x0 + 31 * x2 <= 184"
  ]
}
```

```python
import gurobipy as gp
from gurobipy import GRB

try:
    # Create a new model
    m = gp.Model("vitamin_optimization")

    # Create variables
    vitamin_a = m.addVar(vtype=GRB.INTEGER, name="vitamin_a")
    vitamin_b5 = m.addVar(vtype=GRB.INTEGER, name="vitamin_b5")
    vitamin_b3 = m.addVar(vtype=GRB.CONTINUOUS, name="vitamin_b3")
    iron = m.addVar(vtype=GRB.CONTINUOUS, name="iron")

    # Set objective function
    m.setObjective(9.87 * vitamin_a + 2.03 * vitamin_b5 + 7.26 * vitamin_b3 + 4.87 * iron, GRB.MINIMIZE)

    # Add constraints
    m.addConstr(29 * vitamin_a + 21 * vitamin_b5 + 31 * vitamin_b3 + 29 * iron <= 303, "r0")
    m.addConstr(21 * vitamin_b5 + 29 * iron >= 26, "c1")
    m.addConstr(29 * vitamin_a + 29 * iron >= 41, "c2")
    m.addConstr(29 * vitamin_a + 21 * vitamin_b5 >= 27, "c3")
    m.addConstr(21 * vitamin_b5 + 31 * vitamin_b3 >= 71, "c4")
    m.addConstr(31 * vitamin_b3 + 29 * iron >= 31, "c5")
    m.addConstr(29 * vitamin_a + 31 * vitamin_b3 >= 39, "c6")
    m.addConstr(21 * vitamin_b5 + 31 * vitamin_b3 + 29 * iron >= 56, "c7")
    m.addConstr(29 * vitamin_a + 21 * vitamin_b5 + 31 * vitamin_b3 + 29 * iron >= 56, "c8")
    m.addConstr(7 * vitamin_b5 - 4 * iron >= 0, "c9")
    m.addConstr(21 * vitamin_b5 + 31 * vitamin_b3 <= 293, "c10")
    m.addConstr(29 * vitamin_a + 31 * vitamin_b3 <= 184, "c11")


    # Optimize model
    m.optimize()

    if m.status == GRB.OPTIMAL:
        print('Obj: %g' % m.objVal)
        print('vitamin_a:', vitamin_a.x)
        print('vitamin_b5:', vitamin_b5.x)
        print('vitamin_b3:', vitamin_b3.x)
        print('iron:', iron.x)
    elif m.status == GRB.INFEASIBLE:
        print('The model is infeasible.')
    else:
        print('Optimization ended with status %d' % m.status)


except gp.GurobiError as e:
    print('Error code ' + str(e.errno) + ': ' + str(e))

except AttributeError:
    print('Encountered an attribute error')
```