```json
{
  "sym_variables": [
    ("x0", "milligrams of calcium"),
    ("x1", "milligrams of vitamin E"),
    ("x2", "milligrams of vitamin D")
  ],
  "objective_function": "4*x0 + 3*x1 + 2*x2",
  "constraints": [
    "1*x1 + 10*x2 >= 44",
    "1*x0 + 10*x1 >= 58",
    "1*x0 + 10*x2 >= 54",
    "1*x0 + 10*x1 + 10*x2 >= 39",
    "10*x1 + 2*x2 >= 31",
    "2*x0 + 2*x2 >= 74",
    "2*x0 + 10*x1 + 2*x2 >= 74",
    "3*x0 - 9*x2 >= 0",
    "-9*x0 + 5*x1 >= 0",
    "2*x0 + 2*x2 <= 189",
    "2*x0 + 10*x1 <= 201",
    "10*x1 + 2*x2 <= 117",
    "x0 integer",
    "x2 integer"

  ]
}
```

```python
import gurobipy as gp

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

    # Create variables
    calcium = m.addVar(vtype=gp.GRB.INTEGER, name="calcium")
    vitamin_e = m.addVar(vtype=gp.GRB.CONTINUOUS, name="vitamin_e")
    vitamin_d = m.addVar(vtype=gp.GRB.INTEGER, name="vitamin_d")


    # Set objective function
    m.setObjective(4*calcium + 3*vitamin_e + 2*vitamin_d, gp.GRB.MINIMIZE)

    # Add constraints
    m.addConstr(10*vitamin_e + 10*vitamin_d >= 44, "muscle_growth_e_d")
    m.addConstr(calcium + 10*vitamin_e >= 58, "muscle_growth_ca_e")
    m.addConstr(calcium + 10*vitamin_d >= 54, "muscle_growth_ca_d")
    m.addConstr(calcium + 10*vitamin_e + 10*vitamin_d >= 39, "muscle_growth_all")

    m.addConstr(10*vitamin_e + 2*vitamin_d >= 31, "immune_support_e_d")
    m.addConstr(2*calcium + 2*vitamin_d >= 74, "immune_support_ca_d")
    m.addConstr(2*calcium + 10*vitamin_e + 2*vitamin_d >= 74, "immune_support_all")

    m.addConstr(3*calcium - 9*vitamin_d >= 0, "constraint_1")
    m.addConstr(-9*calcium + 5*vitamin_e >= 0, "constraint_2")

    m.addConstr(2*calcium + 2*vitamin_d <= 189, "immune_support_ca_d_upper")
    m.addConstr(2*calcium + 10*vitamin_e <= 201, "immune_support_ca_e_upper")
    m.addConstr(10*vitamin_e + 2*vitamin_d <= 117, "immune_support_e_d_upper")


    # Optimize model
    m.optimize()

    if m.status == gp.GRB.OPTIMAL:
        print('Obj: %g' % m.objVal)
        print('calcium:', calcium.x)
        print('vitamin_e:', vitamin_e.x)
        print('vitamin_d:', vitamin_d.x)
    elif m.status == gp.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')

```