```json
{
  "sym_variables": [
    ("x0", "milligrams of vitamin B3"),
    ("x1", "milligrams of vitamin A"),
    ("x2", "milligrams of iron"),
    ("x3", "milligrams of vitamin D")
  ],
  "objective_function": "7*x0 + 4*x1 + 7*x2 + 8*x3",
  "constraints": [
    "1.04*x0 + 1.01*x2 >= 12",
    "0.21*x1 + 1.01*x2 >= 14",
    "1.04*x0 + 0.21*x1 >= 15",
    "0.21*x1 + 0.23*x3 >= 30",
    "1.04*x0 + 0.21*x1 + 0.23*x3 >= 27",
    "0.87*x2 + 1.64*x3 >= 15",
    "0.27*x0 + 1.64*x3 >= 33",
    "1.39*x1 + 1.64*x3 >= 19",
    "1.39*x1 + 0.87*x2 >= 24",
    "0.27*x0 + 1.39*x1 >= 15",
    "0.27*x0 + 1.39*x1 + 1.64*x3 >= 30",
    "0.27*x0 + 0.87*x2 + 1.64*x3 >= 30",
    "0.27*x0 + 1.39*x1 + 0.87*x2 >= 30",
    "0.27*x0 + 1.39*x1 + 1.64*x3 >= 34",  
    "0.27*x0 + 0.87*x2 + 1.64*x3 >= 34",
    "0.27*x0 + 1.39*x1 + 0.87*x2 >= 34",
    "0.27*x0 + 1.39*x1 + 1.64*x3 >= 33",
    "0.27*x0 + 0.87*x2 + 1.64*x3 >= 33",
    "0.27*x0 + 1.39*x1 + 0.87*x2 >= 33",
    "0.21*x1 + 1.01*x2 <= 40",
    "0.21*x1 + 0.23*x3 <= 110",
    "1.04*x0 + 1.01*x2 <= 58",
    "1.04*x0 + 0.21*x1 + 1.01*x2 + 0.23*x3 <= 58",
    "0.27*x0 + 0.87*x2 <= 108",
    "1.39*x1 + 1.64*x3 <= 60",
    "0.27*x0 + 1.39*x1 <= 53",
    "1.39*x1 + 0.87*x2 <= 53",
    "0.87*x2 + 1.64*x3 <= 93",
    "0.27*x0 + 0.87*x2 + 1.64*x3 <= 46",
    "0.27*x0 + 1.39*x1 + 0.87*x2 + 1.64*x3 <= 46",
    "x0 == int(x0)",
    "x1 == int(x1)",
    "x3 == int(x3)"

  ]
}
```

```python
import gurobipy as gp

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

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


# Set objective function
m.setObjective(7 * vitamin_b3 + 4 * vitamin_a + 7 * iron + 8 * vitamin_d, gp.GRB.MAXIMIZE)

# Add constraints
m.addConstr(1.04 * vitamin_b3 + 1.01 * iron >= 12)
m.addConstr(0.21 * vitamin_a + 1.01 * iron >= 14)
m.addConstr(1.04 * vitamin_b3 + 0.21 * vitamin_a >= 15)
m.addConstr(0.21 * vitamin_a + 0.23 * vitamin_d >= 30)
m.addConstr(1.04 * vitamin_b3 + 0.21 * vitamin_a + 0.23 * vitamin_d >= 27)
m.addConstr(0.87 * iron + 1.64 * vitamin_d >= 15)
m.addConstr(0.27 * vitamin_b3 + 1.64 * vitamin_d >= 33)
m.addConstr(1.39 * vitamin_a + 1.64 * vitamin_d >= 19)
m.addConstr(1.39 * vitamin_a + 0.87 * iron >= 24)
m.addConstr(0.27 * vitamin_b3 + 1.39 * vitamin_a >= 15)
m.addConstr(0.27 * vitamin_b3 + 1.39 * vitamin_a + 1.64 * vitamin_d >= 30)
m.addConstr(0.27 * vitamin_b3 + 0.87 * iron + 1.64 * vitamin_d >= 30)
m.addConstr(0.27 * vitamin_b3 + 1.39 * vitamin_a + 0.87 * iron >= 30)
m.addConstr(0.27 * vitamin_b3 + 1.39 * vitamin_a + 1.64 * vitamin_d >= 34)
m.addConstr(0.27 * vitamin_b3 + 0.87 * iron + 1.64 * vitamin_d >= 34)
m.addConstr(0.27 * vitamin_b3 + 1.39 * vitamin_a + 0.87 * iron >= 34)
m.addConstr(0.27 * vitamin_b3 + 1.39 * vitamin_a + 1.64 * vitamin_d >= 33)
m.addConstr(0.27 * vitamin_b3 + 0.87 * iron + 1.64 * vitamin_d >= 33)
m.addConstr(0.27 * vitamin_b3 + 1.39 * vitamin_a + 0.87 * iron >= 33)
m.addConstr(0.21 * vitamin_a + 1.01 * iron <= 40)
m.addConstr(0.21 * vitamin_a + 0.23 * vitamin_d <= 110)
m.addConstr(1.04 * vitamin_b3 + 1.01 * iron <= 58)
m.addConstr(1.04 * vitamin_b3 + 0.21 * vitamin_a + 1.01 * iron + 0.23 * vitamin_d <= 58)
m.addConstr(0.27 * vitamin_b3 + 0.87 * iron <= 108)
m.addConstr(1.39 * vitamin_a + 1.64 * vitamin_d <= 60)
m.addConstr(0.27 * vitamin_b3 + 1.39 * vitamin_a <= 53)
m.addConstr(1.39 * vitamin_a + 0.87 * iron <= 53)
m.addConstr(0.87 * iron + 1.64 * vitamin_d <= 93)
m.addConstr(0.27 * vitamin_b3 + 0.87 * iron + 1.64 * vitamin_d <= 46)
m.addConstr(0.27 * vitamin_b3 + 1.39 * vitamin_a + 0.87 * iron + 1.64 * vitamin_d <= 46)



# Optimize model
m.optimize()

# Print results
if m.status == gp.GRB.OPTIMAL:
    print('Obj: %g' % m.objVal)
    print('vitamin_b3:', vitamin_b3.x)
    print('vitamin_a:', vitamin_a.x)
    print('iron:', iron.x)
    print('vitamin_d:', vitamin_d.x)

elif m.status == gp.GRB.INFEASIBLE:
    print("The model is infeasible.")
else:
    print("The model could not be solved to optimality.")

```