To tackle this problem, we first need to understand and translate the given natural language description into a symbolic representation. This involves identifying variables, the objective function, and constraints.

### Symbolic Representation:

Let's denote:
- $x_1$ as the milligrams of vitamin B12,
- $x_2$ as the milligrams of vitamin B3.

The **objective function** is to maximize: $5.84x_1 + 1.76x_2$

Given constraints:
1. Digestive support index: $3x_1 + 7x_2 \geq 13$
2. Cardiovascular support index: $4x_1 + 4x_2 \geq 3$
3. Cognitive performance index: $5x_1 + 9x_2 \geq 13$
4. Additional constraint: $5x_1 - 9x_2 \geq 0$
5. Maximum digestive support index: $3x_1 + 7x_2 \leq 55$
6. Maximum cardiovascular support index: $4x_1 + 4x_2 \leq 14$
7. Maximum cognitive performance index: $5x_1 + 9x_2 \leq 15$

### Symbolic Representation in JSON Format:

```json
{
    'sym_variables': [('x1', 'milligrams of vitamin B12'), ('x2', 'milligrams of vitamin B3')],
    'objective_function': '5.84*x1 + 1.76*x2',
    'constraints': [
        '3*x1 + 7*x2 >= 13',
        '4*x1 + 4*x2 >= 3',
        '5*x1 + 9*x2 >= 13',
        '5*x1 - 9*x2 >= 0',
        '3*x1 + 7*x2 <= 55',
        '4*x1 + 4*x2 <= 14',
        '5*x1 + 9*x2 <= 15'
    ]
}
```

### Gurobi Code:

To solve this optimization problem, we will use the Gurobi Python interface. Note that `x1` is restricted to be an integer, while `x2` can be a continuous variable.

```python
from gurobipy import *

# Create a new model
m = Model("Vitamin_Optimization")

# Define variables
x1 = m.addVar(vtype=GRB.INTEGER, name="milligrams_of_vitamin_B12")
x2 = m.addVar(vtype=GRB.CONTINUOUS, name="milligrams_of_vitamin_B3")

# Set objective function
m.setObjective(5.84*x1 + 1.76*x2, GRB.MAXIMIZE)

# Add constraints
m.addConstr(3*x1 + 7*x2 >= 13, name="digestive_support_index_min")
m.addConstr(4*x1 + 4*x2 >= 3, name="cardiovascular_support_index_min")
m.addConstr(5*x1 + 9*x2 >= 13, name="cognitive_performance_index_min")
m.addConstr(5*x1 - 9*x2 >= 0, name="additional_constraint")
m.addConstr(3*x1 + 7*x2 <= 55, name="digestive_support_index_max")
m.addConstr(4*x1 + 4*x2 <= 14, name="cardiovascular_support_index_max")
m.addConstr(5*x1 + 9*x2 <= 15, name="cognitive_performance_index_max")

# Optimize model
m.optimize()

# Print solution
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Milligrams of Vitamin B12: {x1.x}")
    print(f"Milligrams of Vitamin B3: {x2.x}")
else:
    print("No optimal solution found")
```