To tackle the given optimization problem, we first need to translate the natural language description into a symbolic representation. This involves defining variables, an objective function, and constraints using algebraic terms.

### Symbolic Representation:

Let's define:
- $x_1$ as the milligrams of vitamin B9,
- $x_2$ as the milligrams of vitamin B5.

The **objective function** to maximize is: $1.18x_1 + 8.37x_2$

The **constraints** are:
1. $7x_1 + 5x_2 \geq 31$
2. $14x_1 + 13x_2 \geq 21$
3. $4x_1 + 6x_2 \geq 42$
4. $-7x_1 + 8x_2 \geq 0$
5. $7x_1 + 5x_2 \leq 101$
6. $14x_1 + 13x_2 \leq 61$
7. $4x_1 + 6x_2 \leq 113$

Given this, the symbolic representation in JSON format is:
```json
{
    'sym_variables': [('x1', 'milligrams of vitamin B9'), ('x2', 'milligrams of vitamin B5')],
    'objective_function': '1.18*x1 + 8.37*x2',
    'constraints': [
        '7*x1 + 5*x2 >= 31',
        '14*x1 + 13*x2 >= 21',
        '4*x1 + 6*x2 >= 42',
        '-7*x1 + 8*x2 >= 0',
        '7*x1 + 5*x2 <= 101',
        '14*x1 + 13*x2 <= 61',
        '4*x1 + 6*x2 <= 113'
    ]
}
```

### Gurobi Code:

To solve this optimization problem using Gurobi, we'll write the Python code as follows:
```python
from gurobipy import *

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

# Define variables
x1 = m.addVar(lb=0, name="milligrams_of_vitamin_B9")
x2 = m.addVar(lb=0, name="milligrams_of_vitamin_B5")

# Set the objective function
m.setObjective(1.18*x1 + 8.37*x2, GRB.MAXIMIZE)

# Add constraints
m.addConstr(7*x1 + 5*x2 >= 31, "immune_support_index_min")
m.addConstr(14*x1 + 13*x2 >= 21, "energy_stability_index_min")
m.addConstr(4*x1 + 6*x2 >= 42, "digestive_support_index_min")
m.addConstr(-7*x1 + 8*x2 >= 0, "vitamin_ratio_constraint")
m.addConstr(7*x1 + 5*x2 <= 101, "immune_support_index_max")
m.addConstr(14*x1 + 13*x2 <= 61, "energy_stability_index_max")
m.addConstr(4*x1 + 6*x2 <= 113, "digestive_support_index_max")

# Optimize the model
m.optimize()

# Print solution
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Milligrams of Vitamin B9: {x1.x}")
    print(f"Milligrams of Vitamin B5: {x2.x}")
    print(f"Objective Function Value: {m.objVal}")
else:
    print("No optimal solution found.")
```