To tackle this problem, let's break down the given information and translate it into a symbolic representation of an optimization problem. We have two variables: milligrams of vitamin A (let's denote this as `x1`) and milligrams of vitamin B9 (denoted as `x2`). The objective function to maximize is described as "4 multiplied by the amount of milligrams of vitamin A added to 3 times the quantity of milligrams of vitamin B9," which translates algebraically to `4*x1 + 3*x2`.

The constraints given are:
- The digestive support index for milligrams of vitamin A is 7, which implies `x1` contributes 7 units per unit of `x1`.
- The cardiovascular support index of milligrams of vitamin A is 16.
- Milligrams of vitamin A have an immune support index of 15.
- The kidney support index of milligrams of vitamin A is 9.
- Similar indices are given for milligrams of vitamin B9: digestive (14), cardiovascular (7), immune (6), and kidney (17).
- Combined minimum support indices for digestion, cardiovascular, immune system, and kidney are specified as 42, 29, 69, and 43 respectively.
- An additional constraint involves `5*x1 - 3*x2 >= 0`.
- Maximum combined support indices for digestion, cardiovascular, immune, and kidney are given as 132, 94, 129, and 113 respectively.

Given this breakdown, we can represent our problem symbolically as follows:
```json
{
    'sym_variables': [('x1', 'milligrams of vitamin A'), ('x2', 'milligrams of vitamin B9')],
    'objective_function': '4*x1 + 3*x2',
    'constraints': [
        '7*x1 + 14*x2 >= 42',  # Minimum digestive support index
        '16*x1 + 7*x2 >= 29',  # Minimum cardiovascular support index
        '15*x1 + 6*x2 >= 69',  # Minimum immune support index
        '9*x1 + 17*x2 >= 43',  # Minimum kidney support index
        '5*x1 - 3*x2 >= 0',    # Additional constraint
        '7*x1 + 14*x2 <= 132', # Maximum digestive support index
        '16*x1 + 7*x2 <= 94',  # Maximum cardiovascular support index
        '15*x1 + 6*x2 <= 129', # Maximum immune support index
        '9*x1 + 17*x2 <= 113'  # Maximum kidney support index
    ]
}
```

Now, let's write the Gurobi code to solve this optimization problem. We'll use Python with the Gurobi library.

```python
from gurobipy import *

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

# Define variables (allowing for fractional numbers of milligrams)
x1 = m.addVar(vtype=GRB.CONTINUOUS, name="milligrams_of_vitamin_A")
x2 = m.addVar(vtype=GRB.CONTINUOUS, name="milligrams_of_vitamin_B9")

# Objective function: Maximize 4*x1 + 3*x2
m.setObjective(4*x1 + 3*x2, GRB.MAXIMIZE)

# Constraints
m.addConstr(7*x1 + 14*x2 >= 42, "min_digestive_support")
m.addConstr(16*x1 + 7*x2 >= 29, "min_cardiovascular_support")
m.addConstr(15*x1 + 6*x2 >= 69, "min_immune_support")
m.addConstr(9*x1 + 17*x2 >= 43, "min_kidney_support")
m.addConstr(5*x1 - 3*x2 >= 0, "additional_constraint")
m.addConstr(7*x1 + 14*x2 <= 132, "max_digestive_support")
m.addConstr(16*x1 + 7*x2 <= 94, "max_cardiovascular_support")
m.addConstr(15*x1 + 6*x2 <= 129, "max_immune_support")
m.addConstr(9*x1 + 17*x2 <= 113, "max_kidney_support")

# Optimize model
m.optimize()

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