To solve this optimization problem, we first need to understand and translate the given natural language description into a symbolic representation that can be used in mathematical terms. The variables of interest are 'grams of fat' and 'milligrams of vitamin B12', which will be represented symbolically as `x0` and `x1`, respectively.

The objective function aims to maximize the value calculated by `5.14 * x0 + 5.3 * x1`.

Given constraints:
- The cognitive performance index for grams of fat is 17.
- The cardiovascular support index for grams of fat is 7.
- Milligrams of vitamin B12 have a cognitive performance index of 17.
- Milligrams of vitamin B12 have a cardiovascular support index of 17.
- The total combined cognitive performance index must be at least 16.
- The total combined cardiovascular support index should be at least 48.
- `-4 * x0 + 10 * x1 >= 0`.
- The total combined cognitive performance index should not exceed 38.
- The total combined cardiovascular support index should not exceed 104.

Let's represent the problem symbolically:

```json
{
    'sym_variables': [('x0', 'grams of fat'), ('x1', 'milligrams of vitamin B12')],
    'objective_function': '5.14*x0 + 5.3*x1',
    'constraints': [
        '17*x0 + 17*x1 >= 16',
        '7*x0 + 17*x1 >= 48',
        '-4*x0 + 10*x1 >= 0',
        '17*x0 + 17*x1 <= 38',
        '7*x0 + 17*x1 <= 104'
    ]
}
```

Now, let's write the Gurobi code to solve this optimization problem. We'll use Python as our programming language for this purpose.

```python
from gurobipy import *

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

# Add variables to the model
x0 = m.addVar(vtype=GRB.CONTINUOUS, name="grams_of_fat")
x1 = m.addVar(vtype=GRB.CONTINUOUS, name="milligrams_of_vitamin_B12")

# Set the objective function
m.setObjective(5.14*x0 + 5.3*x1, GRB.MAXIMIZE)

# Add constraints
m.addConstr(17*x0 + 17*x1 >= 16, "cognitive_performance_min")
m.addConstr(7*x0 + 17*x1 >= 48, "cardiovascular_support_min")
m.addConstr(-4*x0 + 10*x1 >= 0, "additional_constraint")
m.addConstr(17*x0 + 17*x1 <= 38, "cognitive_performance_max")
m.addConstr(7*x0 + 17*x1 <= 104, "cardiovascular_support_max")

# Optimize the model
m.optimize()

# Print solution
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"grams_of_fat: {x0.x}")
    print(f"milligrams_of_vitamin_B12: {x1.x}")
    print(f"Objective function value: {m.objVal}")
else:
    print("No optimal solution found")
```