To solve 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.

### Symbolic Representation:

Let's define:
- $x_1$ as 'grams of fat'
- $x_2$ as 'milligrams of vitamin C'

The objective function to minimize is: $8x_1 + 4x_2$

Constraints are:
1. Digestive support index for grams of fat: $14x_1$
2. Cognitive performance index of grams of fat: $7x_1$
3. Digestive support index of milligrams of vitamin C: $12x_2$
4. Cognitive performance index of milligrams of vitamin C: $15x_2$
5. Total combined digestive support index $\geq 21$: $14x_1 + 12x_2 \geq 21$
6. Same as constraint 5, emphasizing the total must be at least 21.
7. Total combined cognitive performance index $\geq 38$: $7x_1 + 15x_2 \geq 38$
8. Same as constraint 7, restating the requirement for a minimum of 38.
9. Linear inequality: $-x_1 + 6x_2 \geq 0$
10. Maximum total combined digestive support index $\leq 71$: $14x_1 + 12x_2 \leq 71$
11. Maximum total combined cognitive performance index $\leq 88$: $7x_1 + 15x_2 \leq 88$

Since both variables can be non-integer, they are continuous.

### Symbolic Representation in JSON Format:

```json
{
    'sym_variables': [('x1', 'grams of fat'), ('x2', 'milligrams of vitamin C')],
    'objective_function': '8*x1 + 4*x2',
    'constraints': [
        '14*x1 + 12*x2 >= 21',
        '7*x1 + 15*x2 >= 38',
        '-x1 + 6*x2 >= 0',
        '14*x1 + 12*x2 <= 71',
        '7*x1 + 15*x2 <= 88'
    ]
}
```

### Gurobi Code:

To solve this problem using Gurobi, we'll write the Python code below. This code defines the model, adds variables and constraints according to our symbolic representation, sets the objective function, and then optimizes it.

```python
from gurobipy import *

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

# Add variables
x1 = m.addVar(lb=0, vtype=GRB.CONTINUOUS, name="grams_of_fat")
x2 = m.addVar(lb=0, vtype=GRB.CONTINUOUS, name="milligrams_of_vitamin_C")

# Set the objective function
m.setObjective(8*x1 + 4*x2, GRB.MINIMIZE)

# Add constraints
m.addConstr(14*x1 + 12*x2 >= 21, "digestive_support_index")
m.addConstr(7*x1 + 15*x2 >= 38, "cognitive_performance_index")
m.addConstr(-x1 + 6*x2 >= 0, "linear_inequality")
m.addConstr(14*x1 + 12*x2 <= 71, "max_digestive_support")
m.addConstr(7*x1 + 15*x2 <= 88, "max_cognitive_performance")

# Optimize model
m.optimize()

# Print solution
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Grams of fat: {x1.x}")
    print(f"Milligrams of vitamin C: {x2.x}")
    print(f"Objective function value: {m.objVal}")
else:
    print("No optimal solution found")
```