## Step 1: Define the symbolic representation of the variables
The variables are 'grams of fat' and 'milligrams of vitamin C', which we can denote as $x_1$ and $x_2$ respectively.

## Step 2: Convert the objective function into a symbolic representation
The objective function to minimize is $8x_1 + 4x_2$.

## Step 3: Convert the constraints into a symbolic representation
The constraints given are:
- $14x_1 + 12x_2 \geq 21$
- $7x_1 + 15x_2 \geq 38$
- $-x_1 + 6x_2 \geq 0$
- $14x_1 + 12x_2 \leq 71$
- $7x_1 + 15x_2 \leq 88$

## 4: Define the symbolic representation of the problem
The symbolic representation is:
- Variables: $x_1$ ('grams of fat'), $x_2$ ('milligrams of vitamin C')
- Objective function: $8x_1 + 4x_2$
- Constraints:
  1. $14x_1 + 12x_2 \geq 21$
  2. $7x_1 + 15x_2 \geq 38$
  3. $-x_1 + 6x_2 \geq 0$
  4. $14x_1 + 12x_2 \leq 71$
  5. $7x_1 + 15x_2 \leq 88$

## 5: Write down the problem in the required 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'
  ]
}
```

## 6: Implement the optimization problem using Gurobi
```python
import gurobi

def solve_optimization_problem():
    # Create a new model
    model = gurobi.Model()

    # Define the variables
    x1 = model.addVar(name="grams_of_fat", lb=-gurobi.GRB.INFINITY, ub=gurobi.GRB.INFINITY)
    x2 = model.addVar(name="milligrams_of_vitamin_C", lb=-gurobi.GRB.INFINITY, ub=gurobi.GRB.INFINITY)

    # Define the objective function
    model.setObjective(8 * x1 + 4 * x2, gurobi.GRB.MINIMIZE)

    # Add constraints
    model.addConstr(14 * x1 + 12 * x2 >= 21, name="digestive_support_index_min")
    model.addConstr(7 * x1 + 15 * x2 >= 38, name="cognitive_performance_index_min")
    model.addConstr(-x1 + 6 * x2 >= 0, name="fat_vitamin_C_relation")
    model.addConstr(14 * x1 + 12 * x2 <= 71, name="digestive_support_index_max")
    model.addConstr(7 * x1 + 15 * x2 <= 88, name="cognitive_performance_index_max")

    # Optimize the model
    model.optimize()

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

solve_optimization_problem()
```