## Step 1: Define the symbolic representation of the problem
The problem involves two variables: 'grams of fiber' and 'milligrams of vitamin B4', which we can denote as $x_1$ and $x_2$ respectively.

## Step 2: Translate the objective function into symbolic notation
The objective function to maximize is $8.07x_1^2 + 6.39x_1x_2 + 7.85x_2^2 + 3.82x_1 + 5.89x_2$.

## 3: List the constraints in symbolic notation
The constraints are:
- $8.53x_1 + 6.05x_2 \geq 38$
- $13.96x_1 + 17.69x_2 \geq 67$
- $28.71x_1 + 26.27x_2 \geq 61$
- $2.14x_1 + 17.25x_2 \geq 27$
- $-8x_1^2 + 4x_2^2 \geq 0$
- $8.53x_1 + 6.05x_2 \leq 115$
- $13.96x_1 + 17.69x_2 \leq 90$
- $28.71x_1 + 26.27x_2 \leq 193$
- $2.14x_1 + 17.25x_2 \leq 68$
- $x_1$ is an integer
- $x_2$ can be any real number

## 4: Correcting and Simplifying Constraints for Accuracy
Upon review, there seems to be a duplication in the constraints regarding the upper bounds for digestive support and energy stability indices. The correct and unique constraints should be considered as:
- Digestive support index: $8.53x_1 + 6.05x_2 \geq 38$ and $8.53x_1 + 6.05x_2 \leq 115$
- Energy stability index: $13.96x_1 + 17.69x_2 \geq 67$ and $13.96x_1 + 17.69x_2 \leq 90$
- Immune support index: $28.71x_1 + 26.27x_2 \geq 61$ and $28.71x_1 + 26.27x_2 \leq 193$
- Muscle growth index: $2.14x_1 + 17.25x_2 \geq 27$ and $2.14x_1 + 17.25x_2 \leq 68$

## 5: Symbolic Representation
The symbolic representation is:
```json
{
'sym_variables': [('x1', 'grams of fiber'), ('x2', 'milligrams of vitamin B4')],
'objective_function': '8.07*x1^2 + 6.39*x1*x2 + 7.85*x2^2 + 3.82*x1 + 5.89*x2',
'constraints': [
    '8.53*x1 + 6.05*x2 >= 38',
    '13.96*x1 + 17.69*x2 >= 67',
    '28.71*x1 + 26.27*x2 >= 61',
    '2.14*x1 + 17.25*x2 >= 27',
    '-8*x1^2 + 4*x2^2 >= 0',
    '8.53*x1 + 6.05*x2 <= 115',
    '13.96*x1 + 17.69*x2 <= 90',
    '28.71*x1 + 26.27*x2 <= 193',
    '2.14*x1 + 17.25*x2 <= 68',
    'x1 % 1 == 0'  # Ensuring x1 is an integer
]
}
```

## 6: Gurobi Code
```python
import gurobi

def solve_optimization_problem():
    model = gurobi.Model()
    
    # Define variables
    x1 = model.addVar(name="x1", vtype=gurobi.GRB.INTEGER)  # grams of fiber
    x2 = model.addVar(name="x2")  # milligrams of vitamin B4
    
    # Objective function
    model.setObjective(8.07 * x1**2 + 6.39 * x1 * x2 + 7.85 * x2**2 + 3.82 * x1 + 5.89 * x2, gurobi.GRB.MAXIMIZE)
    
    # Constraints
    model.addConstr(8.53 * x1 + 6.05 * x2 >= 38)
    model.addConstr(13.96 * x1 + 17.69 * x2 >= 67)
    model.addConstr(28.71 * x1 + 26.27 * x2 >= 61)
    model.addConstr(2.14 * x1 + 17.25 * x2 >= 27)
    model.addConstr(-8 * x1**2 + 4 * x2**2 >= 0)
    model.addConstr(8.53 * x1 + 6.05 * x2 <= 115)
    model.addConstr(13.96 * x1 + 17.69 * x2 <= 90)
    model.addConstr(28.71 * x1 + 26.27 * x2 <= 193)
    model.addConstr(2.14 * x1 + 17.25 * x2 <= 68)
    
    # Optimize
    model.optimize()
    
    # Print solution
    if model.status == gurobi.GRB.OPTIMAL:
        print("Optimal solution found.")
        print(f"Grams of fiber: {x1.varValue}")
        print(f"Milligrams of vitamin B4: {x2.varValue}")
        print(f"Objective function value: {model.objVal}")
    else:
        print("No optimal solution found.")

solve_optimization_problem()
```