## Step 1: Define the symbolic representation of the problem
The problem involves maximizing an objective function subject to several constraints. The variables are:
- $x_0$: grams of fat
- $x_1$: milligrams of vitamin B3
- $x_2$: milligrams of vitamin B2
- $x_3$: milligrams of potassium

The objective function to maximize is:
\[ 8x_0^2 + 3x_0x_2 + 8x_1x_2 + 3x_1x_3 + 6x_2^2 + 2x_1 \]

## Step 2: List the constraints
The constraints based on the given indices and limits are:
- Digestive support index constraints:
  - $0.53x_0 + 0.99x_1 + 1.79x_2 + 1.35x_3 \leq 224$
  - $x_2^2 + x_3^2 \geq 20$
  - $x_1^2 + x_2^2 + x_3^2 \geq 40$
  - $0.53x_0 + 0.99x_1 + 1.35x_3 \geq 40$
  - $0.53x_0^2 + 0.99x_1^2 + 1.35x_3^2 \geq 40$
- Cognitive performance index constraints:
  - $1.25x_0 + 2.94x_1 + 0.12x_2 + 3.33x_3 \geq 48$
  - $1.25x_0^2 + 3.33x_3^2 \geq 50$
  - $1.25x_0 + 2.94x_1 \geq 54$
  - $2.94x_1 + 0.12x_2 \geq 41$
  - $0.12x_2 + 3.33x_3 \geq 31$
  - $1.25x_0^2 + 0.12x_2^2 \geq 20$
  - $1.25x_0^2 + 2.94x_1^2 + 3.33x_3^2 \geq 33$
- Energy stability index constraints:
  - $1.96x_0 + 2.67x_1 + 0.3x_3 \geq 27$
  - $1.96x_0 + 3.07x_2 \geq 41$
  - $2.67x_1 + 3.07x_2 \geq 38$
- Upper bound constraints:
  - $0.53x_2^2 + 1.35x_3^2 \leq 205$
  - $0.99x_1 + 1.35x_3 \leq 216$
  - $1.79x_2 + 1.35x_3 \leq 64$
  - $0.53x_0^2 + 1.79x_2^2 + 1.35x_3^2 \leq 62$
  - $0.53x_0 + 0.99x_1 + 1.79x_2 + 1.35x_3 \leq 188$
  - $1.25x_0^2 + 0.12x_2^2 \leq 149$
  - $2.94x_1 + 3.33x_3 \leq 66$
  - $1.25x_0^2 + 3.33x_3^2 \leq 66$
  - $0.12x_2 + 3.33x_3 \leq 199$
  - $2.94x_1 + 0.12x_2 \leq 183$
  - $1.25x_0 + 2.94x_1 \leq 160$
  - $1.25x_0^2 + 2.94x_1^2 + 3.33x_3^2 \leq 121$
  - $1.25x_0^2 + 0.12x_2^2 + 3.33x_3^2 \leq 58$
  - $1.96x_0 + 2.67x_1 + 3.07x_2 + 0.3x_3 \leq 61$
  - $2.67x_1 + 3.07x_2 \leq 107$
  - $3.07x_2 + 0.3x_3 \leq 88$
  - $1.96x_0 + 2.67x_1 \leq 61$

## Step 3: Provide the symbolic representation in JSON format
```json
{
  "sym_variables": [
    ["x0", "grams of fat"],
    ["x1", "milligrams of vitamin B3"],
    ["x2", "milligrams of vitamin B2"],
    ["x3", "milligrams of potassium"]
  ],
  "objective_function": "8*x0^2 + 3*x0*x2 + 8*x1*x2 + 3*x1*x3 + 6*x2^2 + 2*x1",
  "constraints": [
    "0.53*x0 + 0.99*x1 + 1.79*x2 + 1.35*x3 <= 224",
    "x2^2 + x3^2 >= 20",
    "x1^2 + x2^2 + x3^2 >= 40",
    "0.53*x0 + 0.99*x1 + 1.35*x3 >= 40",
    "0.53*x0^2 + 0.99*x1^2 + 1.35*x3^2 >= 40",
    "1.25*x0 + 2.94*x1 + 0.12*x2 + 3.33*x3 >= 48",
    "1.25*x0^2 + 3.33*x3^2 >= 50",
    "1.25*x0 + 2.94*x1 >= 54",
    "2.94*x1 + 0.12*x2 >= 41",
    "0.12*x2 + 3.33*x3 >= 31",
    "1.25*x0^2 + 0.12*x2^2 >= 20",
    "1.25*x0^2 + 2.94*x1^2 + 3.33*x3^2 >= 33",
    "1.96*x0 + 2.67*x1 + 0.3*x3 >= 27",
    "1.96*x0 + 3.07*x2 >= 41",
    "2.67*x1 + 3.07*x2 >= 38",
    "0.53*x2^2 + 1.35*x3^2 <= 205",
    "0.99*x1 + 1.35*x3 <= 216",
    "1.79*x2 + 1.35*x3 <= 64",
    "0.53*x0^2 + 1.79*x2^2 + 1.35*x3^2 <= 62",
    "0.53*x0 + 0.99*x1 + 1.79*x2 + 1.35*x3 <= 188",
    "1.25*x0^2 + 0.12*x2^2 <= 149",
    "2.94*x1 + 3.33*x3 <= 66",
    "1.25*x0^2 + 3.33*x3^2 <= 66",
    "0.12*x2 + 3.33*x3 <= 199",
    "2.94*x1 + 0.12*x2 <= 183",
    "1.25*x0 + 2.94*x1 <= 160",
    "1.25*x0^2 + 2.94*x1^2 + 3.33*x3^2 <= 121",
    "1.25*x0^2 + 0.12*x2^2 + 3.33*x3^2 <= 58",
    "1.96*x0 + 2.67*x1 + 3.07*x2 + 0.3*x3 <= 61",
    "2.67*x1 + 3.07*x2 <= 107",
    "3.07*x2 + 0.3*x3 <= 88",
    "1.96*x0 + 2.67*x1 <= 61"
  ]
}
```

## Step 4: Implement the optimization problem using Gurobi
```python
import gurobi

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

    # Define the variables
    x0 = model.addVar(name="x0", lb=-float('inf'), ub=float('inf'))
    x1 = model.addVar(name="x1", lb=-float('inf'), ub=float('inf'))
    x2 = model.addVar(name="x2", lb=-float('inf'), ub=float('inf'))
    x3 = model.addVar(name="x3", lb=-float('inf'), ub=float('inf'))

    # Define the objective function
    model.setObjective(8*x0**2 + 3*x0*x2 + 8*x1*x2 + 3*x1*x3 + 6*x2**2 + 2*x1, gurobi.GRB.MAXIMIZE)

    # Add constraints
    model.addConstr(0.53*x0 + 0.99*x1 + 1.79*x2 + 1.35*x3 <= 224)
    model.addConstr(x2**2 + x3**2 >= 20)
    model.addConstr(x1**2 + x2**2 + x3**2 >= 40)
    model.addConstr(0.53*x0 + 0.99*x1 + 1.35*x3 >= 40)
    model.addConstr(0.53*x0**2 + 0.99*x1**2 + 1.35*x3**2 >= 40)
    model.addConstr(1.25*x0 + 2.94*x1 + 0.12*x2 + 3.33*x3 >= 48)
    model.addConstr(1.25*x0**2 + 3.33*x3**2 >= 50)
    model.addConstr(1.25*x0 + 2.94*x1 >= 54)
    model.addConstr(2.94*x1 + 0.12*x2 >= 41)
    model.addConstr(0.12*x2 + 3.33*x3 >= 31)
    model.addConstr(1.25*x0**2 + 0.12*x2**2 >= 20)
    model.addConstr(1.25*x0**2 + 2.94*x1**2 + 3.33*x3**2 >= 33)
    model.addConstr(1.96*x0 + 2.67*x1 + 0.3*x3 >= 27)
    model.addConstr(1.96*x0 + 3.07*x2 >= 41)
    model.addConstr(2.67*x1 + 3.07*x2 >= 38)
    model.addConstr(0.53*x2**2 + 1.35*x3**2 <= 205)
    model.addConstr(0.99*x1 + 1.35*x3 <= 216)
    model.addConstr(1.79*x2 + 1.35*x3 <= 64)
    model.addConstr(0.53*x0**2 + 1.79*x2**2 + 1.35*x3**2 <= 62)
    model.addConstr(0.53*x0 + 0.99*x1 + 1.79*x2 + 1.35*x3 <= 188)
    model.addConstr(1.25*x0**2 + 0.12*x2**2 <= 149)
    model.addConstr(2.94*x1 + 3.33*x3 <= 66)
    model.addConstr(1.25*x0**2 + 3.33*x3**2 <= 66)
    model.addConstr(0.12*x2 + 3.33*x3 <= 199)
    model.addConstr(2.94*x1 + 0.12*x2 <= 183)
    model.addConstr(1.25*x0 + 2.94*x1 <= 160)
    model.addConstr(1.25*x0**2 + 2.94*x1**2 + 3.33*x3**2 <= 121)
    model.addConstr(1.25*x0**2 + 0.12*x2**2 + 3.33*x3**2 <= 58)
    model.addConstr(1.96*x0 + 2.67*x1 + 3.07*x2 + 0.3*x3 <= 61)
    model.addConstr(2.67*x1 + 3.07*x2 <= 107)
    model.addConstr(3.07*x2 + 0.3*x3 <= 88)
    model.addConstr(1.96*x0 + 2.67*x1 <= 61)

    # Solve the model
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.OPTIMAL:
        print("Objective: ", model.objVal)
        print("x0: ", x0.varValue)
        print("x1: ", x1.varValue)
        print("x2: ", x2.varValue)
        print("x3: ", x3.varValue)
    else:
        print("The model is infeasible")

optimize_problem()
```