## Step 1: Define the symbolic representation of the variables
The variables are defined as follows:
- $x_0$ represents 'milligrams of vitamin D'
- $x_1$ represents 'milligrams of vitamin B7'
- $x_2$ represents 'grams of carbohydrates'

## Step 2: Translate the objective function into symbolic notation
The objective function to minimize is $6.02x_0^2 + 9.35x_0x_2 + 8.77x_2^2$.

## 3: List the constraints in symbolic notation
The constraints are:
- $1x_0 \leq 107$ (digestive support index for $x_0$)
- $4x_0 \leq 162$ (immune support index for $x_0$)
- $17x_1 \leq 107$ (digestive support index for $x_1$)
- $14x_1 \leq 162$ (immune support index for $x_1$)
- $6x_2 \leq 107$ (digestive support index for $x_2$)
- $8x_2 \leq 162$ (immune support index for $x_2$)
- $17x_1 + 6x_2 \geq 33$ (total digestive support index from $x_1$ and $x_2$)
- $1x_0 + 6x_2 \geq 28$ (total digestive support index from $x_0$ and $x_2$)
- $1x_0 + 17x_1 + 6x_2 \geq 26$ (total digestive support index from $x_0$, $x_1$, and $x_2$)
- $14x_1 + 8x_2 \geq 38$ (total immune support index from $x_1$ and $x_2$)
- $4x_0 + 14x_1 + 8x_2 \geq 38$ (total immune support index from $x_0$, $x_1$, and $x_2$)
- $2x_0 - 1x_2 \geq 0$ (relationship between $x_0$ and $x_2$)
- $-3x_0^2 + 9x_1^2 \geq 0$ (relationship between $x_0$ and $x_1$)

## 4: Create the symbolic representation of the problem
```json
{
    'sym_variables': [
        ('x0', 'milligrams of vitamin D'),
        ('x1', 'milligrams of vitamin B7'),
        ('x2', 'grams of carbohydrates')
    ],
    'objective_function': '6.02*x0^2 + 9.35*x0*x2 + 8.77*x2^2',
    'constraints': [
        '1*x0 <= 107',
        '4*x0 <= 162',
        '17*x1 <= 107',
        '14*x1 <= 162',
        '6*x2 <= 107',
        '8*x2 <= 162',
        '17*x1 + 6*x2 >= 33',
        '1*x0 + 6*x2 >= 28',
        '1*x0 + 17*x1 + 6*x2 >= 26',
        '14*x1 + 8*x2 >= 38',
        '4*x0 + 14*x1 + 8*x2 >= 38',
        '2*x0 - 1*x2 >= 0',
        '-3*x0^2 + 9*x1^2 >= 0'
    ]
}
```

## Step 5: 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(lb=-gurobi.GRB.INFINITY, ub=gurobi.GRB.INFINITY, name='x0')  # milligrams of vitamin D
    x1 = model.addVar(lb=-gurobi.GRB.INFINITY, ub=gurobi.GRB.INFINITY, name='x1')  # milligrams of vitamin B7
    x2 = model.addVar(lb=-gurobi.GRB.INFINITY, ub=gurobi.GRB.INFINITY, name='x2')  # grams of carbohydrates

    # Objective function
    model.setObjective(6.02 * x0**2 + 9.35 * x0 * x2 + 8.77 * x2**2, gurobi.GRB.MINIMIZE)

    # Constraints
    model.addConstr(x0 <= 107)
    model.addConstr(4 * x0 <= 162)
    model.addConstr(17 * x1 <= 107)
    model.addConstr(14 * x1 <= 162)
    model.addConstr(6 * x2 <= 107)
    model.addConstr(8 * x2 <= 162)
    model.addConstr(17 * x1 + 6 * x2 >= 33)
    model.addConstr(x0 + 6 * x2 >= 28)
    model.addConstr(x0 + 17 * x1 + 6 * x2 >= 26)
    model.addConstr(14 * x1 + 8 * x2 >= 38)
    model.addConstr(4 * x0 + 14 * x1 + 8 * x2 >= 38)
    model.addConstr(2 * x0 - x2 >= 0)
    model.addConstr(-3 * x0**2 + 9 * x1**2 >= 0)

    # Optimize 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)
    else:
        print('The model is infeasible')

optimize_problem()
```