## Step 1: Define the symbolic representation of the variables
The variables are 'apples', 'eggs', and 'bowls of instant ramen', which can be represented symbolically as $x_1$, $x_2$, and $x_3$ respectively.

## Step 2: Convert the objective function into a symbolic representation
The objective function to maximize is $9.29x_1^2 + 3.05x_1x_2 + 9.45x_2x_3 + 7.93x_1 + 6.27x_2 + 8.08x_3$.

## 3: Define the constraints in symbolic notation
The constraints are:
1. $0.43x_2 + 2.94x_3 \geq 31$ (at least 31 grams of fiber from eggs and bowls of instant ramen),
2. $2.67^2x_1^2 + 2.94^2x_3^2 \geq 16$ (at least 16 grams of fiber from apples squared and bowls of instant ramen squared),
3. $0.43^2x_2^2 + 2.94^2x_3^2 \leq 97$ (at most 97 grams of fiber from eggs squared and bowls of instant ramen squared),
4. $2.67x_1 + 0.43x_2 \leq 90$ (at most 90 grams of fiber from apples and eggs),
5. $2.67x_1 + 0.43x_2 + 2.94x_3 \leq 90$ (at most 90 grams of fiber from apples, eggs, and bowls of instant ramen).

## 4: Represent the problem in the required JSON format
```json
{
    'sym_variables': [('x1', 'apples'), ('x2', 'eggs'), ('x3', 'bowls of instant ramen')],
    'objective_function': '9.29*x1^2 + 3.05*x1*x2 + 9.45*x2*x3 + 7.93*x1 + 6.27*x2 + 8.08*x3',
    'constraints': [
        '0.43*x2 + 2.94*x3 >= 31',
        '2.67^2*x1^2 + 2.94^2*x3^2 >= 16',
        '0.43^2*x2^2 + 2.94^2*x3^2 <= 97',
        '2.67*x1 + 0.43*x2 <= 90',
        '2.67*x1 + 0.43*x2 + 2.94*x3 <= 90'
    ]
}
```

## 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
    apples = model.addVar(name="apples", lb=-float('inf'), ub=float('inf'))
    eggs = model.addVar(name="eggs", lb=-float('inf'), ub=float('inf'))
    bowls_of_instant_ramen = model.addVar(name="bowls_of_instant_ramen", lb=-float('inf'), ub=float('inf'))

    # Define the objective function
    model.setObjective(9.29 * apples ** 2 + 3.05 * apples * eggs + 9.45 * eggs * bowls_of_instant_ramen + 7.93 * apples + 6.27 * eggs + 8.08 * bowls_of_instant_ramen, gurobi.GRB.MAXIMIZE)

    # Define the constraints
    model.addConstr(0.43 * eggs + 2.94 * bowls_of_instant_ramen >= 31)
    model.addConstr(2.67 ** 2 * apples ** 2 + 2.94 ** 2 * bowls_of_instant_ramen ** 2 >= 16)
    model.addConstr(0.43 ** 2 * eggs ** 2 + 2.94 ** 2 * bowls_of_instant_ramen ** 2 <= 97)
    model.addConstr(2.67 * apples + 0.43 * eggs <= 90)
    model.addConstr(2.67 * apples + 0.43 * eggs + 2.94 * bowls_of_instant_ramen <= 90)

    # Optimize the model
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.OPTIMAL:
        print("Optimal solution found.")
        print(f"Apples: {apples.varValue}")
        print(f"Eggs: {eggs.varValue}")
        print(f"Bowls of instant ramen: {bowls_of_instant_ramen.varValue}")
        print(f"Objective function value: {model.objVal}")
    else:
        print("No optimal solution found.")

optimize_problem()
```