## Step 1: Define the symbolic representation of the variables
The variables are 'hours worked by Jean' and 'hours worked by George', which can be represented symbolically as $x_1$ and $x_2$ respectively.

## Step 2: Convert the objective function into a symbolic representation
The objective function to maximize is $8.61x_1^2 + 8.54x_1x_2 + 1.04x_2^2 + 3.32x_1 + 8.36x_2$.

## 3: Define the constraints in symbolic notation
The constraints are:
1. $17x_1$ is not a constraint on $x_1$ itself but a given work quality rating, so we ignore it as a constraint but note $x_0 = 17$ for Jean.
2. $6x_2$ is similarly a given, so $x_1 = 17$ and $x_2 = 6$ for quality ratings.
3. $x_1^2 + x_2^2 \geq 49$.
4. $3x_1^2 - 9x_2^2 \geq 0$.
5. $x_1 + x_2 \leq 152$ and also $x_1 + x_2 \leq 152$ which is redundant.

## 4: Correctly interpret the problem constraints and objective
Given that $x_0 = 17$ and $x_1 = 6$ seem to represent work quality ratings per hour for Jean and George respectively, we need to adjust our understanding:
- Let $x_1$ be hours worked by Jean and $x_2$ be hours worked by George.
- The work quality ratings are given but seem to be constants rather than variables in the optimization problem.

## 5: Formulate the optimization problem with Gurobi
We need to maximize $8.61x_1^2 + 8.54x_1x_2 + 1.04x_2^2 + 3.32x_1 + 8.36x_2$ subject to:
- $x_1^2 + x_2^2 \geq 49$
- $3x_1^2 - 9x_2^2 \geq 0$
- $x_1 + x_2 \leq 152$
- $x_1, x_2$ are integers.

## 6: Write down the symbolic representation
```json
{
'sym_variables': [('x1', 'hours worked by Jean'), ('x2', 'hours worked by George')],
'objective_function': '8.61*x1^2 + 8.54*x1*x2 + 1.04*x2^2 + 3.32*x1 + 8.36*x2',
'constraints': [
    'x1^2 + x2^2 >= 49',
    '3*x1^2 - 9*x2^2 >= 0',
    'x1 + x2 <= 152',
    'x1 >= 0', 'x2 >= 0',  # Assuming non-negativity
    'x1 % 1 == 0', 'x2 % 1 == 0'  # Integer constraint
]
}
```

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

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

        # Define variables
        x1 = m.addVar(name="hours_worked_by_Jean", vtype=gurobi.GRB.INTEGER)
        x2 = m.addVar(name="hours_worked_by_George", vtype=gurobi.GRB.INTEGER)

        # Objective function
        m.setObjective(8.61*x1**2 + 8.54*x1*x2 + 1.04*x2**2 + 3.32*x1 + 8.36*x2, gurobi.GRB.MAXIMIZE)

        # Constraints
        m.addConstr(x1**2 + x2**2 >= 49)
        m.addConstr(3*x1**2 - 9*x2**2 >= 0)
        m.addConstr(x1 + x2 <= 152)

        # Non-negativity constraints (implicit in Gurobi for continuous variables, but we make sure)
        # Not needed explicitly for integer variables as they default to 0 lower bound

        # Solve the problem
        m.optimize()

        # Print the solution
        if m.status == gurobi.GRB.OPTIMAL:
            print("Optimal solution found.")
            print(f"Hours worked by Jean: {x1.varValue}")
            print(f"Hours worked by George: {x2.varValue}")
            print(f"Objective: {m.objVal}")
        else:
            print("No optimal solution found.")

    except gurobi.GUROBI_ERROR as e:
        print(f"Gurobi error: {e}")

optimize_problem()
```