To solve the optimization problem described, we first need to translate the natural language description into a symbolic representation. This involves defining variables for each of the entities mentioned (hours worked by George, hours worked by Paul, hours worked by Laura) and then representing the objective function and constraints using these variables.

Let's define:
- \(x_1\) as the hours worked by George,
- \(x_2\) as the hours worked by Paul,
- \(x_3\) as the hours worked by Laura.

The objective function to maximize is given as:
\[1 \cdot x_1 \cdot x_2 + 9 \cdot x_1 \cdot x_3 + 1 \cdot x_2 \cdot x_3 + 2 \cdot x_3^2 + 9 \cdot x_1 + 8 \cdot x_2\]

The constraints are:
1. \(29x_1 \leq 284\)
2. \(23x_2 \leq 284\)
3. \(25x_3 \leq 284\)
4. \(23^2x_2^2 + 25^2x_3^2 \leq 266\)
5. \(29x_1 + 23x_2 \leq 208\)
6. \(29x_1 + 25x_3 \leq 106\)
7. \(29^2x_1^2 + 23^2x_2^2 + 25^2x_3^2 \leq 268\)
8. \(29x_1 + 23x_2 + 25x_3 \leq 268\)

Symbolic representation:
```json
{
    'sym_variables': [('x1', 'hours worked by George'), ('x2', 'hours worked by Paul'), ('x3', 'hours worked by Laura')],
    'objective_function': '1*x1*x2 + 9*x1*x3 + 1*x2*x3 + 2*x3**2 + 9*x1 + 8*x2',
    'constraints': [
        '29*x1 <= 284',
        '23*x2 <= 284',
        '25*x3 <= 284',
        '529*x2**2 + 625*x3**2 <= 266',
        '29*x1 + 23*x2 <= 208',
        '29*x1 + 25*x3 <= 106',
        '841*x1**2 + 529*x2**2 + 625*x3**2 <= 268',
        '29*x1 + 23*x2 + 25*x3 <= 268'
    ]
}
```

Now, let's implement this optimization problem using Gurobi in Python:

```python
from gurobipy import *

# Create a new model
m = Model("Optimization_Problem")

# Define the variables
x1 = m.addVar(lb=0, name="hours_worked_by_George")
x2 = m.addVar(lb=0, name="hours_worked_by_Paul")
x3 = m.addVar(lb=0, name="hours_worked_by_Laura")

# Set the objective function
m.setObjective(1*x1*x2 + 9*x1*x3 + 1*x2*x3 + 2*x3**2 + 9*x1 + 8*x2, GRB.MAXIMIZE)

# Add constraints
m.addConstr(29*x1 <= 284)
m.addConstr(23*x2 <= 284)
m.addConstr(25*x3 <= 284)
m.addConstr(529*x2**2 + 625*x3**2 <= 266)
m.addConstr(29*x1 + 23*x2 <= 208)
m.addConstr(29*x1 + 25*x3 <= 106)
m.addConstr(841*x1**2 + 529*x2**2 + 625*x3**2 <= 268)
m.addConstr(29*x1 + 23*x2 + 25*x3 <= 268)

# Optimize the model
m.optimize()

# Print the solution
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Hours worked by George: {x1.x}")
    print(f"Hours worked by Paul: {x2.x}")
    print(f"Hours worked by Laura: {x3.x}")
else:
    print("No optimal solution found")
```