To solve this optimization problem, we will first convert the natural language description into a symbolic representation. Then, we'll use Gurobi to implement and solve the problem.

### Symbolic Representation:

Let's denote:
- \(x_1\) as 'hours worked by Peggy',
- \(x_2\) as 'hours worked by Paul',
- \(x_3\) as 'hours worked by Bill'.

The objective function is to maximize: \(8.96x_1 + 1.78x_2 + 9.49x_3\).

Constraints:
1. Organization score for Peggy: \(20x_1\)
2. Organization score for Paul: \(17x_2\)
3. Organization score for Bill: \(4x_3\)
4. Combined organization score for Peggy and Paul: \(20x_1 + 17x_2 \geq 38\)
5. Combined organization score for Peggy and Bill: \(20x_1 + 4x_3 \geq 35\)
6. Combined organization score for Paul and Bill: \(17x_2 + 4x_3 \geq 50\)
7. Total combined organization score: \(20x_1 + 17x_2 + 4x_3 \geq 83\)
8. Combined organization score for Paul and Bill is less than or equal to 198: \(17x_2 + 4x_3 \leq 198\)
9. Combined organization score for Peggy and Paul is less than or equal to 166: \(20x_1 + 17x_2 \leq 166\)
10. Total combined organization score is less than or equal to 166: \(20x_1 + 17x_2 + 4x_3 \leq 166\)

### JSON Representation:

```json
{
    'sym_variables': [('x1', 'hours worked by Peggy'), ('x2', 'hours worked by Paul'), ('x3', 'hours worked by Bill')],
    'objective_function': '8.96*x1 + 1.78*x2 + 9.49*x3',
    'constraints': [
        '20*x1 + 17*x2 >= 38',
        '20*x1 + 4*x3 >= 35',
        '17*x2 + 4*x3 >= 50',
        '20*x1 + 17*x2 + 4*x3 >= 83',
        '17*x2 + 4*x3 <= 198',
        '20*x1 + 17*x2 <= 166',
        '20*x1 + 17*x2 + 4*x3 <= 166'
    ]
}
```

### Gurobi Code:

```python
from gurobipy import *

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

# Define variables
x1 = m.addVar(name='hours_worked_by_Peggy')
x2 = m.addVar(name='hours_worked_by_Paul')
x3 = m.addVar(name='hours_worked_by_Bill')

# Set the objective function
m.setObjective(8.96*x1 + 1.78*x2 + 9.49*x3, GRB.MAXIMIZE)

# Add constraints
m.addConstr(20*x1 + 17*x2 >= 38, name='Peggy_and_Paul_min_score')
m.addConstr(20*x1 + 4*x3 >= 35, name='Peggy_and_Bill_min_score')
m.addConstr(17*x2 + 4*x3 >= 50, name='Paul_and_Bill_min_score')
m.addConstr(20*x1 + 17*x2 + 4*x3 >= 83, name='Total_min_score')
m.addConstr(17*x2 + 4*x3 <= 198, name='Paul_and_Bill_max_score')
m.addConstr(20*x1 + 17*x2 <= 166, name='Peggy_and_Paul_max_score')
m.addConstr(20*x1 + 17*x2 + 4*x3 <= 166, name='Total_max_score')

# Optimize model
m.optimize()

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