## Step 1: Define the symbolic representation of the variables
The variables are 'hours worked by George', 'hours worked by Peggy', 'hours worked by Laura', 'hours worked by Mary', which can be represented symbolically as $x_0$, $x_1$, $x_2$, $x_3$ respectively.

## Step 2: Convert the objective function into symbolic notation
The objective function to minimize is $5x_0 + 1x_1 + 9x_2 + 4x_3$.

## Step 3: List the constraints in symbolic notation
1. $13x_0 \leq 329$ is not a direct constraint but $x_0 \geq 0$ and organization score constraints will be considered directly.
2. $4x_0 \leq 509$ similarly.
3. $4x_1 \leq 329$.
4. $16x_1 \leq 509$.
5. $6x_2 \leq 329$.
6. $7x_2 \leq 509$.
7. $29x_3 \leq 329$.
8. $7x_3 \leq 509$.
9. $4x_1 + 29x_3 \geq 76$.
10. $13x_0 + 4x_1 \geq 45$.
11. $13x_0 + 6x_2 \geq 82$.
12. $13x_0 + 29x_3 \geq 60$.
13. $6x_2 + 29x_3 \geq 59$.
14. $4x_1 + 6x_2 + 29x_3 \geq 58$.
15. $13x_0 + 6x_2 + 29x_3 \geq 58$.
16. $4x_1 + 6x_2 + 29x_3 \geq 57$.
17. $13x_0 + 6x_2 + 29x_3 \geq 57$.
18. $13x_0 + 4x_1 + 6x_2 + 29x_3 \geq 57$.
19. $4x_0 + 7x_3 \geq 118$.
20. $4x_0 + 7x_2 \geq 50$.
21. $16x_1 + 7x_2 \geq 67$.
22. $4x_0 + 7x_2 + 7x_3 \geq 64$.
23. $4x_0 + 16x_1 + 7x_2 + 7x_3 \geq 64$.
24. $4x_0 - 7x_1 \geq 0$.
25. $13x_0 + 6x_2 \leq 156$.
26. $13x_0 + 4x_1 + 6x_2 \leq 270$.
27. $4x_0 + 16x_1 \leq 391$.
28. $16x_1 + 7x_3 \leq 317$.
29. $16x_1 + 7x_2 \leq 357$.

## 4: Create the Gurobi model and variables
We will use Gurobi to solve this linear programming problem.

```python
import gurobi as gp

# Create a new model
m = gp.Model("optimization_problem")

# Define the variables
x0 = m.addVar(name="hours_worked_by_George", lb=0)  # George
x1 = m.addVar(name="hours_worked_by_Peggy", lb=0)  # Peggy
x2 = m.addVar(name="hours_worked_by_Laura", lb=0)  # Laura
x3 = m.addVar(name="hours_worked_by_Mary", lb=0)  # Mary

# Objective function
m.setObjective(5 * x0 + x1 + 9 * x2 + 4 * x3, gp.GRB.MINIMIZE)

# Constraints
m.addConstr(4 * x1 + 29 * x3 >= 76)
m.addConstr(13 * x0 + 4 * x1 >= 45)
m.addConstr(13 * x0 + 6 * x2 >= 82)
m.addConstr(13 * x0 + 29 * x3 >= 60)
m.addConstr(6 * x2 + 29 * x3 >= 59)
m.addConstr(4 * x1 + 6 * x2 + 29 * x3 >= 58)
m.addConstr(13 * x0 + 6 * x2 + 29 * x3 >= 58)
m.addConstr(4 * x1 + 6 * x2 + 29 * x3 >= 57)
m.addConstr(13 * x0 + 6 * x2 + 29 * x3 >= 57)
m.addConstr(13 * x0 + 4 * x1 + 6 * x2 + 29 * x3 >= 57)
m.addConstr(4 * x0 + 7 * x3 >= 118)
m.addConstr(4 * x0 + 7 * x2 >= 50)
m.addConstr(16 * x1 + 7 * x2 >= 67)
m.addConstr(4 * x0 + 7 * x2 + 7 * x3 >= 64)
m.addConstr(4 * x0 + 16 * x1 + 7 * x2 + 7 * x3 >= 64)
m.addConstr(4 * x0 - 7 * x1 >= 0)
m.addConstr(13 * x0 + 6 * x2 <= 156)
m.addConstr(13 * x0 + 4 * x1 + 6 * x2 <= 270)
m.addConstr(4 * x0 + 16 * x1 <= 391)
m.addConstr(16 * x1 + 7 * x3 <= 317)
m.addConstr(16 * x1 + 7 * x2 <= 357)

# Solve the model
m.optimize()

# Print the solution
if m.status == gp.GRB.OPTIMAL:
    print("Objective: ", m.objVal)
    print("Hours worked by George: ", x0.varValue)
    print("Hours worked by Peggy: ", x1.varValue)
    print("Hours worked by Laura: ", x2.varValue)
    print("Hours worked by Mary: ", x3.varValue)
else:
    print("The model is infeasible")
```

## 5: Symbolic Representation
```json
{
    'sym_variables': [
        ('x0', 'hours worked by George'),
        ('x1', 'hours worked by Peggy'),
        ('x2', 'hours worked by Laura'),
        ('x3', 'hours worked by Mary')
    ],
    'objective_function': '5*x0 + x1 + 9*x2 + 4*x3',
    'constraints': [
        '4*x1 + 29*x3 >= 76',
        '13*x0 + 4*x1 >= 45',
        '13*x0 + 6*x2 >= 82',
        '13*x0 + 29*x3 >= 60',
        '6*x2 + 29*x3 >= 59',
        '4*x1 + 6*x2 + 29*x3 >= 58',
        '13*x0 + 6*x2 + 29*x3 >= 58',
        '4*x1 + 6*x2 + 29*x3 >= 57',
        '13*x0 + 6*x2 + 29*x3 >= 57',
        '13*x0 + 4*x1 + 6*x2 + 29*x3 >= 57',
        '4*x0 + 7*x3 >= 118',
        '4*x0 + 7*x2 >= 50',
        '16*x1 + 7*x2 >= 67',
        '4*x0 + 7*x2 + 7*x3 >= 64',
        '4*x0 + 16*x1 + 7*x2 + 7*x3 >= 64',
        '4*x0 - 7*x1 >= 0',
        '13*x0 + 6*x2 <= 156',
        '13*x0 + 4*x1 + 6*x2 <= 270',
        '4*x0 + 16*x1 <= 391',
        '16*x1 + 7*x3 <= 317',
        '16*x1 + 7*x2 <= 357'
    ]
}
```