To address the given problem, we first need to translate the natural language description into a symbolic representation. This involves defining the variables, the objective function, and the constraints using mathematical notation.

### Symbolic Representation

Let's denote:
- $x_1$ as the hours worked by Hank,
- $x_2$ as the hours worked by Peggy,
- $x_3$ as the hours worked by Paul.

The objective function to minimize is: $3x_1 + 6x_2 + 3x_3$

The constraints are:
1. $x_1 + x_2 \geq 22$ (Total combined organization score from Hank and Peggy must be 22 or more)
2. $x_1 + x_2 + 8x_3 \geq 19$ (Total combined organization score from all three must be at least 19)
3. $x_1 + x_2 + 8x_3 \geq 19$ (This constraint is the same as the previous one, so it's redundant and can be ignored)
4. $x_1 + 8x_3 \leq 72$ (Total combined organization score from Hank and Paul must be 72 or less)

Since there are no requirements for integer solutions for any of the variables, all variables are continuous.

### Symbolic Representation in JSON Format

```json
{
    'sym_variables': [('x1', 'hours worked by Hank'), ('x2', 'hours worked by Peggy'), ('x3', 'hours worked by Paul')],
    'objective_function': '3*x1 + 6*x2 + 3*x3',
    'constraints': ['x1 + x2 >= 22', 'x1 + x2 + 8*x3 >= 19', 'x1 + 8*x3 <= 72']
}
```

### Gurobi Code

To solve this optimization problem, we can use the following Gurobi code 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_Hank")
x2 = m.addVar(lb=0, name="hours_worked_by_Peggy")
x3 = m.addVar(lb=0, name="hours_worked_by_Paul")

# Define the objective function
m.setObjective(3*x1 + 6*x2 + 3*x3, GRB.MINIMIZE)

# Add constraints
m.addConstr(x1 + x2 >= 22, "Hank_and_Peggy_score")
m.addConstr(x1 + x2 + 8*x3 >= 19, "Total_score")
m.addConstr(x1 + 8*x3 <= 72, "Hank_and_Paul_score")

# Optimize the model
m.optimize()

# Print the solution
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Hank works {x1.x} hours")
    print(f"Peggy works {x2.x} hours")
    print(f"Paul works {x3.x} hours")
else:
    print("No optimal solution found")

```