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

## Step 2: Define the attributes or resources for each variable
The attributes are given as:
- $r_0$: organization score, with $x_0 = 15$ for Laura and $x_0 = 20$ for Paul, and an upper bound of 144.
- $r_1$: paperwork competence rating, with $x_1 = 22$ for Laura and $x_1 = 4$ for Paul, and an upper bound of 92.
- $r_2$: work quality rating, with $x_2 = 4$ for Laura and $x_2 = 23$ for Paul, and an upper bound of 108.

## 3: Formulate the objective function
The objective function to maximize is $9x_1 + 6x_2$.

## 4: Formulate the constraints
The constraints are:
1. $15x_1 + 20x_2 \geq 45$
2. $22x_1 + 4x_2 \geq 16$
3. $4x_1 + 23x_2 \geq 29$
4. $5x_1 - 5x_2 \geq 0$
5. $15x_1 + 20x_2 \leq 130$
6. $22x_1 + 4x_2 \leq 87$
7. $4x_1 + 23x_2 \leq 102$
8. $x_1$ is a continuous variable.
9. $x_2$ is an integer variable.

## 5: Symbolic Representation
The symbolic representation of the problem is:
```json
{
'sym_variables': [('x1', 'hours worked by Laura'), ('x2', 'hours worked by Paul')],
'objective_function': '9*x1 + 6*x2',
'constraints': [
'15*x1 + 20*x2 >= 45',
'22*x1 + 4*x2 >= 16',
'4*x1 + 23*x2 >= 29',
'5*x1 - 5*x2 >= 0',
'15*x1 + 20*x2 <= 130',
'22*x1 + 4*x2 <= 87',
'4*x1 + 23*x2 <= 102'
]
}
```

## 6: Gurobi Code
```python
import gurobi

def solve_optimization_problem():
    # Create a new model
    model = gurobi.Model()

    # Define the variables
    x1 = model.addVar(name="hours_worked_by_Laura", lb=0, ub=None)
    x2 = model.addVar(name="hours_worked_by_Paul", lb=0, integer=True)

    # Define the objective function
    model.setObjective(9 * x1 + 6 * x2, gurobi.GRB.MAXIMIZE)

    # Define the constraints
    model.addConstr(15 * x1 + 20 * x2 >= 45)
    model.addConstr(22 * x1 + 4 * x2 >= 16)
    model.addConstr(4 * x1 + 23 * x2 >= 29)
    model.addConstr(5 * x1 - 5 * x2 >= 0)
    model.addConstr(15 * x1 + 20 * x2 <= 130)
    model.addConstr(22 * x1 + 4 * x2 <= 87)
    model.addConstr(4 * x1 + 23 * x2 <= 102)

    # Optimize the model
    model.optimize()

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

solve_optimization_problem()
```