To solve this optimization problem, we need to first define the symbolic representation of the variables and the objective function, followed by the list of constraints. 

The variables are:
- $x_1$: hours worked by Laura
- $x_2$: hours worked by Paul

The objective function is to maximize: 
$9x_1 + 6x_2$

The constraints are:

* Organization score constraint: $15x_1 + 20x_2 \geq 45$
* Paperwork competence rating constraint: $22x_1 + 4x_2 \geq 16$
* Work quality rating constraint: $4x_1 + 23x_2 \geq 29$
* Constraint on hours worked by Laura and Paul: $5x_1 - 5x_2 \geq 0$
* Upper bound organization score constraint: $15x_1 + 20x_2 \leq 130$
* Upper bound paperwork competence rating constraint: $22x_1 + 4x_2 \leq 87$
* Upper bound work quality rating constraint: $4x_1 + 23x_2 \leq 102$

The symbolic representation of the problem in JSON format 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'
    ]
}
```

Here's the Gurobi code to solve this optimization problem:
```python
from gurobipy import *

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

# Define variables
x1 = m.addVar(lb=0, vtype=GRB.CONTINUOUS, name="hours_worked_by_Laura")
x2 = m.addVar(lb=0, vtype=GRB.INTEGER, name="hours_worked_by_Paul")

# Set objective function
m.setObjective(9*x1 + 6*x2, GRB.MAXIMIZE)

# Add constraints
m.addConstr(15*x1 + 20*x2 >= 45, "organization_score_constraint")
m.addConstr(22*x1 + 4*x2 >= 16, "paperwork_competence_rating_constraint")
m.addConstr(4*x1 + 23*x2 >= 29, "work_quality_rating_constraint")
m.addConstr(5*x1 - 5*x2 >= 0, "hours_worked_by_Laura_and_Paul_constraint")
m.addConstr(15*x1 + 20*x2 <= 130, "upper_bound_organization_score_constraint")
m.addConstr(22*x1 + 4*x2 <= 87, "upper_bound_paperwork_competence_rating_constraint")
m.addConstr(4*x1 + 23*x2 <= 102, "upper_bound_work_quality_rating_constraint")

# Optimize model
m.optimize()

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