To solve this problem, we need to define the variables and the objective function symbolically first, then translate these into Gurobi code.

### Symbolic Representation of the Problem:

- Let `x0` represent the hours worked by Paul.
- Let `x1` represent the hours worked by Hank.

The objective function is to maximize: `6*x0 + 4*x1`.

The constraints are:
1. Organization score constraint: `13*x0 + 3*x1 >= 8`.
2. Likelihood to quit index constraint: `6*x0 + 14*x1 >= 29`.
3. Dollar cost per hour constraint: `6*x0 + 13*x1 >= 7`.
4. Paperwork competence rating constraint: `11*x0 + 11*x1 >= 17`.
5. Mixed constraint: `4*x0 - 7*x1 >= 0`.
6. Organization score upper bound: `13*x0 + 3*x1 <= 42`.
7. Likelihood to quit index upper bound: `6*x0 + 14*x1 <= 42`.
8. Dollar cost per hour upper bound: `6*x0 + 13*x1 <= 38`.
9. Paperwork competence rating upper bound: `11*x0 + 11*x1 <= 20`.

Given the problem's requirements, we have non-integer hours worked by both Paul and Hank.

### JSON Representation:
```json
{
    'sym_variables': [('x0', 'hours worked by Paul'), ('x1', 'hours worked by Hank')],
    'objective_function': '6*x0 + 4*x1',
    'constraints': [
        '13*x0 + 3*x1 >= 8',
        '6*x0 + 14*x1 >= 29',
        '6*x0 + 13*x1 >= 7',
        '11*x0 + 11*x1 >= 17',
        '4*x0 - 7*x1 >= 0',
        '13*x0 + 3*x1 <= 42',
        '6*x0 + 14*x1 <= 42',
        '6*x0 + 13*x1 <= 38',
        '11*x0 + 11*x1 <= 20'
    ]
}
```

### Gurobi Code:
```python
from gurobipy import *

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

# Define the variables
x0 = m.addVar(lb=0, vtype=GRB.CONTINUOUS, name="hours_worked_by_Paul")
x1 = m.addVar(lb=0, vtype=GRB.CONTINUOUS, name="hours_worked_by_Hank")

# Set the objective function
m.setObjective(6*x0 + 4*x1, GRB.MAXIMIZE)

# Add constraints
m.addConstr(13*x0 + 3*x1 >= 8, "organization_score_min")
m.addConstr(6*x0 + 14*x1 >= 29, "quit_index_min")
m.addConstr(6*x0 + 13*x1 >= 7, "dollar_cost_per_hour_min")
m.addConstr(11*x0 + 11*x1 >= 17, "paperwork_competence_rating_min")
m.addConstr(4*x0 - 7*x1 >= 0, "mixed_constraint")
m.addConstr(13*x0 + 3*x1 <= 42, "organization_score_max")
m.addConstr(6*x0 + 14*x1 <= 42, "quit_index_max")
m.addConstr(6*x0 + 13*x1 <= 38, "dollar_cost_per_hour_max")
m.addConstr(11*x0 + 11*x1 <= 20, "paperwork_competence_rating_max")

# Optimize the model
m.optimize()

# Print the solution
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Hours worked by Paul: {x0.x}")
    print(f"Hours worked by Hank: {x1.x}")
    print(f"Objective function value: {m.objVal}")
else:
    print("No optimal solution found.")
```