```json
{
  "sym_variables": [
    ("x0", "hours worked by Paul"),
    ("x1", "hours worked by Dale")
  ],
  "objective_function": "3*x0 + 1*x1",
  "constraints": [
    "14*x0 <= 171",  // Paul's likelihood to quit index upper bound (redundant)
    "21*x0 <= 152",  // Paul's work quality rating upper bound (redundant)
    "7*x1 <= 171",   // Dale's likelihood to quit index upper bound (redundant)
    "13*x1 <= 152",  // Dale's work quality rating upper bound (redundant)
    "14*x0 + 7*x1 >= 77",
    "21*x0 + 13*x1 >= 39",
    "9*x0 - 4*x1 >= 0",
    "14*x0 + 7*x1 <= 130",
    "14*x0 + 7*x1 = 130",
    "21*x0 + 13*x1 <= 116",
    "21*x0 + 13*x1 = 116"
  ]
}
```

The provided individual likelihood to quit index and work quality rating constraints for Paul and Dale, along with their respective upper bounds, are redundant given the combined constraints and the nature of the objective function (maximization).  The solver will naturally push the variables as high as possible within the feasible region defined by the combined constraints.

```python
import gurobipy as gp

try:
    # Create a new model
    m = gp.Model("optimize_work_hours")

    # Create variables
    paul_hours = m.addVar(lb=0, vtype=gp.GRB.CONTINUOUS, name="paul_hours")
    dale_hours = m.addVar(lb=0, vtype=gp.GRB.CONTINUOUS, name="dale_hours")


    # Set objective function
    m.setObjective(3 * paul_hours + dale_hours, gp.GRB.MAXIMIZE)

    # Add constraints
    m.addConstr(14 * paul_hours + 7 * dale_hours >= 77, "combined_likelihood_min")
    m.addConstr(21 * paul_hours + 13 * dale_hours >= 39, "combined_quality_min")
    m.addConstr(9 * paul_hours - 4 * dale_hours >= 0, "paul_dale_ratio")
    m.addConstr(14 * paul_hours + 7 * dale_hours == 130, "combined_likelihood_max")  # Note: equality constraint
    m.addConstr(21 * paul_hours + 13 * dale_hours == 116, "combined_quality_max") # Note: equality constraint


    # Optimize model
    m.optimize()

    # Print results
    if m.status == gp.GRB.OPTIMAL:
        print('Optimal solution found:')
        print(f"Paul's hours: {paul_hours.x}")
        print(f"Dale's hours: {dale_hours.x}")
        print(f"Objective value: {m.objVal}")
    elif m.status == gp.GRB.INFEASIBLE:
        print('Model is infeasible.')
    else:
        print(f'Optimization ended with status {m.status}.')


except gp.GurobiError as e:
    print('Error code ' + str(e.errno) + ': ' + str(e))

except AttributeError:
    print('Encountered an attribute error')
```
