```json
{
  "sym_variables": [
    ("x0", "hours worked by Paul"),
    ("x1", "hours worked by Hank"),
    ("x2", "hours worked by Laura")
  ],
  "objective_function": "x0**2 + 8*x0*x1 + 2*x0*x2 + 9*x1**2 + 5*x1*x2 + 2*x2**2 + 9*x0 + 2*x1",
  "constraints": [
    "17*x0 + 15*x1 + 12*x2 <= 240",  // Work quality rating
    "9*x0 + 9*x1 + 5*x2 <= 284",  // Paperwork competence rating
    "9*x0**2 + 9*x1**2 >= 76",
    "9*x1**2 + 5*x2**2 >= 61",
    "15*x1 + 12*x2 <= 190",
    "17*x0 + 15*x1 <= 108",
    "17*x0 + 15*x1 + 12*x2 <= 108",
    "9*x1 + 5*x2 <= 191",
    "9*x0 + 9*x1 <= 250",
    "9*x0**2 + 5*x2**2 <= 207",
    "9*x0 + 9*x1 + 5*x2 <= 207"
  ]
}
```

```python
import gurobipy as gp

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

    # Create variables
    paul = model.addVar(lb=0, name="paul")  # hours worked by Paul
    hank = model.addVar(lb=0, name="hank")  # hours worked by Hank
    laura = model.addVar(lb=0, name="laura") # hours worked by Laura


    # Set objective function
    obj = paul**2 + 8*paul*hank + 2*paul*laura + 9*hank**2 + 5*hank*laura + 2*laura**2 + 9*paul + 2*hank
    model.setObjective(obj, gp.GRB.MAXIMIZE)

    # Add constraints
    model.addConstr(17*paul + 15*hank + 12*laura <= 240, "c0") # Work quality
    model.addConstr(9*paul + 9*hank + 5*laura <= 284, "c1") # Paperwork competence
    model.addConstr(9*paul**2 + 9*hank**2 >= 76, "c2")
    model.addConstr(9*hank**2 + 5*laura**2 >= 61, "c3")
    model.addConstr(15*hank + 12*laura <= 190, "c4")
    model.addConstr(17*paul + 15*hank <= 108, "c5")
    model.addConstr(17*paul + 15*hank + 12*laura <= 108, "c6")
    model.addConstr(9*hank + 5*laura <= 191, "c7")
    model.addConstr(9*paul + 9*hank <= 250, "c8")
    model.addConstr(9*paul**2 + 5*laura**2 <= 207, "c9")
    model.addConstr(9*paul + 9*hank + 5*laura <= 207, "c10")


    # Optimize model
    model.optimize()

    if model.status == gp.GRB.OPTIMAL:
        print('Obj: %g' % model.objVal)
        print('Paul: %g' % paul.x)
        print('Hank: %g' % hank.x)
        print('Laura: %g' % laura.x)
    elif model.status == gp.GRB.INFEASIBLE:
        print('The model is infeasible.')
    else:
        print('Optimization ended with status %d' % model.status)


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

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