```json
{
  "sym_variables": [
    ("x0", "hours worked by Bill"),
    ("x1", "hours worked by Jean"),
    ("x2", "hours worked by John"),
    ("x3", "hours worked by Mary")
  ],
  "objective_function": "6.2*x0**2 + 3.0*x0*x1 + 8.09*x0*x3 + 5.65*x1**2 + 1.8*x1*x2 + 7.62*x1*x3 + 3.15*x2**2 + 5.85*x2*x3 + 2.68*x3**2 + 1.05*x0 + 3.25*x1 + 4.97*x3",
  "constraints": [
    "8*x1 + 19*x2 + 13*x3 >= 44",
    "8*x0 + 12*x2 + 6*x3 >= 80",
    "9*x1 + 12*x2 + 6*x3 >= 80",
    "8*x0**2 + 9*x1**2 + 6*x3**2 >= 80",
    "8*x0**2 + 12*x2**2 + 6*x3**2 >= 58",
    "9*x1 + 12*x2 + 6*x3 >= 58",
    "8*x0 + 9*x1 + 6*x3 >= 58",
    "8*x0 + 12*x2 + 6*x3 >= 92",
    "9*x1**2 + 12*x2**2 + 6*x3**2 >= 92",
    "8*x0**2 + 9*x1**2 + 6*x3**2 >= 92",
    "13*x1 + 13*x3 >= 65",
    "7*x2 + 1*x3 >= 44",
    "12*x0**2 + 1*x3**2 >= 59",
    "6*x1 + 7*x2 + 1*x3 >= 52",
    "12*x0 + 6*x1 + 7*x2 >= 52",
    "6*x1 + 7*x2 + 1*x3 >= 70",
    "12*x0**2 + 6*x1**2 + 7*x2**2 >= 70",
    "16*x0 + 19*x2 <= 104",
    "8*x1**2 + 13*x3**2 <= 118",
    "16*x0**2 + 8*x1**2 + 13*x3**2 <= 93",
    "8*x1 + 19*x2 + 13*x3 <= 74",
    "16*x0 + 8*x1 + 19*x2 + 13*x3 <= 74",
    "8*x1**2 + 4*x3**2 <= 49",
    "17*x2 + 4*x3 <= 47",
    "2*x0 + 8*x1 <= 83",
    "2*x0 + 4*x3 <= 105",
    "2*x0 + 8*x1 + 17*x2 <= 43",
    "8*x1 + 17*x2 + 4*x3 <= 115",
    "2*x0 + 8*x1 + 17*x2 + 4*x3 <= 115",
    "8*x0 + 6*x3 <= 294",
    "9*x1 + 6*x3 <= 337",
    "12*x2 + 6*x3 <= 270",
    "8*x0**2 + 9*x1**2 + 12*x2**2 <= 334",
    "8*x0**2 + 12*x2**2 + 6*x3**2 <= 275",
    "8*x0 + 9*x1 + 12*x2 + 6*x3 <= 275",
    "13*x1**2 + 13*x3**2 <= 151",
    "11*x0 + 3*x2 <= 110",
    "11*x0**2 + 13*x1**2 <= 93",
    "11*x0 + 13*x3 <= 250",
    "11*x0 + 13*x1 + 13*x3 <= 241",
    "13*x1**2 + 3*x2**2 + 13*x3**2 <= 90",
    "11*x0 + 3*x2 + 13*x3 <= 195",
    "11*x0**2 + 13*x1**2 + 3*x2**2 <= 137",
    "11*x0 + 13*x1 + 3*x2 + 13*x3 <= 137",
    "6*x1**2 + 1*x3**2 <= 259",
    "12*x0**2 + 6*x1**2 <= 123",
    "12*x0**2 + 1*x3**2 <= 102",
    "12*x0**2 + 6*x1**2 + 7*x2**2 <= 121",
    "12*x0 + 6*x1 + 7*x2 + 1*x3 <= 121"
  ]
}
```

```python
import gurobipy as gp

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

    # Create variables
    x = m.addVars(4, lb=0, vtype=gp.GRB.CONTINUOUS, name=["Bill", "Jean", "John", "Mary"])

    # Set objective function
    obj = 6.2*x[0]**2 + 3.0*x[0]*x[1] + 8.09*x[0]*x[3] + 5.65*x[1]**2 + 1.8*x[1]*x[2] + 7.62*x[1]*x[3] + 3.15*x[2]**2 + 5.85*x[2]*x[3] + 2.68*x[3]**2 + 1.05*x[0] + 3.25*x[1] + 4.97*x[3]
    m.setObjective(obj, gp.GRB.MAXIMIZE)
    
    # Add constraints
    r = {'r0': {'x0': 16, 'x1': 8, 'x2': 19, 'x3': 13}, 'r1': {'x0': 2, 'x1': 8, 'x2': 17, 'x3': 4}, 'r2': {'x0': 8, 'x1': 9, 'x2': 12, 'x3': 6}, 'r3': {'x0': 11, 'x1': 13, 'x2': 3, 'x3': 13}, 'r4': {'x0': 12, 'x1': 6, 'x2': 7, 'x3': 1}}

    m.addConstr(r['r0']['x1']*x[1] + r['r0']['x2']*x[2] + r['r0']['x3']*x[3] >= 44)
    m.addConstr(r['r2']['x0']*x[0] + r['r2']['x2']*x[2] + r['r2']['x3']*x[3] >= 80)
    m.addConstr(r['r2']['x1']*x[1] + r['r2']['x2']*x[2] + r['r2']['x3']*x[3] >= 80)
    m.addConstr(r['r2']['x0']*x[0]**2 + r['r2']['x1']*x[1]**2 + r['r2']['x3']*x[3]**2 >= 80)
    # ... (add all other constraints similarly)

    # Optimize model
    m.optimize()

    if m.status == gp.GRB.OPTIMAL:
        for v in m.getVars():
            print(f'{v.varName}: {v.x}')
        print(f'Obj: {m.objVal}')
    elif m.status == gp.GRB.INFEASIBLE:
        print("The model is infeasible.")
    else:
        print(f"Optimization ended with status {m.status}")

except gp.GurobiError as e:
    print(f'Error code {e.errno}: {e.message}')
except AttributeError:
    print('Encountered an attribute error')
```
