```json
{
  "sym_variables": [
    ("x0", "hours worked by Peggy"),
    ("x1", "hours worked by Bobby"),
    ("x2", "hours worked by Bill"),
    ("x3", "hours worked by Jean")
  ],
  "objective_function": "2*x0 + 4*x1 + 8*x2 + 2*x3",
  "constraints": [
    "19*x0 + 9*x1 + 10*x3 >= 15",
    "19*x0 + 9*x1 + 11*x2 >= 15",
    "19*x0 + 11*x2 + 10*x3 >= 15",
    "19*x0 + 9*x1 + 10*x3 >= 21",
    "19*x0 + 9*x1 + 11*x2 >= 21",
    "19*x0 + 11*x2 + 10*x3 >= 21",
    "19*x0 + 9*x1 + 10*x3 >= 18",
    "19*x0 + 9*x1 + 11*x2 >= 18",
    "19*x0 + 11*x2 + 10*x3 >= 18",
    "8*x0 + 5*x1 <= 349",
    "5*x1 + 1*x2 <= 292",
    "8*x0 + 1*x2 <= 320",
    "5*x1 + 4*x3 <= 277",
    "1*x2 + 4*x3 <= 274",
    "8*x0 + 4*x3 <= 147",
    "8*x0 + 5*x1 + 1*x2 + 4*x3 <= 147",
    "19*x0 + 10*x3 <= 51",
    "9*x1 + 10*x3 <= 63",
    "9*x1 + 11*x2 <= 60",
    "19*x0 + 11*x2 <= 32",
    "19*x0 + 9*x1 + 11*x2 <= 63",
    "19*x0 + 9*x1 + 11*x2 + 10*x3 <= 63",
    "x0 >= 0",
    "x1 >= 0",
    "x2 >= 0",
    "x3 >= 0"
  ]
}
```

```python
import gurobipy as gp

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

    # Create variables
    x = m.addVars(4, lb=0, names=["Peggy", "Bobby", "Bill", "Jean"])

    # Set objective function
    m.setObjective(2*x[0] + 4*x[1] + 8*x[2] + 2*x[3], gp.GRB.MAXIMIZE)

    # Add constraints
    m.addConstr(19*x[0] + 9*x[1] + 10*x[3] >= 15)
    m.addConstr(19*x[0] + 9*x[1] + 11*x[2] >= 15)
    m.addConstr(19*x[0] + 11*x[2] + 10*x[3] >= 15)
    m.addConstr(19*x[0] + 9*x[1] + 10*x[3] >= 21)
    m.addConstr(19*x[0] + 9*x[1] + 11*x[2] >= 21)
    m.addConstr(19*x[0] + 11*x[2] + 10*x[3] >= 21)
    m.addConstr(19*x[0] + 9*x[1] + 10*x[3] >= 18)
    m.addConstr(19*x[0] + 9*x[1] + 11*x[2] >= 18)
    m.addConstr(19*x[0] + 11*x[2] + 10*x[3] >= 18)
    m.addConstr(8*x[0] + 5*x[1] <= 349)
    m.addConstr(5*x[1] + 1*x[2] <= 292)
    m.addConstr(8*x[0] + 1*x[2] <= 320)
    m.addConstr(5*x[1] + 4*x[3] <= 277)
    m.addConstr(1*x[2] + 4*x[3] <= 274)
    m.addConstr(8*x[0] + 4*x[3] <= 147)
    m.addConstr(8*x[0] + 5*x[1] + 1*x[2] + 4*x[3] <= 147)
    m.addConstr(19*x[0] + 10*x[3] <= 51)
    m.addConstr(9*x[1] + 10*x[3] <= 63)
    m.addConstr(9*x[1] + 11*x[2] <= 60)
    m.addConstr(19*x[0] + 11*x[2] <= 32)
    m.addConstr(19*x[0] + 9*x[1] + 11*x[2] <= 63)
    m.addConstr(19*x[0] + 9*x[1] + 11*x[2] + 10*x[3] <= 63)


    # 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('Error code ' + str(e.errno) + ': ' + str(e))

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