```json
{
  "sym_variables": [
    ("x0", "hours worked by Dale"),
    ("x1", "hours worked by Peggy"),
    ("x2", "hours worked by George"),
    ("x3", "hours worked by Bobby")
  ],
  "objective_function": "4.89*x0 + 2.71*x1 + 2.84*x2 + 2.81*x3",
  "constraints": [
    "1.32*x2 + 1.19*x3 >= 36",
    "6.87*x1 + 1.19*x3 >= 40",
    "7.93*x2 + 12.05*x3 >= 14",
    "3.76*x0 + 9.8*x1 >= 19",
    "2.77*x2 + 1.19*x3 <= 109",
    "6.87*x1 + 2.77*x2 <= 70",
    "6.87*x1 + 2.77*x2 + 1.19*x3 <= 157",
    "1.32*x0 + 2.77*x2 + 1.19*x3 <= 72",
    "1.32*x0 + 6.87*x1 + 2.77*x2 + 1.19*x3 <= 72",
    "7.93*x2 + 12.05*x3 <= 134",
    "3.76*x0 + 9.8*x1 <= 70",
    "3.76*x0 + 12.05*x3 <= 113",
    "9.8*x1 + 12.05*x3 <= 138",
    "3.76*x0 + 9.8*x1 + 12.05*x3 <= 142",
    "9.8*x1 + 7.93*x2 + 12.05*x3 <= 84",
    "3.76*x0 + 9.8*x1 + 7.93*x2 <= 57",
    "3.76*x0 + 9.8*x1 + 7.93*x2 + 12.05*x3 <= 57"
  ]
}
```

```python
import gurobipy as gp

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

    # Create variables
    dale = model.addVar(vtype=gp.GRB.INTEGER, name="dale")
    peggy = model.addVar(vtype=gp.GRB.INTEGER, name="peggy")
    george = model.addVar(vtype=gp.GRB.INTEGER, name="george")
    bobby = model.addVar(vtype=gp.GRB.INTEGER, name="bobby")

    # Set objective function
    model.setObjective(4.89 * dale + 2.71 * peggy + 2.84 * george + 2.81 * bobby, gp.GRB.MAXIMIZE)

    # Add constraints
    model.addConstr(2.77 * george + 1.19 * bobby >= 36)
    model.addConstr(6.87 * peggy + 1.19 * bobby >= 40)
    model.addConstr(7.93 * george + 12.05 * bobby >= 14)
    model.addConstr(3.76 * dale + 9.8 * peggy >= 19)
    model.addConstr(2.77 * george + 1.19 * bobby <= 109)
    model.addConstr(6.87 * peggy + 2.77 * george <= 70)
    model.addConstr(6.87 * peggy + 2.77 * george + 1.19 * bobby <= 157)
    model.addConstr(1.32 * dale + 2.77 * george + 1.19 * bobby <= 72)
    model.addConstr(1.32 * dale + 6.87 * peggy + 2.77 * george + 1.19 * bobby <= 72)
    model.addConstr(7.93 * george + 12.05 * bobby <= 134)
    model.addConstr(3.76 * dale + 9.8 * peggy <= 70)
    model.addConstr(3.76 * dale + 12.05 * bobby <= 113)
    model.addConstr(9.8 * peggy + 12.05 * bobby <= 138)
    model.addConstr(3.76 * dale + 9.8 * peggy + 12.05 * bobby <= 142)
    model.addConstr(9.8 * peggy + 7.93 * george + 12.05 * bobby <= 84)
    model.addConstr(3.76 * dale + 9.8 * peggy + 7.93 * george <= 57)
    model.addConstr(3.76 * dale + 9.8 * peggy + 7.93 * george + 12.05 * bobby <= 57)


    # Optimize model
    model.optimize()

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


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

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