```json
{
  "sym_variables": [
    ("x0", "hours worked by Peggy"),
    ("x1", "hours worked by Dale"),
    ("x2", "hours worked by Bill"),
    ("x3", "hours worked by Mary"),
    ("x4", "hours worked by Bobby")
  ],
  "objective_function": "7.48 * x0 + 6.82 * x1 + 4.25 * x2 + 2.38 * x3 + 7.91 * x4",
  "constraints": [
    "2 * x1 + 5 * x3 >= 33",
    "11 * x2 + 12 * x4 >= 31",
    "2 * x0 + 14 * x1 >= 44",
    "14 * x1 + 11 * x2 >= 24",
    "14 * x1 + 12 * x4 >= 33",
    "5 * x3 + 12 * x4 >= 20",
    "2 * x0 + 12 * x4 >= 38",
    "11 * x2 + 5 * x3 >= 22",
    "14 * x1 + 5 * x3 <= 231",
    "14 * x1 + 11 * x2 <= 178",
    "2 * x0 + 11 * x2 <= 232",
    "14 * x1 + 11 * x2 + 12 * x4 <= 133",
    "2 * x0 + 14 * x1 + 11 * x2 + 5 * x3 + 12 * x4 <= 133"
  ]
}
```

```python
import gurobipy as gp
from gurobipy import GRB

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

    # Create variables
    peggy = model.addVar(vtype=GRB.INTEGER, name="peggy")
    dale = model.addVar(vtype=GRB.INTEGER, name="dale")
    bill = model.addVar(vtype=GRB.CONTINUOUS, name="bill")
    mary = model.addVar(vtype=GRB.CONTINUOUS, name="mary")
    bobby = model.addVar(vtype=GRB.CONTINUOUS, name="bobby")

    # Set objective function
    model.setObjective(7.48 * peggy + 6.82 * dale + 4.25 * bill + 2.38 * mary + 7.91 * bobby, GRB.MAXIMIZE)

    # Add constraints
    model.addConstr(14 * dale + 5 * mary >= 33, "c0")
    model.addConstr(11 * bill + 12 * bobby >= 31, "c1")
    model.addConstr(2 * peggy + 14 * dale >= 44, "c2")
    model.addConstr(14 * dale + 11 * bill >= 24, "c3")
    model.addConstr(14 * dale + 12 * bobby >= 33, "c4")
    model.addConstr(5 * mary + 12 * bobby >= 20, "c5")
    model.addConstr(2 * peggy + 12 * bobby >= 38, "c6")
    model.addConstr(11 * bill + 5 * mary >= 22, "c7")
    model.addConstr(14 * dale + 5 * mary <= 231, "c8")
    model.addConstr(14 * dale + 11 * bill <= 178, "c9")
    model.addConstr(2 * peggy + 11 * bill <= 232, "c10")
    model.addConstr(14 * dale + 11 * bill + 12 * bobby <= 133, "c11")
    model.addConstr(2 * peggy + 14 * dale + 11 * bill + 5 * mary + 12 * bobby <= 133, "c12")


    # Optimize model
    model.optimize()

    if model.status == GRB.OPTIMAL:
        print('Obj: %g' % model.objVal)
        for v in model.getVars():
            print('%s %g' % (v.varName, v.x))
    elif model.status == 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')
```