```json
{
  "sym_variables": [
    ("x0", "hours worked by Paul"),
    ("x1", "hours worked by Hank"),
    ("x2", "hours worked by John"),
    ("x3", "hours worked by Mary")
  ],
  "objective_function": "3.68 * x0 + 2.07 * x1 + 5.86 * x2 + 3.14 * x3",
  "constraints": [
    "8 * x0 + 4 * x1 >= 12",
    "8 * x0 + 13 * x2 >= 11",
    "13 * x2 + 7 * x3 >= 13",
    "4 * x1 + 7 * x3 >= 30",
    "4 * x1 + 7 * x3 <= 127",
    "13 * x2 + 7 * x3 <= 34",
    "8 * x0 + 4 * x1 <= 96",
    "4 * x1 + 13 * x2 + 7 * x3 <= 38",
    "8 * x0 + 4 * x1 + 13 * x2 + 7 * x3 <= 38"
  ]
}
```

```python
import gurobipy as gp

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

    # Create variables
    paul = model.addVar(lb=0, vtype=gp.GRB.CONTINUOUS, name="paul")
    hank = model.addVar(lb=0, vtype=gp.GRB.CONTINUOUS, name="hank")
    john = model.addVar(lb=0, vtype=gp.GRB.CONTINUOUS, name="john")
    mary = model.addVar(lb=0, vtype=gp.GRB.CONTINUOUS, name="mary")


    # Set objective function
    model.setObjective(3.68 * paul + 2.07 * hank + 5.86 * john + 3.14 * mary, gp.GRB.MAXIMIZE)

    # Add constraints
    model.addConstr(8 * paul + 4 * hank >= 12, "c0")
    model.addConstr(8 * paul + 13 * john >= 11, "c1")
    model.addConstr(13 * john + 7 * mary >= 13, "c2")
    model.addConstr(4 * hank + 7 * mary >= 30, "c3")
    model.addConstr(4 * hank + 7 * mary <= 127, "c4")
    model.addConstr(13 * john + 7 * mary <= 34, "c5")
    model.addConstr(8 * paul + 4 * hank <= 96, "c6")
    model.addConstr(4 * hank + 13 * john + 7 * mary <= 38, "c7")
    model.addConstr(8 * paul + 4 * hank + 13 * john + 7 * mary <= 38, "c8")


    # 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')
```