```json
{
  "sym_variables": [
    ("x0", "hours worked by George"),
    ("x1", "hours worked by Peggy"),
    ("x2", "hours worked by Laura"),
    ("x3", "hours worked by Mary")
  ],
  "objective_function": "5*x0 + 1*x1 + 9*x2 + 4*x3",
  "constraints": [
    "4*x1 + 29*x3 >= 76",
    "13*x0 + 4*x1 >= 45",
    "13*x0 + 6*x2 >= 82",
    "13*x0 + 29*x3 >= 60",
    "6*x2 + 29*x3 >= 59",
    "4*x1 + 6*x2 + 29*x3 >= 58",
    "13*x0 + 6*x2 + 29*x3 >= 58",
    "4*x1 + 6*x2 + 29*x3 >= 57",
    "13*x0 + 6*x2 + 29*x3 >= 57",
    "13*x0 + 4*x1 + 6*x2 + 29*x3 >= 57",
    "4*x0 + 7*x3 >= 118",
    "4*x0 + 7*x2 >= 50",
    "16*x1 + 7*x2 >= 67",
    "4*x0 + 7*x2 + 7*x3 >= 64",
    "4*x0 + 16*x1 + 7*x2 + 7*x3 >= 64",
    "4*x0 - 7*x1 >= 0",
    "13*x0 + 6*x2 <= 156",
    "13*x0 + 4*x1 + 6*x2 <= 270",
    "4*x0 + 16*x1 <= 391",
    "16*x1 + 7*x3 <= 317",
    "16*x1 + 7*x2 <= 357"
  ]
}
```

```python
import gurobipy as gp

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

    # Create variables
    x = m.addVars(4, lb=0, vtype=gp.GRB.CONTINUOUS, names=["George", "Peggy", "Laura", "Mary"])

    # Set objective function
    m.setObjective(5*x[0] + 1*x[1] + 9*x[2] + 4*x[3], gp.GRB.MINIMIZE)

    # Add constraints
    m.addConstr(4*x[1] + 29*x[3] >= 76)
    m.addConstr(13*x[0] + 4*x[1] >= 45)
    m.addConstr(13*x[0] + 6*x[2] >= 82)
    m.addConstr(13*x[0] + 29*x[3] >= 60)
    m.addConstr(6*x[2] + 29*x[3] >= 59)
    m.addConstr(4*x[1] + 6*x[2] + 29*x[3] >= 58)
    m.addConstr(13*x[0] + 6*x[2] + 29*x[3] >= 58)
    m.addConstr(4*x[1] + 6*x[2] + 29*x[3] >= 57)
    m.addConstr(13*x[0] + 6*x[2] + 29*x[3] >= 57)
    m.addConstr(13*x[0] + 4*x[1] + 6*x[2] + 29*x[3] >= 57)
    m.addConstr(4*x[0] + 7*x[3] >= 118)
    m.addConstr(4*x[0] + 7*x[2] >= 50)
    m.addConstr(16*x[1] + 7*x[2] >= 67)
    m.addConstr(4*x[0] + 7*x[2] + 7*x[3] >= 64)
    m.addConstr(4*x[0] + 16*x[1] + 7*x[2] + 7*x[3] >= 64)
    m.addConstr(4*x[0] - 7*x[1] >= 0)
    m.addConstr(13*x[0] + 6*x[2] <= 156)
    m.addConstr(13*x[0] + 4*x[1] + 6*x[2] <= 270)
    m.addConstr(4*x[0] + 16*x[1] <= 391)
    m.addConstr(16*x[1] + 7*x[3] <= 317)
    m.addConstr(16*x[1] + 7*x[2] <= 357)


    # 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}")

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