```json
{
  "sym_variables": [
    ("x0", "hours worked by Mary"),
    ("x1", "hours worked by Dale"),
    ("x2", "hours worked by Laura")
  ],
  "objective_function": "8.72 * x0 + 5.55 * x1 + 1.19 * x2",
  "constraints": [
    "9.26 * x0 + 4.77 * x1 + 11.23 * x2 >= 29",
    "4.77 * x1 + 11.23 * x2 >= 34",
    "9.26 * x0 + 11.23 * x2 >= 29",
    "9.26 * x0 + 4.77 * x1 + 11.23 * x2 >= 29",
    "-4 * x1 + 8 * x2 >= 0",
    "9.26 * x0 + 4.77 * x1 <= 43"
  ]
}
```

```python
import gurobipy as gp

# Create a new model
model = gp.Model("Minimize Likelihood to Quit Index")

# Create variables
mary_hours = model.addVar(lb=0, vtype=gp.GRB.CONTINUOUS, name="mary_hours")
dale_hours = model.addVar(lb=0, vtype=gp.GRB.CONTINUOUS, name="dale_hours")
laura_hours = model.addVar(lb=0, vtype=gp.GRB.CONTINUOUS, name="laura_hours")


# Set objective function
model.setObjective(8.72 * mary_hours + 5.55 * dale_hours + 1.19 * laura_hours, gp.GRB.MINIMIZE)

# Add constraints
model.addConstr(9.26 * mary_hours + 4.77 * dale_hours + 11.23 * laura_hours >= 29, "c1")
model.addConstr(4.77 * dale_hours + 11.23 * laura_hours >= 34, "c2")
model.addConstr(9.26 * mary_hours + 11.23 * laura_hours >= 29, "c3")
model.addConstr(-4 * dale_hours + 8 * laura_hours >= 0, "c4")
model.addConstr(9.26 * mary_hours + 4.77 * dale_hours <= 43, "c5")



# Optimize model
model.optimize()

# Print results
if model.status == gp.GRB.OPTIMAL:
    print(f"Optimal objective value: {model.objVal}")
    print(f"Mary's hours: {mary_hours.x}")
    print(f"Dale's hours: {dale_hours.x}")
    print(f"Laura's hours: {laura_hours.x}")
elif model.status == gp.GRB.INFEASIBLE:
    print("The model is infeasible.")
else:
    print(f"Optimization terminated with status {model.status}")

```
