```json
{
  "sym_variables": [
    ("x0", "hours worked by Hank"),
    ("x1", "hours worked by Jean"),
    ("x2", "hours worked by Mary")
  ],
  "objective_function": "6.35 * x0 + 4.82 * x1 + 7.75 * x2",
  "constraints": [
    "5.9 * x0 + 20.41 * x2 >= 87",
    "5.9 * x0 + 19.39 * x1 >= 61",
    "5.9 * x0 + 19.39 * x1 + 20.41 * x2 >= 61",
    "-10 * x0 + 6 * x2 >= 0",
    "7 * x1 - 9 * x2 >= 0",
    "5.9 * x0 + 19.39 * x1 <= 175"
  ]
}
```

```python
import gurobipy as gp

# Create a new model
model = gp.Model("Minimize Labor Cost")

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


# Set objective function
model.setObjective(6.35 * hank_hours + 4.82 * jean_hours + 7.75 * mary_hours, gp.GRB.MINIMIZE)

# Add constraints
model.addConstr(5.9 * hank_hours + 20.41 * mary_hours >= 87, "c1")
model.addConstr(5.9 * hank_hours + 19.39 * jean_hours >= 61, "c2")
model.addConstr(5.9 * hank_hours + 19.39 * jean_hours + 20.41 * mary_hours >= 61, "c3")
model.addConstr(-10 * hank_hours + 6 * mary_hours >= 0, "c4")
model.addConstr(7 * jean_hours - 9 * mary_hours >= 0, "c5")
model.addConstr(5.9 * hank_hours + 19.39 * jean_hours <= 175, "c6")



# Optimize model
model.optimize()

# Print results
if model.status == gp.GRB.OPTIMAL:
    print(f"Optimal solution found: {model.objVal}")
    print(f"Hank's hours: {hank_hours.x}")
    print(f"Jean's hours: {jean_hours.x}")
    print(f"Mary's hours: {mary_hours.x}")
elif model.status == gp.GRB.INFEASIBLE:
    print("Model is infeasible.")
else:
    print(f"Optimization terminated with status {model.status}")

```