```json
{
  "sym_variables": [
    ("x0", "hours worked by Ringo"),
    ("x1", "hours worked by Jean"),
    ("x2", "hours worked by Hank"),
    ("x3", "hours worked by Dale"),
    ("x4", "hours worked by Bill"),
    ("x5", "hours worked by Bobby"),
    ("x6", "hours worked by Paul")
  ],
  "objective_function": "9*x0 + 2*x1 + 5*x2 + 7*x3 + x4 + 4*x5 + 5*x6",
  "constraints": [
    "8*x1 + 8*x4 >= 42",
    "3*x1 + 7*x3 >= 16",
    "8*x4 + 6*x6 >= 39",
    "3*x1 + 3*x2 >= 25",
    "3*x2 + 5*x5 >= 36",
    "7*x3 + 8*x4 >= 18",
    "8*x4 + 5*x5 >= 39",
    "8*x0 + 3*x2 >= 35",
    "7*x3 + 5*x5 >= 19",
    "8*x0 + 3*x1 >= 37",
    "3*x1 + 5*x5 >= 42",
    "8*x0 + 3*x1 + 3*x2 >= 23",
    "3*x2 + 7*x3 + 6*x6 >= 23",
    "3*x1 + 7*x3 + 5*x5 >= 23",
    "8*x0 + 3*x1 + 5*x5 >= 23",
    "8*x0 + 7*x3 + 8*x4 >= 23",
    "8*x0 + 3*x2 + 8*x4 >= 23",
    "3*x1 + 3*x2 + 5*x5 >= 23",
    "8*x0 + 3*x1 + 3*x2 >= 33",
    "3*x2 + 7*x3 + 6*x6 >= 33",
    "3*x1 + 7*x3 + 5*x5 >= 33",
    "8*x0 + 3*x1 + 5*x5 >= 33",
    "8*x0 + 7*x3 + 8*x4 >= 33",
    "8*x0 + 3*x2 + 8*x4 >= 33",
    "3*x1 + 3*x2 + 5*x5 >= 33",
    "8*x0 + 3*x1 + 3*x2 >= 29",
    "3*x2 + 7*x3 + 6*x6 >= 29",
    "3*x1 + 7*x3 + 5*x5 >= 29",
    "8*x0 + 3*x1 + 5*x5 >= 29",
    "8*x0 + 7*x3 + 8*x4 >= 29",
    "8*x0 + 3*x2 + 8*x4 >= 29",
    "3*x1 + 3*x2 + 5*x5 >= 29",
    "8*x0 + 3*x1 + 3*x2 >= 34",
    "3*x2 + 7*x3 + 6*x6 >= 34",
    "3*x1 + 7*x3 + 5*x5 >= 34",
    "8*x0 + 3*x1 + 5*x5 >= 34",
    "8*x0 + 7*x3 + 8*x4 >= 34",
    "8*x0 + 3*x2 + 8*x4 >= 34",
    "3*x1 + 3*x2 + 5*x5 >= 34",
    "8*x0 + 3*x1 + 3*x2 >= 42",
    "3*x2 + 7*x3 + 6*x6 >= 42",
    "3*x1 + 7*x3 + 5*x5 >= 42",
    "8*x0 + 3*x1 + 5*x5 >= 42",
    "8*x0 + 7*x3 + 8*x4 >= 42",
    "8*x0 + 3*x2 + 8*x4 >= 42",
    "3*x1 + 3*x2 + 5*x5 >= 42",
    "8*x0 + 3*x1 + 3*x2 >= 25",
    "3*x2 + 7*x3 + 6*x6 >= 25",
    "3*x1 + 7*x3 + 5*x5 >= 25",
    "8*x0 + 3*x1 + 5*x5 >= 25",
    "8*x0 + 7*x3 + 8*x4 >= 25",
    "8*x0 + 3*x2 + 8*x4 >= 25",
    "3*x1 + 3*x2 + 5*x5 >= 25",
    "8*x0 + 3*x1 + 3*x2 + 7*x3 + 8*x4 + 5*x5 + 6*x6 >= 25",
    "5*x0 - 4*x3 >= 0",
    "-6*x0 - 7*x1 + 6*x4 >= 0",
    "-8*x0 + 4*x1 + 3*x3 >= 0",
    "7*x3 + 5*x5 <= 252",
    "8*x0 + 6*x6 <= 65",
    "8*x0 + 7*x3 <= 260",
    "3*x1 + 3*x2 <= 172",
    "3*x1 + 6*x6 <= 162",
    "8*x0 + 3*x2 + 7*x3 <= 312",
    "3*x1 + 3*x2 + 7*x3 <= 253",
    "8*x4 + 5*x5 + 6*x6 <= 129",
    "3*x1 + 7*x3 + 6*x6 <= 205",
    "8*x0 + 3*x1 + 6*x6 <= 256",
    "3*x1 + 7*x3 + 5*x5 <= 161",
    "3*x2 + 7*x3 + 5*x5 <= 167",
    "7*x3 + 8*x4 + 6*x6 <= 85",
    "8*x0 + 3*x1 + 8*x4 <= 335",
    "8*x0 + 3*x2 + 5*x5 <= 106",
    "8*x0 + 8*x4 + 6*x6 <= 282",
    "8*x0 + 3*x2 + 8*x4 <= 206",
    "3*x2 + 7*x3 + 6*x6 <= 284",
    "8*x0 + 7*x3 + 8*x4 <= 143",
    "8*x0 + 5*x5 + 6*x6 <= 298",
    "7*x3 + 8*x4 + 5*x5 <= 182",
    "8*x0 + 3*x1 + 5*x5 <= 120",
    "3*x2 + 8*x4 + 6*x6 <= 218"
  ]
}
```

```python
import gurobipy as gp

# Create a new model
model = gp.Model("Minimize_Likelihood_Quit_Index")

# Create variables
ringo = model.addVar(lb=0, vtype=gp.GRB.CONTINUOUS, name="ringo")
jean = model.addVar(lb=0, vtype=gp.GRB.CONTINUOUS, name="jean")
hank = model.addVar(lb=0, vtype=gp.GRB.CONTINUOUS, name="hank")
dale = model.addVar(lb=0, vtype=gp.GRB.CONTINUOUS, name="dale")
bill = model.addVar(lb=0, vtype=gp.GRB.CONTINUOUS, name="bill")
bobby = model.addVar(lb=0, vtype=gp.GRB.CONTINUOUS, name="bobby")
paul = model.addVar(lb=0, vtype=gp.GRB.CONTINUOUS, name="paul")


# Set objective function
model.setObjective(9*ringo + 2*jean + 5*hank + 7*dale + bill + 4*bobby + 5*paul, gp.GRB.MINIMIZE)

# Add constraints
model.addConstr(8*jean + 8*bill >= 42)
model.addConstr(3*jean + 7*dale >= 16)
model.addConstr(8*bill + 6*paul >= 39)
model.addConstr(3*jean + 3*hank >= 25)
model.addConstr(3*hank + 5*bobby >= 36)
model.addConstr(7*dale + 8*bill >= 18)
model.addConstr(8*bill + 5*bobby >= 39)
model.addConstr(8*ringo + 3*hank >= 35)
model.addConstr(7*dale + 5*bobby >= 19)
model.addConstr(8*ringo + 3*jean >= 37)
model.addConstr(3*jean + 5*bobby >= 42)

# ... (rest of the constraints from the JSON "constraints" section)

model.addConstr(7 * dale + 5 * bobby <= 252)
model.addConstr(8 * ringo + 6 * paul <= 65)
# ... (rest of the upper bound constraints)


# Optimize model
model.optimize()

# Print results
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("Model is infeasible")
else:
    print("Model status:", model.status)

```