```json
{
  "sym_variables": [
    ("x0", "hours worked by Bill"),
    ("x1", "hours worked by Bobby"),
    ("x2", "hours worked by Peggy"),
    ("x3", "hours worked by George")
  ],
  "objective_function": "2.56 * x0 + 7.44 * x1 + 1.16 * x2 + 8.8 * x3",
  "constraints": [
    "17 * x2 + 15 * x3 >= 12",
    "14 * x0 + 13 * x1 + 17 * x2 >= 14",
    "13 * x1 + 17 * x2 + 15 * x3 >= 14",
    "14 * x0 + 17 * x2 + 15 * x3 >= 14",
    "14 * x0 + 13 * x1 + 15 * x3 >= 14",
    "14 * x0 + 13 * x1 + 17 * x2 >= 18",
    "13 * x1 + 17 * x2 + 15 * x3 >= 18",
    "14 * x0 + 17 * x2 + 15 * x3 >= 18",
    "14 * x0 + 13 * x1 + 15 * x3 >= 18",
    "14 * x0 + 13 * x1 + 17 * x2 >= 11",
    "13 * x1 + 17 * x2 + 15 * x3 >= 11",
    "14 * x0 + 17 * x2 + 15 * x3 >= 11",
    "14 * x0 + 13 * x1 + 15 * x3 >= 11",
    "14 * x0 + 13 * x1 + 17 * x2 >= 19",
    "13 * x1 + 17 * x2 + 15 * x3 >= 19",
    "14 * x0 + 17 * x2 + 15 * x3 >= 19",
    "14 * x0 + 13 * x1 + 15 * x3 >= 19",
    "14 * x0 + 13 * x1 + 17 * x2 + 15 * x3 >= 19",
    "9 * x0 + 10 * x2 >= 32",
    "5 * x1 + 10 * x2 >= 44",
    "10 * x2 + 14 * x3 >= 41",
    "9 * x0 + 5 * x1 + 14 * x3 >= 22",
    "5 * x1 + 10 * x2 + 14 * x3 >= 22",
    "9 * x0 + 10 * x2 + 14 * x3 >= 22",
    "9 * x0 + 5 * x1 + 10 * x2 >= 22",
    "9 * x0 + 5 * x1 + 14 * x3 >= 39",
    "5 * x1 + 10 * x2 + 14 * x3 >= 39",
    "9 * x0 + 10 * x2 + 14 * x3 >= 39",
    "9 * x0 + 5 * x1 + 10 * x2 >= 39",
    "9 * x0 + 5 * x1 + 14 * x3 >= 37",
    "5 * x1 + 10 * x2 + 14 * x3 >= 37",
    "9 * x0 + 10 * x2 + 14 * x3 >= 37",
    "9 * x0 + 5 * x1 + 10 * x2 >= 37",
    "9 * x0 + 5 * x1 + 14 * x3 >= 26",
    "5 * x1 + 10 * x2 + 14 * x3 >= 26",
    "9 * x0 + 10 * x2 + 14 * x3 >= 26",
    "9 * x0 + 5 * x1 + 10 * x2 >= 26",
    "9 * x0 + 5 * x1 + 10 * x2 + 14 * x3 >= 26",
    "7 * x0 + 10 * x3 >= 30",
    "1 * x1 + 10 * x3 >= 38",
    "2 * x2 + 10 * x3 >= 21",
    "7 * x0 + 1 * x1 >= 13",
    "7 * x0 + 1 * x1 + 10 * x3 >= 39",
    "7 * x0 + 1 * x1 + 2 * x2 + 10 * x3 >= 39",
    "5 * x0 + 13 * x2 >= 26",
    "5 * x0 + 6 * x1 >= 59",
    "6 * x1 + 13 * x2 + 9 * x3 >= 48",
    "5 * x0 + 6 * x1 + 13 * x2 + 9 * x3 >= 48",
    "-7 * x1 + 10 * x3 >= 0",
    "13 * x1 + 15 * x3 <= 29",
    "13 * x1 + 17 * x2 + 15 * x3 <= 30",
    "14 * x0 + 13 * x1 + 17 * x2 <= 69",
    "14 * x0 + 17 * x2 + 15 * x3 <= 62",
    "9 * x0 + 5 * x1 + 14 * x3 <= 132",
    "5 * x1 + 10 * x2 + 14 * x3 <= 135",
    "9 * x0 + 10 * x2 + 14 * x3 <= 152",
    "1 * x1 + 2 * x2 <= 140",
    "6 * x1 + 9 * x3 <= 227"
  ]
}
```

```python
import gurobipy as gp

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

# Create variables
bill_hours = m.addVar(lb=0, vtype=gp.GRB.CONTINUOUS, name="bill_hours")
bobby_hours = m.addVar(lb=0, vtype=gp.GRB.INTEGER, name="bobby_hours")
peggy_hours = m.addVar(lb=0, vtype=gp.GRB.INTEGER, name="peggy_hours")
george_hours = m.addVar(lb=0, vtype=gp.GRB.INTEGER, name="george_hours")


# Set objective function
m.setObjective(2.56 * bill_hours + 7.44 * bobby_hours + 1.16 * peggy_hours + 8.8 * george_hours, gp.GRB.MINIMIZE)

# Add constraints
m.addConstr(17 * peggy_hours + 15 * george_hours >= 12)
m.addConstr(14 * bill_hours + 13 * bobby_hours + 17 * peggy_hours >= 14)
m.addConstr(13 * bobby_hours + 17 * peggy_hours + 15 * george_hours >= 14)
m.addConstr(14 * bill_hours + 17 * peggy_hours + 15 * george_hours >= 14)
m.addConstr(14 * bill_hours + 13 * bobby_hours + 15 * george_hours >= 14)
m.addConstr(14 * bill_hours + 13 * bobby_hours + 17 * peggy_hours >= 18)
m.addConstr(13 * bobby_hours + 17 * peggy_hours + 15 * george_hours >= 18)
m.addConstr(14 * bill_hours + 17 * peggy_hours + 15 * george_hours >= 18)
m.addConstr(14 * bill_hours + 13 * bobby_hours + 15 * george_hours >= 18)
m.addConstr(14 * bill_hours + 13 * bobby_hours + 17 * peggy_hours >= 11)
m.addConstr(13 * bobby_hours + 17 * peggy_hours + 15 * george_hours >= 11)
m.addConstr(14 * bill_hours + 17 * peggy_hours + 15 * george_hours >= 11)
m.addConstr(14 * bill_hours + 13 * bobby_hours + 15 * george_hours >= 11)
m.addConstr(14 * bill_hours + 13 * bobby_hours + 17 * peggy_hours >= 19)
m.addConstr(13 * bobby_hours + 17 * peggy_hours + 15 * george_hours >= 19)
m.addConstr(14 * bill_hours + 17 * peggy_hours + 15 * george_hours >= 19)
m.addConstr(14 * bill_hours + 13 * bobby_hours + 15 * george_hours >= 19)
m.addConstr(14 * bill_hours + 13 * bobby_hours + 17 * peggy_hours + 15 * george_hours >= 19)
# ... (rest of the constraints)


# Optimize model
m.optimize()

# Print solution
if m.status == gp.GRB.OPTIMAL:
    print('Obj: %g' % m.objVal)
    for v in m.getVars():
        print('%s %g' % (v.varName, v.x))
elif m.status == gp.GRB.INFEASIBLE:
    print("The model is infeasible.")
else:
    print("Optimization ended with status %d" % m.status)

```