```json
{
  "sym_variables": [
    ("x0", "hours worked by George"),
    ("x1", "hours worked by Paul"),
    ("x2", "hours worked by Peggy"),
    ("x3", "hours worked by Jean"),
    ("x4", "hours worked by Bill")
  ],
  "objective_function": "8*x0 + 6*x1 + 1*x2 + 9*x3 + 9*x4",
  "constraints": [
    "3*x0 + 1*x3 >= 5",
    "3*x0 + 2*x2 + 1*x3 >= 8",
    "3*x0 + 3*x1 + 2*x2 >= 8",
    "3*x0 + 3*x1 + 1*x3 >= 8",
    "3*x0 + 1*x3 + 5*x4 >= 8",
    "3*x1 + 2*x2 + 5*x4 >= 8",
    "2*x2 + 1*x3 + 5*x4 >= 8",
    "3*x0 + 2*x2 + 1*x3 >= 10",
    "3*x0 + 3*x1 + 2*x2 >= 10",
    "3*x0 + 3*x1 + 1*x3 >= 10",
    "3*x0 + 1*x3 + 5*x4 >= 10",
    "3*x1 + 2*x2 + 5*x4 >= 10",
    "2*x2 + 1*x3 + 5*x4 >= 10",
    "3*x0 + 2*x2 + 1*x3 >= 12",
    "3*x0 + 3*x1 + 2*x2 >= 12",
    "3*x0 + 3*x1 + 1*x3 >= 12",
    "3*x0 + 1*x3 + 5*x4 >= 12",
    "3*x1 + 2*x2 + 5*x4 >= 12",
    "2*x2 + 1*x3 + 5*x4 >= 12",
    "3*x0 + 2*x2 + 1*x3 >= 15",
    "3*x0 + 3*x1 + 2*x2 >= 15",
    "3*x0 + 3*x1 + 1*x3 >= 15",
    "3*x0 + 1*x3 + 5*x4 >= 15",
    "3*x1 + 2*x2 + 5*x4 >= 15",
    "2*x2 + 1*x3 + 5*x4 >= 15",    
    "3*x0 + 2*x4 >= 4",
    "3*x0 + 3*x2 >= 7",
    "3*x1 + 5*x4 <= 48",
    "1*x3 + 5*x4 <= 54",
    "3*x0 + 1*x3 <= 50",
    "2*x2 + 1*x3 <= 19",
    "3*x0 + 2*x2 <= 61",
    "3*x1 + 1*x3 <= 29",
    "3*x0 + 1*x3 + 5*x4 <= 75",
    "3*x1 + 2*x2 + 1*x3 <= 59",
    "3*x0 + 3*x1 + 2*x2 + 1*x3 + 5*x4 <= 59",
    "5*x2 + 4*x3 <= 32",
    "4*x3 + 2*x4 <= 53",
    "1*x0 + 5*x2 <= 65",
    "4*x1 + 2*x4 <= 49",
    "4*x1 + 5*x2 <= 77",
    "4*x1 + 5*x2 + 4*x3 <= 61",
    "5*x2 + 4*x3 + 2*x4 <= 29",
    "4*x1 + 4*x3 + 2*x4 <= 55",
    "1*x0 + 4*x1 + 5*x2 + 4*x3 + 2*x4 <= 55",
    "3*x0 + 3*x2 <= 64",
    "2*x1 + 2*x4 <= 61",
    "3*x0 + 2*x4 <= 45",
    "3*x0 + 2*x1 <= 64",
    "5*x3 + 2*x4 <= 35",
    "3*x2 + 5*x3 <= 28",
    "2*x1 + 3*x2 <= 57",
    "3*x2 + 2*x4 <= 58",
    "3*x0 + 2*x1 + 3*x2 + 5*x3 + 2*x4 <= 58"
  ]
}
```

```python
import gurobipy as gp

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

# Create variables
x = m.addVars(5, lb=0, vtype=gp.GRB.CONTINUOUS, name=["George", "Paul", "Peggy", "Jean", "Bill"])


# Set objective function
m.setObjective(8*x[0] + 6*x[1] + 1*x[2] + 9*x[3] + 9*x[4], gp.GRB.MAXIMIZE)

# Add constraints
m.addConstr(3*x[0] + 1*x[3] >= 5)
m.addConstr(3*x[0] + 2*x[2] + 1*x[3] >= 8)
m.addConstr(3*x[0] + 3*x[1] + 2*x[2] >= 8)
m.addConstr(3*x[0] + 3*x[1] + 1*x[3] >= 8)
m.addConstr(3*x[0] + 1*x[3] + 5*x[4] >= 8)
m.addConstr(3*x[1] + 2*x[2] + 5*x[4] >= 8)
m.addConstr(2*x[2] + 1*x[3] + 5*x[4] >= 8)
m.addConstr(3*x[0] + 2*x[2] + 1*x[3] >= 10)
m.addConstr(3*x[0] + 3*x[1] + 2*x[2] >= 10)
m.addConstr(3*x[0] + 3*x[1] + 1*x[3] >= 10)
m.addConstr(3*x[0] + 1*x[3] + 5*x[4] >= 10)
m.addConstr(3*x[1] + 2*x[2] + 5*x[4] >= 10)
m.addConstr(2*x[2] + 1*x[3] + 5*x[4] >= 10)
m.addConstr(3*x[0] + 2*x[2] + 1*x[3] >= 12)
m.addConstr(3*x[0] + 3*x[1] + 2*x[2] >= 12)
m.addConstr(3*x[0] + 3*x[1] + 1*x[3] >= 12)
m.addConstr(3*x[0] + 1*x[3] + 5*x[4] >= 12)
m.addConstr(3*x[1] + 2*x[2] + 5*x[4] >= 12)
m.addConstr(2*x[2] + 1*x[3] + 5*x[4] >= 12)
m.addConstr(3*x[0] + 2*x[2] + 1*x[3] >= 15)
m.addConstr(3*x[0] + 3*x[1] + 2*x[2] >= 15)
m.addConstr(3*x[0] + 3*x[1] + 1*x[3] >= 15)
m.addConstr(3*x[0] + 1*x[3] + 5*x[4] >= 15)
m.addConstr(3*x[1] + 2*x[2] + 5*x[4] >= 15)
m.addConstr(2*x[2] + 1*x[3] + 5*x[4] >= 15)
m.addConstr(3*x[0] + 2*x[4] >= 4)
m.addConstr(3*x[0] + 3*x[2] >= 7)
m.addConstr(3*x[1] + 5*x[4] <= 48)
m.addConstr(1*x[3] + 5*x[4] <= 54)
m.addConstr(3*x[0] + 1*x[3] <= 50)
m.addConstr(2*x[2] + 1*x[3] <= 19)
m.addConstr(3*x[0] + 2*x[2] <= 61)
m.addConstr(3*x[1] + 1*x[3] <= 29)
m.addConstr(3*x[0] + 1*x[3] + 5*x[4] <= 75)
m.addConstr(3*x[1] + 2*x[2] + 1*x[3] <= 59)
m.addConstr(3*x[0] + 3*x[1] + 2*x[2] + 1*x[3] + 5*x[4] <= 59)
m.addConstr(5*x[2] + 4*x[3] <= 32)
m.addConstr(4*x[3] + 2*x[4] <= 53)
m.addConstr(1*x[0] + 5*x[2] <= 65)
m.addConstr(4*x[1] + 2*x[4] <= 49)
m.addConstr(4*x[1] + 5*x[2] <= 77)
m.addConstr(4*x[1] + 5*x[2] + 4*x[3] <= 61)
m.addConstr(5*x[2] + 4*x[3] + 2*x[4] <= 29)
m.addConstr(4*x[1] + 4*x[3] + 2*x[4] <= 55)
m.addConstr(1*x[0] + 4*x[1] + 5*x[2] + 4*x[3] + 2*x[4] <= 55)
m.addConstr(3*x[0] + 3*x[2] <= 64)
m.addConstr(2*x[1] + 2*x[4] <= 61)
m.addConstr(3*x[0] + 2*x[4] <= 45)
m.addConstr(3*x[0] + 2*x[1] <= 64)
m.addConstr(5*x[3] + 2*x[4] <= 35)
m.addConstr(3*x[2] + 5*x[3] <= 28)
m.addConstr(2*x[1] + 3*x[2] <= 57)
m.addConstr(3*x[2] + 2*x[4] <= 58)
m.addConstr(3*x[0] + 2*x[1] + 3*x[2] + 5*x[3] + 2*x[4] <= 58)


# Optimize model
m.optimize()

# Print results
if m.status == gp.GRB.OPTIMAL:
    for v in m.getVars():
        print(f"{v.varName}: {v.x}")
    print(f"Objective Value: {m.objVal}")
elif m.status == gp.GRB.INFEASIBLE:
    print("The model is infeasible.")
else:
    print(f"Optimization terminated with status {m.status}")

```
