```json
{
  "sym_variables": [
    ("x0", "hours worked by Jean"),
    ("x1", "hours worked by Bobby"),
    ("x2", "hours worked by Laura"),
    ("x3", "hours worked by Hank"),
    ("x4", "hours worked by Peggy"),
    ("x5", "hours worked by Dale")
  ],
  "objective_function": "2.49 * x0 + 6.25 * x1 + 1.54 * x2 + 3.01 * x3 + 2.69 * x4 + 9.45 * x5",
  "constraints": [
    "35 * x0 + 14 * x1 >= 71",
    "5 * x3 + 34 * x4 >= 69",
    "35 * x0 + 9 * x5 >= 69",
    "3 * x1 + 10 * x5 >= 71",
    "14 * x0 + 10 * x5 >= 80",
    "24 * x2 + 30 * x4 >= 106",
    "30 * x4 + 10 * x5 >= 94",
    "3 * x1 + 24 * x2 >= 99",
    "24 * x2 + 30 * x3 >= 115",
    "30 * x3 + 10 * x5 >= 108",
    "24 * x2 + 10 * x5 >= 67",
    "14 * x0 + 3 * x1 + 10 * x5 >= 72",
    "10 * x0 + 6 * x3 - x5 >= 0",
    "-5 * x0 - 7 * x2 + x3 >= 0",
    "35 * x0 + 9 * x5 <= 113",
    "34 * x4 + 9 * x5 <= 162",
    "35 * x0 + 10 * x2 <= 441",
    "14 * x1 + 9 * x5 <= 125",
    "10 * x2 + 34 * x4 <= 521",
    "5 * x3 + 34 * x4 <= 533",
    "5 * x3 + 9 * x5 <= 263",
    "35 * x0 + 14 * x1 + 10 * x2 + 5 * x3 + 34 * x4 + 9 * x5 <= 263",
    "14 * x0 + 3 * x1 <= 573",
    "3 * x1 + 24 * x2 <= 358",
    "14 * x0 + 10 * x5 <= 602",
    "3 * x1 + 30 * x4 <= 632",
    "24 * x2 + 10 * x5 <= 513",
    "24 * x2 + 30 * x4 <= 200",
    "14 * x0 + 3 * x1 + 24 * x2 <= 352",
    "14 * x0 + 30 * x4 + 10 * x5 <= 197",
    "14 * x0 + 30 * x3 + 30 * x4 <= 732",
    "14 * x0 + 3 * x1 + 10 * x5 <= 502",
    "14 * x0 + 24 * x2 + 30 * x3 <= 584",
    "24 * x2 + 30 * x3 + 30 * x4 <= 477",
    "3 * x1 + 30 * x4 + 10 * x5 <= 515",
    "3 * x1 + 24 * x2 + 30 * x4 <= 484",
    "14 * x0 + 3 * x1 + 30 * x4 <= 329",
    "3 * x1 + 24 * x2 + 10 * x5 <= 360",
    "14 * x0 + 24 * x2 + 10 * x5 <= 526",
    "14 * x0 + 3 * x1 + 24 * x2 + 30 * x3 + 30 * x4 + 10 * x5 <= 526"
  ]
}
```

```python
import gurobipy as gp

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

# Create variables
x = m.addVars(6, vtype=gp.GRB.INTEGER, name=["Jean", "Bobby", "Laura", "Hank", "Peggy", "Dale"])

# Set objective function
m.setObjective(2.49 * x[0] + 6.25 * x[1] + 1.54 * x[2] + 3.01 * x[3] + 2.69 * x[4] + 9.45 * x[5], gp.GRB.MAXIMIZE)

# Add constraints
m.addConstr(35 * x[0] + 14 * x[1] >= 71)
m.addConstr(5 * x[3] + 34 * x[4] >= 69)
m.addConstr(35 * x[0] + 9 * x[5] >= 69)
m.addConstr(3 * x[1] + 10 * x[5] >= 71)
m.addConstr(14 * x[0] + 10 * x[5] >= 80)
m.addConstr(24 * x[2] + 30 * x[4] >= 106)
m.addConstr(30 * x[4] + 10 * x[5] >= 94)
m.addConstr(3 * x[1] + 24 * x[2] >= 99)
m.addConstr(24 * x[2] + 30 * x[3] >= 115)
m.addConstr(30 * x[3] + 10 * x[5] >= 108)
m.addConstr(24 * x[2] + 10 * x[5] >= 67)
m.addConstr(14 * x[0] + 3 * x[1] + 10 * x[5] >= 72)
m.addConstr(10 * x[0] + 6 * x[3] - x[5] >= 0)
m.addConstr(-5 * x[0] - 7 * x[2] + x[3] >= 0)
m.addConstr(35 * x[0] + 9 * x[5] <= 113)
m.addConstr(34 * x[4] + 9 * x[5] <= 162)
m.addConstr(35 * x[0] + 10 * x[2] <= 441)
m.addConstr(14 * x[1] + 9 * x[5] <= 125)
m.addConstr(10 * x[2] + 34 * x[4] <= 521)
m.addConstr(5 * x[3] + 34 * x[4] <= 533)
m.addConstr(5 * x[3] + 9 * x[5] <= 263)
m.addConstr(35 * x[0] + 14 * x[1] + 10 * x[2] + 5 * x[3] + 34 * x[4] + 9 * x[5] <= 263)
m.addConstr(14 * x[0] + 3 * x[1] <= 573)
m.addConstr(3 * x[1] + 24 * x[2] <= 358)
m.addConstr(14 * x[0] + 10 * x[5] <= 602)
m.addConstr(3 * x[1] + 30 * x[4] <= 632)
m.addConstr(24 * x[2] + 10 * x[5] <= 513)
m.addConstr(24 * x[2] + 30 * x[4] <= 200)
m.addConstr(14 * x[0] + 3 * x[1] + 24 * x[2] <= 352)
m.addConstr(14 * x[0] + 30 * x[4] + 10 * x[5] <= 197)
m.addConstr(14 * x[0] + 30 * x[3] + 30 * x[4] <= 732)
m.addConstr(14 * x[0] + 3 * x[1] + 10 * x[5] <= 502)
m.addConstr(14 * x[0] + 24 * x[2] + 30 * x[3] <= 584)
m.addConstr(24 * x[2] + 30 * x[3] + 30 * x[4] <= 477)
m.addConstr(3 * x[1] + 30 * x[4] + 10 * x[5] <= 515)
m.addConstr(3 * x[1] + 24 * x[2] + 30 * x[4] <= 484)
m.addConstr(14 * x[0] + 3 * x[1] + 30 * x[4] <= 329)
m.addConstr(3 * x[1] + 24 * x[2] + 10 * x[5] <= 360)
m.addConstr(14 * x[0] + 24 * x[2] + 10 * x[5] <= 526)
m.addConstr(14 * x[0] + 3 * x[1] + 24 * x[2] + 30 * x[3] + 30 * x[4] + 10 * x[5] <= 526)


# 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'Obj: {m.objVal}')
elif m.status == gp.GRB.INFEASIBLE:
    print("The model is infeasible.")
else:
    print(f"Optimization ended with status {m.status}")

```
