```json
{
  "sym_variables": [
    ("x0", "hours worked by Peggy"),
    ("x1", "hours worked by Laura"),
    ("x2", "hours worked by Hank"),
    ("x3", "hours worked by Bobby")
  ],
  "objective_function": "9.01*x0 + 4.3*x1 + 5.2*x2 + 7.19*x3",
  "constraints": [
    "7*x1 + 8*x3 >= 13",
    "7*x2 + 8*x3 >= 13",
    "7*x0 + 7*x2 >= 6",
    "7*x0 + 8*x3 >= 11",
    "2*x1 + 7*x2 + 8*x3 >= 11",
    "7*x0 + 2*x1 + 7*x2 >= 11",
    "2*x1 + 7*x2 + 8*x3 >= 8",
    "7*x0 + 2*x1 + 7*x2 >= 8",
    "7*x0 + 2*x1 + 7*x2 + 8*x3 >= 8",
    "1*x0 + 3*x2 >= 15",
    "1*x0 + 1*x1 >= 14",
    "1*x0 + 3*x2 + 1*x3 >= 21",
    "1*x0 + 1*x1 + 3*x2 >= 21",
    "1*x0 + 3*x2 + 1*x3 >= 10",
    "1*x0 + 1*x1 + 3*x2 >= 10",
    "1*x0 + 1*x1 + 3*x2 + 1*x3 >= 10",
    "10*x1 - 2*x3 >= 0",
    "-6*x0 + 9*x1 >= 0",
    "2*x1 + 7*x2 <= 24",
    "7*x0 + 2*x1 <= 52",
    "2*x1 + 8*x3 <= 34",
    "1*x0 + 3*x2 + 1*x3 <= 68",
    "x0 == int",
    "x2 == int"

  ]
}
```

```python
import gurobipy as gp

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

# Create variables
peggy = model.addVar(vtype=gp.GRB.INTEGER, name="peggy")
laura = model.addVar(vtype=gp.GRB.CONTINUOUS, name="laura")
hank = model.addVar(vtype=gp.GRB.INTEGER, name="hank")
bobby = model.addVar(vtype=gp.GRB.CONTINUOUS, name="bobby")


# Set objective function
model.setObjective(9.01 * peggy + 4.3 * laura + 5.2 * hank + 7.19 * bobby, gp.GRB.MINIMIZE)

# Add constraints
model.addConstr(7 * laura + 8 * bobby >= 13)
model.addConstr(7 * hank + 8 * bobby >= 13)
model.addConstr(7 * peggy + 7 * hank >= 6)
model.addConstr(7 * peggy + 8 * bobby >= 11)
model.addConstr(2 * laura + 7 * hank + 8 * bobby >= 11)
model.addConstr(7 * peggy + 2 * laura + 7 * hank >= 11)
model.addConstr(2 * laura + 7 * hank + 8 * bobby >= 8)
model.addConstr(7 * peggy + 2 * laura + 7 * hank >= 8)
model.addConstr(7 * peggy + 2 * laura + 7 * hank + 8 * bobby >= 8)
model.addConstr(1 * peggy + 3 * hank >= 15)
model.addConstr(1 * peggy + 1 * laura >= 14)
model.addConstr(1 * peggy + 3 * hank + 1 * bobby >= 21)
model.addConstr(1 * peggy + 1 * laura + 3 * hank >= 21)
model.addConstr(1 * peggy + 3 * hank + 1 * bobby >= 10)
model.addConstr(1 * peggy + 1 * laura + 3 * hank >= 10)
model.addConstr(1 * peggy + 1 * laura + 3 * hank + 1 * bobby >= 10)
model.addConstr(10 * laura - 2 * bobby >= 0)
model.addConstr(-6 * peggy + 9 * laura >= 0)
model.addConstr(2 * laura + 7 * hank <= 24)
model.addConstr(7 * peggy + 2 * laura <= 52)
model.addConstr(2 * laura + 8 * bobby <= 34)
model.addConstr(1 * peggy + 3 * hank + 1 * bobby <= 68)



# Optimize model
model.optimize()

# Print results
if model.status == gp.GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Peggy: {peggy.x}")
    print(f"Laura: {laura.x}")
    print(f"Hank: {hank.x}")
    print(f"Bobby: {bobby.x}")
    print(f"Objective value: {model.objVal}")
elif model.status == gp.GRB.INFEASIBLE:
    print("Model is infeasible.")
else:
    print(f"Optimization terminated with status {model.status}")

```
