```json
{
  "sym_variables": [
    ("x0", "hours worked by Hank"),
    ("x1", "hours worked by Paul"),
    ("x2", "hours worked by Mary"),
    ("x3", "hours worked by Ringo"),
    ("x4", "hours worked by Jean"),
    ("x5", "hours worked by John")
  ],
  "objective_function": "1.73 * x0 + 1.02 * x1 + 2.71 * x2 + 3.81 * x3 + 9.75 * x4 + 3.15 * x5",
  "constraints": [
    "17 * x1 + 8 * x3 >= 32",
    "5 * x0 + 17 * x1 >= 22",
    "8 * x3 + 7 * x4 >= 18",
    "5 * x0 + 8 * x3 >= 19",
    "17 * x1 + 1 * x2 >= 13",
    "7 * x4 + 5 * x5 >= 29",
    "1 * x2 + 5 * x5 >= 31",
    "17 * x1 + 5 * x5 >= 10",
    "5 * x0 + 5 * x5 >= 13",
    "5 * x0 + 7 * x4 >= 12",
    "8 * x3 + 5 * x5 >= 29",
    "5 * x0 + 17 * x1 + 1 * x2 + 8 * x3 + 7 * x4 + 5 * x5 >= 29",
    "12 * x2 + 14 * x5 >= 16",
    "12 * x2 + 8 * x3 >= 27",
    "19 * x0 + 18 * x1 + 12 * x2 + 8 * x3 + 17 * x4 + 14 * x5 >= 27",
    "2 * x1 - 3 * x4 >= 0",
    "8 * x0 - 2 * x4 >= 0",
    "6 * x1 - 3 * x5 >= 0",
    "17 * x1 + 1 * x2 <= 122",
    "5 * x0 + 1 * x2 <= 149",
    "5 * x0 + 7 * x4 <= 110",
    "17 * x1 + 8 * x3 <= 36",
    "8 * x3 + 5 * x5 <= 84",
    "1 * x2 + 5 * x5 <= 37",
    "17 * x1 + 5 * x5 <= 72",
    "8 * x3 + 7 * x4 <= 38",
    "18 * x1 + 12 * x2 + 17 * x4 <= 69",
    "18 * x1 + 17 * x4 + 14 * x5 <= 81",
    "19 * x0 + 17 * x4 + 14 * x5 <= 83",
    "19 * x0 + 18 * x1 + 17 * x4 <= 200",
    "19 * x0 + 18 * x1 + 8 * x3 <= 45",
    "19 * x0 + 12 * x2 + 17 * x4 <= 59",
    "x2 == int",
    "x3 == int",
    "x5 == int"

  ]
}
```

```python
import gurobipy as gp

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

    # Create variables
    x = m.addVars(6, lb=0, vtype=[gp.GRB.CONTINUOUS, gp.GRB.CONTINUOUS, gp.GRB.INTEGER, gp.GRB.INTEGER, gp.GRB.CONTINUOUS, gp.GRB.INTEGER], name=["Hank", "Paul", "Mary", "Ringo", "Jean", "John"])


    # Set objective function
    m.setObjective(1.73 * x[0] + 1.02 * x[1] + 2.71 * x[2] + 3.81 * x[3] + 9.75 * x[4] + 3.15 * x[5], gp.GRB.MINIMIZE)

    # Add constraints
    m.addConstr(17 * x[1] + 8 * x[3] >= 32)
    m.addConstr(5 * x[0] + 17 * x[1] >= 22)
    m.addConstr(8 * x[3] + 7 * x[4] >= 18)
    m.addConstr(5 * x[0] + 8 * x[3] >= 19)
    m.addConstr(17 * x[1] + 1 * x[2] >= 13)
    m.addConstr(7 * x[4] + 5 * x[5] >= 29)
    m.addConstr(1 * x[2] + 5 * x[5] >= 31)
    m.addConstr(17 * x[1] + 5 * x[5] >= 10)
    m.addConstr(5 * x[0] + 5 * x[5] >= 13)
    m.addConstr(5 * x[0] + 7 * x[4] >= 12)
    m.addConstr(8 * x[3] + 5 * x[5] >= 29)
    m.addConstr(5 * x[0] + 17 * x[1] + 1 * x[2] + 8 * x[3] + 7 * x[4] + 5 * x[5] >= 29)
    m.addConstr(12 * x[2] + 14 * x[5] >= 16)
    m.addConstr(12 * x[2] + 8 * x[3] >= 27)
    m.addConstr(19 * x[0] + 18 * x[1] + 12 * x[2] + 8 * x[3] + 17 * x[4] + 14 * x[5] >= 27)
    m.addConstr(2 * x[1] - 3 * x[4] >= 0)
    m.addConstr(8 * x[0] - 2 * x[4] >= 0)
    m.addConstr(6 * x[1] - 3 * x[5] >= 0)
    m.addConstr(17 * x[1] + 1 * x[2] <= 122)
    m.addConstr(5 * x[0] + 1 * x[2] <= 149)
    m.addConstr(5 * x[0] + 7 * x[4] <= 110)
    m.addConstr(17 * x[1] + 8 * x[3] <= 36)
    m.addConstr(8 * x[3] + 5 * x[5] <= 84)
    m.addConstr(1 * x[2] + 5 * x[5] <= 37)
    m.addConstr(17 * x[1] + 5 * x[5] <= 72)
    m.addConstr(8 * x[3] + 7 * x[4] <= 38)
    m.addConstr(18 * x[1] + 12 * x[2] + 17 * x[4] <= 69)
    m.addConstr(18 * x[1] + 17 * x[4] + 14 * x[5] <= 81)
    m.addConstr(19 * x[0] + 17 * x[4] + 14 * x[5] <= 83)
    m.addConstr(19 * x[0] + 18 * x[1] + 17 * x[4] <= 200)
    m.addConstr(19 * x[0] + 18 * x[1] + 8 * x[3] <= 45)
    m.addConstr(19 * x[0] + 12 * x[2] + 17 * x[4] <= 59)


    # Optimize model
    m.optimize()

    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}")


except gp.GurobiError as e:
    print('Error code ' + str(e.errno) + ': ' + str(e))

except AttributeError:
    print('Encountered an attribute error')
```