```json
{
  "sym_variables": [
    ("x0", "hours worked by Jean"),
    ("x1", "hours worked by Hank"),
    ("x2", "hours worked by Bobby"),
    ("x3", "hours worked by Ringo")
  ],
  "objective_function": "2*x0 + 2*x1 + 9*x2 + 7*x3",
  "constraints": [
    "32*x1 + 17*x2 >= 205",
    "23*x0 + 32*x1 + 17*x2 + 12*x3 >= 205",
    "10*x2 + 10*x3 >= 64",
    "15*x1 + 10*x3 >= 70",
    "27*x0 + 10*x3 >= 67",
    "27*x0 + 15*x1 + 10*x2 + 10*x3 >= 67",
    "-7*x0 + 4*x2 >= 0",
    "8*x2 - 6*x3 >= 0",
    "-10*x1 + 2*x2 + 4*x3 >= 0",
    "23*x0 + 32*x1 + 12*x3 <= 632",
    "15*x1 + 10*x3 <= 331",
    "10*x2 + 10*x3 <= 170",
    "27*x0 + 10*x3 <= 228",
    "27*x0 + 15*x1 <= 130",
    "27*x0 + 10*x2 <= 118",
    "27*x0 + 15*x1 + 10*x2 <= 295"
  ]
}
```

```python
import gurobipy as gp

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

    # Create variables
    x = m.addVars(4, lb=0, vtype=gp.GRB.CONTINUOUS, name=["Jean", "Hank", "Bobby", "Ringo"])


    # Set objective function
    m.setObjective(2*x[0] + 2*x[1] + 9*x[2] + 7*x[3], gp.GRB.MINIMIZE)

    # Add constraints
    m.addConstr(32*x[1] + 17*x[2] >= 205, "c1")
    m.addConstr(23*x[0] + 32*x[1] + 17*x[2] + 12*x[3] >= 205, "c2")
    m.addConstr(10*x[2] + 10*x[3] >= 64, "c3")
    m.addConstr(15*x[1] + 10*x[3] >= 70, "c4")
    m.addConstr(27*x[0] + 10*x[3] >= 67, "c5")
    m.addConstr(27*x[0] + 15*x[1] + 10*x[2] + 10*x[3] >= 67, "c6")
    m.addConstr(-7*x[0] + 4*x[2] >= 0, "c7")
    m.addConstr(8*x[2] - 6*x[3] >= 0, "c8")
    m.addConstr(-10*x[1] + 2*x[2] + 4*x[3] >= 0, "c9")
    m.addConstr(23*x[0] + 32*x[1] + 12*x[3] <= 632, "c10")
    m.addConstr(15*x[1] + 10*x[3] <= 331, "c11")
    m.addConstr(10*x[2] + 10*x[3] <= 170, "c12")
    m.addConstr(27*x[0] + 10*x[3] <= 228, "c13")
    m.addConstr(27*x[0] + 15*x[1] <= 130, "c14")
    m.addConstr(27*x[0] + 10*x[2] <= 118, "c15")
    m.addConstr(27*x[0] + 15*x[1] + 10*x[2] <= 295, "c16")


    # 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 problem 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')
```