```json
{
  "sym_variables": [
    ("x0", "hours worked by Ringo"),
    ("x1", "hours worked by Paul"),
    ("x2", "hours worked by Jean"),
    ("x3", "hours worked by George")
  ],
  "objective_function": "6.22*x0 + 7.73*x1 + 5.82*x2 + 2.73*x3",
  "constraints": [
    "1*x0 + 12*x3 >= 98",
    "15*x1 + 12*x3 >= 73",
    "1*x0 + 15*x1 >= 77",
    "1*x0 + 15*x1 + 12*x3 >= 90",
    "1*x0 + 15*x1 + 16*x2 + 12*x3 >= 90",
    "1*x2 + 15*x3 >= 44",
    "4*x0 + 1*x2 >= 47",
    "3*x1 + 1*x2 >= 68",
    "3*x1 + 15*x3 >= 46",
    "4*x0 + 3*x1 >= 68",
    "4*x0 + 3*x1 + 1*x2 + 15*x3 >= 68",
    "12*x2 + 12*x3 >= 43",
    "14*x0 + 9*x1 >= 48",
    "14*x0 + 12*x3 >= 20",
    "14*x0 + 9*x1 + 12*x2 >= 48",
    "14*x0 + 12*x2 + 12*x3 >= 48",
    "14*x0 + 9*x1 + 12*x3 >= 48",
    "14*x0 + 9*x1 + 12*x2 >= 47",
    "14*x0 + 12*x2 + 12*x3 >= 47",
    "14*x0 + 9*x1 + 12*x3 >= 47",
    "14*x0 + 9*x1 + 12*x2 >= 44",
    "14*x0 + 12*x2 + 12*x3 >= 44",
    "14*x0 + 9*x1 + 12*x3 >= 44",
    "14*x0 + 9*x1 + 12*x2 + 12*x3 >= 44",
    "9*x2 + 8*x3 >= 20",
    "2*x0 + 13*x1 >= 33",
    "2*x0 + 8*x3 >= 53",
    "2*x0 + 9*x2 >= 21",
    "13*x1 + 9*x2 >= 54",
    "2*x0 + 13*x1 + 8*x3 >= 43",
    "2*x0 + 13*x1 + 9*x2 + 8*x3 >= 43",
    "2*x2 + 16*x3 >= 49",
    "14*x1 + 2*x2 >= 26",
    "14*x1 + 16*x3 >= 37",
    "3*x0 + 16*x3 >= 28",
    "3*x0 + 14*x1 + 2*x2 + 16*x3 >= 28",
    "8*x1 - 6*x3 >= 0",
    "8*x2 - 4*x3 >= 0",
    "15*x1 + 16*x2 <= 159",
    "4*x0 + 1*x2 <= 150",
    "1*x2 + 15*x3 <= 160",
    "3*x1 + 1*x2 <= 299",
    "4*x0 + 3*x1 <= 286",
    "3*x1 + 15*x3 <= 161",
    "4*x0 + 3*x1 + 15*x3 <= 221",
    "9*x1 + 12*x2 <= 55",
    "14*x0 + 12*x3 <= 110",
    "14*x0 + 9*x1 <= 63",
    "2*x0 + 13*x1 <= 72",
    "13*x1 + 8*x3 <= 62",
    "2*x0 + 9*x2 <= 235",
    "2*x0 + 9*x2 + 8*x3 <= 226",
    "2*x0 + 13*x1 + 8*x3 <= 85",
    "2*x0 + 13*x1 + 9*x2 <= 125",
    "2*x2 + 16*x3 <= 206"
  ]
}
```

```python
import gurobipy as gp

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

    # Create variables
    ringo = m.addVar(lb=0, name="ringo")
    paul = m.addVar(lb=0, name="paul")
    jean = m.addVar(lb=0, name="jean")
    george = m.addVar(lb=0, name="george")


    # Set objective function
    m.setObjective(6.22 * ringo + 7.73 * paul + 5.82 * jean + 2.73 * george, gp.GRB.MINIMIZE)

    # Add constraints
    m.addConstr(1 * ringo + 12 * george >= 98)
    m.addConstr(15 * paul + 12 * george >= 73)
    m.addConstr(1 * ringo + 15 * paul >= 77)
    m.addConstr(1 * ringo + 15 * paul + 12 * george >= 90)
    m.addConstr(1 * ringo + 15 * paul + 16 * jean + 12 * george >= 90)
    m.addConstr(1 * jean + 15 * george >= 44)
    m.addConstr(4 * ringo + 1 * jean >= 47)
    m.addConstr(3 * paul + 1 * jean >= 68)
    m.addConstr(3 * paul + 15 * george >= 46)
    m.addConstr(4 * ringo + 3 * paul >= 68)
    m.addConstr(4 * ringo + 3 * paul + 1 * jean + 15 * george >= 68)
    m.addConstr(12 * jean + 12 * george >= 43)
    m.addConstr(14 * ringo + 9 * paul >= 48)
    m.addConstr(14 * ringo + 12 * george >= 20)
    m.addConstr(14 * ringo + 9 * paul + 12 * jean >= 48)
    m.addConstr(14 * ringo + 12 * jean + 12 * george >= 48)
    m.addConstr(14 * ringo + 9 * paul + 12 * george >= 48)
    m.addConstr(14 * ringo + 9 * paul + 12 * jean >= 47)
    m.addConstr(14 * ringo + 12 * jean + 12 * george >= 47)
    m.addConstr(14 * ringo + 9 * paul + 12 * george >= 47)
    m.addConstr(14 * ringo + 9 * paul + 12 * jean >= 44)
    m.addConstr(14 * ringo + 12 * jean + 12 * george >= 44)
    m.addConstr(14 * ringo + 9 * paul + 12 * george >= 44)
    m.addConstr(14 * ringo + 9 * paul + 12 * jean + 12 * george >= 44)
    m.addConstr(9 * jean + 8 * george >= 20)
    m.addConstr(2 * ringo + 13 * paul >= 33)
    m.addConstr(2 * ringo + 8 * george >= 53)
    m.addConstr(2 * ringo + 9 * jean >= 21)
    m.addConstr(13 * paul + 9 * jean >= 54)
    m.addConstr(2 * ringo + 13 * paul + 8 * george >= 43)
    m.addConstr(2 * ringo + 13 * paul + 9 * jean + 8 * george >= 43)
    m.addConstr(2 * jean + 16 * george >= 49)
    m.addConstr(14 * paul + 2 * jean >= 26)
    m.addConstr(14 * paul + 16 * george >= 37)
    m.addConstr(3 * ringo + 16 * george >= 28)
    m.addConstr(3 * ringo + 14 * paul + 2 * jean + 16 * george >= 28)
    m.addConstr(8 * paul - 6 * george >= 0)
    m.addConstr(8 * jean - 4 * george >= 0)
    m.addConstr(15 * paul + 16 * jean <= 159)
    m.addConstr(4 * ringo + 1 * jean <= 150)
    m.addConstr(1 * jean + 15 * george <= 160)
    m.addConstr(3 * paul + 1 * jean <= 299)
    m.addConstr(4 * ringo + 3 * paul <= 286)
    m.addConstr(3 * paul + 15 * george <= 161)
    m.addConstr(4 * ringo + 3 * paul + 15 * george <= 221)
    m.addConstr(9 * paul + 12 * jean <= 55)
    m.addConstr(14 * ringo + 12 * george <= 110)
    m.addConstr(14 * ringo + 9 * paul <= 63)
    m.addConstr(2 * ringo + 13 * paul <= 72)
    m.addConstr(13 * paul + 8 * george <= 62)
    m.addConstr(2 * ringo + 9 * jean <= 235)
    m.addConstr(2 * ringo + 9 * jean + 8 * george <= 226)
    m.addConstr(2 * ringo + 13 * paul + 8 * george <= 85)
    m.addConstr(2 * ringo + 13 * paul + 9 * jean <= 125)
    m.addConstr(2 * jean + 16 * george <= 206)


    # Optimize model
    m.optimize()

    if m.status == gp.GRB.OPTIMAL:
        print('Obj: %g' % m.objVal)
        for v in m.getVars():
            print('%s %g' % (v.varName, v.x))
    elif m.status == gp.GRB.INFEASIBLE:
        print('Model is infeasible')
    else:
        print('Optimization ended with status %d' % m.status)



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

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