```json
{
  "sym_variables": [
    ("x0", "hours worked by Jean"),
    ("x1", "hours worked by Ringo"),
    ("x2", "hours worked by John"),
    ("x3", "hours worked by Paul")
  ],
  "objective_function": "7.17 * x0 + 7.08 * x1 + 7.84 * x2 + 7.77 * x3",
  "constraints": [
    "1.75 * x1 + 11.48 * x2 + 6.79 * x3 >= 21",
    "3.56 * x0 + 1.75 * x1 + 11.48 * x2 >= 21",
    "3.56 * x0 + 11.48 * x2 + 6.79 * x3 >= 21",
    "1.75 * x1 + 11.48 * x2 + 6.79 * x3 >= 39",
    "3.56 * x0 + 1.75 * x1 + 11.48 * x2 >= 39",
    "3.56 * x0 + 11.48 * x2 + 6.79 * x3 >= 39",
    "1.75 * x1 + 11.48 * x2 + 6.79 * x3 >= 30",
    "3.56 * x0 + 1.75 * x1 + 11.48 * x2 >= 30",
    "3.56 * x0 + 11.48 * x2 + 6.79 * x3 >= 30",
    "1.29 * x2 + 6.69 * x3 >= 22",
    "9.02 * x0 + 15.5 * x1 + 1.29 * x2 >= 24",
    "9.02 * x0 + 15.5 * x1 + 6.69 * x3 >= 24",
    "9.02 * x0 + 15.5 * x1 + 1.29 * x2 >= 21",
    "9.02 * x0 + 15.5 * x1 + 6.69 * x3 >= 21",
    "3.56 * x0 + 6.79 * x3 <= 106",
    "1.75 * x1 + 11.48 * x2 + 6.79 * x3 <= 164",
    "3.56 * x0 + 1.75 * x1 + 6.79 * x3 <= 157",
    "3.56 * x0 + 1.75 * x1 + 11.48 * x2 + 6.79 * x3 <= 157",
    "15.5 * x1 + 6.69 * x3 <= 81",
    "9.02 * x0 + 6.69 * x3 <= 87",
    "15.5 * x1 + 1.29 * x2 + 6.69 * x3 <= 66",
    "9.02 * x0 + 15.5 * x1 + 1.29 * x2 <= 81",
    "9.02 * x0 + 15.5 * x1 + 6.69 * x3 <= 50",
    "9.02 * x0 + 15.5 * x1 + 1.29 * x2 + 6.69 * x3 <= 50"
  ]
}
```

```python
import gurobipy as gp

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

# Create variables
jean = m.addVar(lb=0, vtype=gp.GRB.CONTINUOUS, name="Jean")
ringo = m.addVar(lb=0, vtype=gp.GRB.CONTINUOUS, name="Ringo")
john = m.addVar(lb=0, vtype=gp.GRB.CONTINUOUS, name="John")
paul = m.addVar(lb=0, vtype=gp.GRB.CONTINUOUS, name="Paul")


# Set objective function
m.setObjective(7.17 * jean + 7.08 * ringo + 7.84 * john + 7.77 * paul, gp.GRB.MAXIMIZE)

# Add constraints
m.addConstr(1.75 * ringo + 11.48 * john + 6.79 * paul >= 21)
m.addConstr(3.56 * jean + 1.75 * ringo + 11.48 * john >= 21)
m.addConstr(3.56 * jean + 11.48 * john + 6.79 * paul >= 21)
m.addConstr(1.75 * ringo + 11.48 * john + 6.79 * paul >= 39)
m.addConstr(3.56 * jean + 1.75 * ringo + 11.48 * john >= 39)
m.addConstr(3.56 * jean + 11.48 * john + 6.79 * paul >= 39)
m.addConstr(1.75 * ringo + 11.48 * john + 6.79 * paul >= 30)
m.addConstr(3.56 * jean + 1.75 * ringo + 11.48 * john >= 30)
m.addConstr(3.56 * jean + 11.48 * john + 6.79 * paul >= 30)
m.addConstr(1.29 * john + 6.69 * paul >= 22)
m.addConstr(9.02 * jean + 15.5 * ringo + 1.29 * john >= 24)
m.addConstr(9.02 * jean + 15.5 * ringo + 6.69 * paul >= 24)
m.addConstr(9.02 * jean + 15.5 * ringo + 1.29 * john >= 21)
m.addConstr(9.02 * jean + 15.5 * ringo + 6.69 * paul >= 21)
m.addConstr(3.56 * jean + 6.79 * paul <= 106)
m.addConstr(1.75 * ringo + 11.48 * john + 6.79 * paul <= 164)
m.addConstr(3.56 * jean + 1.75 * ringo + 6.79 * paul <= 157)
m.addConstr(3.56 * jean + 1.75 * ringo + 11.48 * john + 6.79 * paul <= 157)
m.addConstr(15.5 * ringo + 6.69 * paul <= 81)
m.addConstr(9.02 * jean + 6.69 * paul <= 87)
m.addConstr(15.5 * ringo + 1.29 * john + 6.69 * paul <= 66)
m.addConstr(9.02 * jean + 15.5 * ringo + 1.29 * john <= 81)
m.addConstr(9.02 * jean + 15.5 * ringo + 6.69 * paul <= 50)
m.addConstr(9.02 * jean + 15.5 * ringo + 1.29 * john + 6.69 * paul <= 50)


# Optimize model
m.optimize()

# Print results
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("The problem is infeasible.")
else:
    print("The problem could not be solved to optimality.")

```
