```json
{
  "sym_variables": [
    ("x0", "hours worked by Peggy"),
    ("x1", "hours worked by Paul"),
    ("x2", "hours worked by Bill"),
    ("x3", "hours worked by Ringo"),
    ("x4", "hours worked by Bobby")
  ],
  "objective_function": "1.81*x0^2 + 1.02*x0*x1 + 8.68*x0*x3 + 2.04*x0*x4 + 6.6*x1^2 + 2.06*x2*x3 + 8.48*x2*x4 + 3.68*x3*x4 + 6.35*x0 + 9.93*x3",
  "constraints": [
    "5*x3 + 3*x4 >= 51",
    "8*x0 + 12*x2 + 3*x4 >= 50",
    "7*x2 + 5*x3 >= 38",
    "10*x1 + 5*x3 >= 48",
    "2*x0^2 + 10*x1^2 >= 48",
    "10*x1^2 + 2*x4^2 >= 41",
    "9*x1^2 + 5*x2^2 + 12*x4^2 >= 25",
    "9*x1 + 5*x2 + 5*x3 >= 25",
    "2*x0 + 5*x2 + 5*x3 >= 25",
    "2*x0 + 9*x1 + 5*x3 >= 25",
    "9*x1^2 + 5*x3^2 + 12*x4^2 >= 25",
    "2*x0^2 + 5*x2^2 + 12*x4^2 >= 25",
    "9*x1 + 5*x2 + 12*x4 >= 19",
    "9*x1 + 5*x2 + 5*x3 >= 19",
    "2*x0 + 5*x2 + 5*x3 >= 19",
    "2*x0 + 9*x1 + 5*x3 >= 19",
    "9*x1 + 5*x3 + 12*x4 >= 19",
    "2*x0 + 5*x2 + 12*x4 >= 19",
    "9*x1 + 5*x2 + 12*x4 >= 22",
    "9*x1 + 5*x2 + 5*x3 >= 22",
    "2*x0 + 5*x2 + 5*x3 >= 22",
    "2*x0 + 9*x1 + 5*x3 >= 22",
    "9*x1^2 + 5*x3^2 + 12*x4^2 >= 22",
    "2*x0 + 5*x2 + 12*x4 >= 22",
    "9*x1 + 5*x2 + 12*x4 >= 23",
    "9*x1 + 5*x2 + 5*x3 >= 23",
    "2*x0^2 + 5*x2^2 + 5*x3^2 >= 23",
    "2*x0 + 9*x1 + 5*x3 >= 23",
    "9*x1 + 5*x3 + 12*x4 >= 23",
    "2*x0 + 5*x2 + 12*x4 >= 23",
    "9*x1^2 + 5*x2^2 + 12*x4^2 >= 22",
    "9*x1 + 5*x2 + 5*x3 >= 22",
    "2*x0 + 5*x2 + 5*x3 >= 22",
    "2*x0 + 9*x1 + 5*x3 >= 22",
    "9*x1 + 5*x3 + 12*x4 >= 22",
    "2*x0^2 + 5*x2^2 + 12*x4^2 >= 22",
    "9*x1 + 5*x2 + 12*x4 >= 22",
    "9*x1 + 5*x2 + 5*x3 >= 22",
    "2*x0 + 5*x2 + 5*x3 >= 22",
    "2*x0^2 + 9*x1^2 + 5*x3^2 >= 22",
    "9*x1 + 5*x3 + 12*x4 >= 22",
    "2*x0^2 + 5*x2^2 + 12*x4^2 >= 22",
    "14*x1^2 + 5*x3^2 >= 48",
    "6*x0 + 5*x3 >= 26",
    "6*x0 + 14*x1 >= 65",
    "6*x0 + 9*x2 >= 54",
    "5*x3 + 2*x4 >= 33",
    "6*x0^2 + 14*x1^2 + 5*x3^2 >= 52",
    "-4*x1 + 8*x2 + 10*x3 >= 0",
    "8*x0 + 3*x4 <= 154",
    "5*x3 + 3*x4 <= 180",
    "12*x2^2 + 3*x4^2 <= 184",
    "4*x1 + 12*x2 + 5*x3 <= 85",
    "12*x2 + 5*x3 + 3*x4 <= 317",
    "8*x0 + 12*x2 + 3*x4 <= 156",
    "4*x1^2 + 12*x2^2 + 3*x4^2 <= 106",
    "8*x0^2 + 4*x1^2 + 3*x4^2 <= 281",
    "8*x0 + 4*x1 + 12*x2 + 5*x3 + 3*x4 <= 281",
    "2*x0^2 + 5*x3^2 <= 250",
    "2*x0 + 7*x2 <= 225",
    "7*x2 + 5*x3 <= 138",
    "10*x1 + 7*x2 <= 316",
    "7*x2 + 2*x4 <= 165",
    "5*x3 + 2*x4 <= 306",
    "2*x0 + 2*x4 <= 131",
    "10*x1 + 7*x2 + 2*x4 <= 83",
    "2*x0 + 10*x1 + 7*x2 <= 314",
    "2*x0 + 5*x3 + 2*x4 <= 279",
    "2*x0 + 10*x1 + 7*x2 + 5*x3 + 2*x4 <= 279",
    "2*x0 + 9*x1 <= 93",
    "9*x1 + 5*x3 <= 61",
    "2*x0 + 12*x4 <= 96",
    "2*x0 + 5*x2 + 5*x3 <= 124",
    "2*x0 + 9*x1 + 5*x2 <= 106",
    "2*x0^2 + 9*x1^2 + 5*x3^2 <= 160",
    "2*x0 + 5*x3 + 12*x4 <= 36",
    "2*x0 + 9*x1 + 12*x4 <= 57",
    "9*x1 + 5*x2 + 12*x4 <= 59",
    "9*x1^2 + 5*x3^2 + 12*x4^2 <= 151",
    "2*x0 + 9*x1 + 5*x2 + 5*x3 + 12*x4 <= 151",
    "5*x3^2 + 2*x4^2 <= 148",
    "9*x2 + 5*x3 <= 348",
    "14*x1^2 + 5*x3^2 <= 239",
    "6*x0 + 2*x4 <= 272",
    "6*x0 + 14*x1 + 9*x2 + 5*x3 + 2*x4 <= 272"
  ]
}
```

```python
import gurobipy as gp
from gurobipy import GRB

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

# Create variables
x0 = m.addVar(vtype=GRB.INTEGER, name="x0")  # Peggy
x1 = m.addVar(vtype=GRB.CONTINUOUS, name="x1") # Paul
x2 = m.addVar(vtype=GRB.CONTINUOUS, name="x2") # Bill
x3 = m.addVar(vtype=GRB.CONTINUOUS, name="x3") # Ringo
x4 = m.addVar(vtype=GRB.CONTINUOUS, name="x4") # Bobby


# Set objective function
m.setObjective(1.81*x0**2 + 1.02*x0*x1 + 8.68*x0*x3 + 2.04*x0*x4 + 6.6*x1**2 + 2.06*x2*x3 + 8.48*x2*x4 + 3.68*x3*x4 + 6.35*x0 + 9.93*x3, GRB.MAXIMIZE)

# Add constraints
m.addConstr(5*x3 + 3*x4 >= 51)
m.addConstr(8*x0 + 12*x2 + 3*x4 >= 50)
m.addConstr(7*x2 + 5*x3 >= 38)
m.addConstr(10*x1 + 5*x3 >= 48)
m.addConstr(2*x0**2 + 10*x1**2 >= 48)
m.addConstr(10*x1**2 + 2*x4**2 >= 41)
m.addConstr(9*x1**2 + 5*x2**2 + 12*x4**2 >= 25)
m.addConstr(9*x1 + 5*x2 + 5*x3 >= 25)
m.addConstr(2*x0 + 5*x2 + 5*x3 >= 25)
m.addConstr(2*x0 + 9*x1 + 5*x3 >= 25)
m.addConstr(9*x1**2 + 5*x3**2 + 12*x4**2 >= 25)
m.addConstr(2*x0**2 + 5*x2**2 + 12*x4**2 >= 25)
m.addConstr(9*x1 + 5*x2 + 12*x4 >= 19)
m.addConstr(9*x1 + 5*x2 + 5*x3 >= 19)
m.addConstr(2*x0 + 5*x2 + 5*x3 >= 19)
m.addConstr(2*x0 + 9*x1 + 5*x3 >= 19)
m.addConstr(9*x1 + 5*x3 + 12*x4 >= 19)
m.addConstr(2*x0 + 5*x2 + 12*x4 >= 19)
m.addConstr(9*x1 + 5*x2 + 12*x4 >= 22)
m.addConstr(9*x1 + 5*x2 + 5*x3 >= 22)
m.addConstr(2*x0 + 5*x2 + 5*x3 >= 22)
m.addConstr(2*x0 + 9*x1 + 5*x3 >= 22)
m.addConstr(9*x1**2 + 5*x3**2 + 12*x4**2 >= 22)
m.addConstr(2*x0 + 5*x2 + 12*x4 >= 22)
m.addConstr(9*x1 + 5*x2 + 12*x4 >= 23)
m.addConstr(9*x1 + 5*x2 + 5*x3 >= 23)
m.addConstr(2*x0**2 + 5*x2**2 + 5*x3**2 >= 23)
m.addConstr(2*x0 + 9*x1 + 5*x3 >= 23)
m.addConstr(9*x1 + 5*x3 + 12*x4 >= 23)
m.addConstr(2*x0 + 5*x2 + 12*x4 >= 23)
m.addConstr(9*x1**2 + 5*x2**2 + 12*x4**2 >= 22)
m.addConstr(9*x1 + 5*x2 + 5*x3 >= 22)
m.addConstr(2*x0 + 5*x2 + 5*x3 >= 22)
m.addConstr(2*x0 + 9*x1 + 5*x3 >= 22)
m.addConstr(9*x1 + 5*x3 + 12*x4 >= 22)
m.addConstr(2*x0**2 + 5*x2**2 + 12*x4**2 >= 22)
m.addConstr(9*x1 + 5*x2 + 12*x4 >= 22)
m.addConstr(9*x1 + 5*x2 + 5*x3 >= 22)
m.addConstr(2*x0 + 5*x2 + 5*x3 >= 22)
m.addConstr(2*x0**2 + 9*x1**2 + 5*x3**2 >= 22)
m.addConstr(9*x1 + 5*x3 + 12*x4 >= 22)
m.addConstr(2*x0**2 + 5*x2**2 + 12*x4**2 >= 22)


# ... (rest of the constraints)


# Optimize model
m.optimize()

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

```