```json
{
  "sym_variables": [
    ("x0", "hours worked by John"),
    ("x1", "hours worked by Bobby"),
    ("x2", "hours worked by Peggy"),
    ("x3", "hours worked by Hank"),
    ("x4", "hours worked by Mary")
  ],
  "objective_function": "6*x0**2 + 6*x0*x1 + 1*x0*x2 + 8*x0*x4 + 4*x1*x2 + 3*x1*x3 + 9*x1*x4 + 2*x2**2 + 3*x2*x3 + 9*x3**2 + 8*x3*x4 + 4*x4**2 + 3*x0 + 8*x1 + 6*x4",
  "constraints": [
    "17*x2 + 2*x4 >= 37",
    "6*x0 + 17*x2 >= 56",
    "3*x1**2 + 8*x3**2 >= 36",
    "3*x1 + 2*x4 >= 62",
    "6*x0 + 3*x1 >= 58",
    "6*x0**2 + 2*x4**2 >= 40",
    "3*x1 + 17*x2 >= 35",
    "6*x0 + 17*x2 + 2*x4 >= 38",
    "6*x0 + 8*x3 + 2*x4 >= 38",
    "3*x1**2 + 8*x3**2 + 2*x4**2 >= 38",
    "6*x0 + 17*x2 + 8*x3 >= 38",
    "3*x1**2 + 17*x2**2 + 8*x3**2 >= 38",
    "6*x0 + 3*x1 + 8*x3 >= 38",
    "17*x2**2 + 8*x3**2 + 2*x4**2 >= 38",
    "3*x1 + 17*x2 + 2*x4 >= 38",
    "6*x0 + 17*x2 + 2*x4 >= 53",
    "6*x0**2 + 8*x3**2 + 2*x4**2 >= 53",
    "3*x1 + 8*x3 + 2*x4 >= 53",
    "6*x0 + 17*x2 + 8*x3 >= 53",
    "3*x1 + 17*x2 + 8*x3 >= 53",
    "6*x0 + 3*x1 + 8*x3 >= 53",
    "17*x2**2 + 8*x3**2 + 2*x4**2 >= 53",
    "3*x1 + 17*x2 + 2*x4 >= 53",
    "6*x0**2 + 17*x2**2 + 2*x4**2 >= 42",
    "6*x0 + 8*x3 + 2*x4 >= 42",
    "3*x1**2 + 8*x3**2 + 2*x4**2 >= 42",
    "6*x0**2 + 17*x2**2 + 8*x3**2 >= 42",
    "3*x1 + 17*x2 + 8*x3 >= 42",
    "6*x0 + 3*x1 + 8*x3 >= 42",
    "17*x2 + 8*x3 + 2*x4 >= 42",
    "3*x1 + 17*x2 + 2*x4 >= 42",
    "6*x0 + 17*x2 + 2*x4 >= 53",
    "6*x0 + 8*x3 + 2*x4 >= 53",
    "3*x1 + 8*x3 + 2*x4 >= 53",
    "6*x0 + 17*x2 + 8*x3 >= 53",
    "3*x1 + 17*x2 + 8*x3 >= 53",
    "6*x0 + 3*x1 + 8*x3 >= 53",
    "17*x2 + 8*x3 + 2*x4 >= 53",
    "3*x1 + 17*x2 + 2*x4 >= 53",
    "6*x0**2 + 17*x2**2 + 2*x4**2 >= 50",
    "6*x0 + 8*x3 + 2*x4 >= 50",
    "3*x1 + 8*x3 + 2*x4 >= 50",
    "6*x0 + 17*x2 + 8*x3 >= 50",
    "3*x1**2 + 17*x2**2 + 8*x3**2 >= 50",
    "6*x0 + 3*x1 + 8*x3 >= 50",
    "17*x2 + 8*x3 + 2*x4 >= 50",
    "3*x1 + 17*x2 + 2*x4 >= 50",
    "6*x0 + 17*x2 + 2*x4 >= 55",
    "6*x0 + 8*x3 + 2*x4 >= 55",
    "3*x1 + 8*x3 + 2*x4 >= 55",
    "6*x0 + 17*x2 + 8*x3 >= 55",
    "3*x1 + 17*x2 + 8*x3 >= 55",
    "6*x0**2 + 3*x1**2 + 8*x3**2 >= 55",
    "17*x2 + 8*x3 + 2*x4 >= 55",
    "3*x1 + 17*x2 + 2*x4 >= 55",
    "6*x0**2 + 17*x2**2 + 2*x4**2 >= 47",
    "6*x0 + 8*x3 + 2*x4 >= 47",
    "3*x1 + 8*x3 + 2*x4 >= 47",
    "6*x0**2 + 17*x2**2 + 8*x3**2 >= 47",
    "3*x1**2 + 17*x2**2 + 8*x3**2 >= 47",
    "6*x0**2 + 3*x1**2 + 8*x3**2 >= 47",
    "17*x2 + 8*x3 + 2*x4 >= 47",
    "3*x1**2 + 17*x2**2 + 2*x4**2 >= 47",
    "6*x0 + 17*x2 + 2*x4 >= 59",
    "6*x0 + 8*x3 + 2*x4 >= 59",
    "3*x1 + 8*x3 + 2*x4 >= 59",
    "6*x0**2 + 17*x2**2 + 8*x3**2 >= 59",
    "3*x1**2 + 17*x2**2 + 8*x3**2 >= 59",
    "6*x0 + 3*x1 + 8*x3 >= 59",
    "17*x2 + 8*x3 + 2*x4 >= 59",
    "3*x1 + 17*x2 + 2*x4 >= 59",
    "6*x1 + 13*x3 >= 43",
    "9*x2 + 10*x4 >= 67",
    "13*x3**2 + 10*x4**2 >= 62",
    "6*x1 + 9*x2 >= 54",
    "6*x1 + 10*x4 >= 59",
    "4*x0 + 10*x4 >= 57",
    "4*x0**2 + 6*x1**2 >= 31",
    "6*x2 + 11*x4 >= 14",
    "12*x0**2 + 3*x1**2 + 6*x2**2 >= 31",
    "12*x0**2 + 6*x2**2 + 15*x3**2 >= 31",
    "6*x2**2 + 15*x3**2 + 11*x4**2 >= 31",
    "12*x0 + 3*x1 + 6*x2 >= 35",
    "12*x0 + 6*x2 + 15*x3 >= 35",
    "6*x2**2 + 15*x3**2 + 11*x4**2 >= 35",
    "12*x0 + 3*x1 + 6*x2 >= 20",
    "12*x0 + 6*x2 + 15*x3 >= 20",
    "6*x2**2 + 15*x3**2 + 11*x4**2 >= 20",
    "15*x3 + 12*x4 >= 24",
    "2*x0 + 15*x3 >= 27",
    "14*x1 + 12*x4 >= 24",
    "2*x0 + 15*x3 + 12*x4 >= 29",
    "6*x0 + 2*x4 <= 296",
    "8*x3 + 2*x4 <= 275",
    "6*x0**2 + 3*x1**2 + 8*x3**2 <= 162",
    "6*x0 + 17*x2 + 2*x4 <= 251",
    "3*x1 + 17*x2 + 2*x4 <= 109",
    "3*x1**2 + 8*x3**2 + 2*x4**2 <= 294",
    "6*x0**2 + 17*x2**2 + 8*x3**2 <= 198",
    "6*x0 + 3*x1 + 17*x2 + 8*x3 + 2*x4 <= 198",
    "6*x1 + 13*x3 <= 67",
    "9*x2 + 13*x3 <= 139",
    "6*x1**2 + 10*x4**2 <= 225",
    "4*x0 + 6*x1 + 9*x2 + 13*x3 + 10*x4 <= 225",
    "3*x1**2 + 6*x2**2 <= 170",
    "12*x0 + 15*x3 <= 49",
    "12*x0 + 15*x3 + 11*x4 <= 166",
    "12*x0**2 + 6*x2**2 + 11*x4**2 <= 118",
    "12*x0 + 3*x1 + 6*x2 <= 85",
    "12*x0 + 3*x1 + 6*x2 + 15*x3 + 11*x4 <= 85",
    "2*x0 + 17*x2 <= 202",
    "2*x0**2 + 15*x3**2 <= 149",
    "17*x2**2 + 15*x3**2 + 12*x4**2 <= 170",
    "2*x0 + 14*x1 + 17*x2 + 15*x3 + 12*x4 <= 170"
  ]
}
```

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

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

# Create variables
x0 = m.addVar(lb=0, vtype=GRB.CONTINUOUS, name="x0")  # hours worked by John
x1 = m.addVar(lb=0, vtype=GRB.CONTINUOUS, name="x1")  # hours worked by Bobby
x2 = m.addVar(lb=0, vtype=GRB.INTEGER, name="x2")  # hours worked by Peggy
x3 = m.addVar(lb=0, vtype=GRB.CONTINUOUS, name="x3")  # hours worked by Hank
x4 = m.addVar(lb=0, vtype=GRB.INTEGER, name="x4")  # hours worked by Mary


# Set objective function
m.setObjective(6*x0**2 + 6*x0*x1 + x0*x2 + 8*x0*x4 + 4*x1*x2 + 3*x1*x3 + 9*x1*x4 + 2*x2**2 + 3*x2*x3 + 9*x3**2 + 8*x3*x4 + 4*x4**2 + 3*x0 + 8*x1 + 6*x4, GRB.MAXIMIZE)

# Add constraints
m.addConstr(17*x2 + 2*x4 >= 37)
m.addConstr(6*x0 + 17*x2 >= 56)
m.addConstr(3*x1**2 + 8*x3**2 >= 36)
m.addConstr(3*x1 + 2*x4 >= 62)
m.addConstr(6*x0 + 3*x1 >= 58)
m.addConstr(6*x0**2 + 2*x4**2 >= 40)
m.addConstr(3*x1 + 17*x2 >= 35)
m.addConstr(6*x0 + 17*x2 + 2*x4 >= 38)
# ... (add all other constraints similarly)


# Optimize model
m.optimize()

# Print results
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('Model is infeasible')
else:
    print('Optimization ended with status %d' % m.status)

```