```json
{
  "sym_variables": [
    ("x0", "slices of pizza"),
    ("x1", "cherry pies"),
    ("x2", "peanutbutter sandwiches"),
    ("x3", "protein bars")
  ],
  "objective_function": "8*x0*x1 + 8*x1**2 + 9*x2**2 + 1*x2",
  "constraints": [
    "8*x0 + 15*x1 + 10*x2 + 18*x3 <= 255",
    "6*x0 + 5*x1 + 14*x2 + 24*x3 <= 271",
    "3*x0 + 8*x1 + 1*x2 + 15*x3 <= 146",
    "10*x2**2 + 18*x3**2 >= 42",
    "8*x0 + 18*x3 >= 37",
    "8*x0 + 15*x1 >= 21",
    "8*x0 + 15*x1 + 10*x2 + 18*x3 >= 21",
    "6*x0 + 5*x1 >= 30",
    "6*x0**2 + 24*x3**2 >= 50",
    "14*x2 + 24*x3 >= 41",
    "6*x0 + 14*x2 >= 49",
    "6*x0 + 5*x1 + 14*x2 + 24*x3 >= 49",
    "3*x0**2 + 1*x2**2 >= 19",
    "3*x0 + 8*x1 >= 15",
    "8*x1**2 + 15*x3**2 >= 22",
    "3*x0 + 8*x1 + 1*x2 + 15*x3 >= 22",
    "4*x0**2 - 7*x2**2 >= 0",
    "15*x1 + 18*x3 <= 223",
    "8*x0 + 18*x3 <= 182",
    "8*x0**2 + 10*x2**2 <= 85",
    "10*x2**2 + 18*x3**2 <= 189",
    "15*x1**2 + 10*x2**2 <= 159",
    "8*x0 + 15*x1 <= 140",
    "8*x0 + 10*x2 + 18*x3 <= 241",
    "15*x1 + 10*x2 + 18*x3 <= 130",
    "8*x0 + 15*x1 + 18*x3 <= 231",
    "8*x0 + 15*x1 + 10*x2 <= 216",
    "6*x0 + 14*x2 <= 139",
    "6*x0 + 5*x1 <= 110",
    "5*x1**2 + 14*x2**2 <= 200",
    "6*x0 + 24*x3 <= 239",
    "6*x0 + 5*x1 + 24*x3 <= 156",
    "8*x1 + 15*x3 <= 86"
  ]
}
```

```python
import gurobipy as gp

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

    # Create variables
    pizza = m.addVar(lb=0, vtype=gp.GRB.CONTINUOUS, name="pizza")
    pies = m.addVar(lb=0, vtype=gp.GRB.CONTINUOUS, name="pies")
    sandwiches = m.addVar(lb=0, vtype=gp.GRB.INTEGER, name="sandwiches")
    bars = m.addVar(lb=0, vtype=gp.GRB.INTEGER, name="bars")

    # Set objective function
    m.setObjective(8*pizza*pies + 8*pies**2 + 9*sandwiches**2 + sandwiches, gp.GRB.MINIMIZE)

    # Add constraints
    m.addConstr(8*pizza + 15*pies + 10*sandwiches + 18*bars <= 255, "dollar_cost")
    m.addConstr(6*pizza + 5*pies + 14*sandwiches + 24*bars <= 271, "calcium")
    m.addConstr(3*pizza + 8*pies + sandwiches + 15*bars <= 146, "protein")
    m.addConstr(10*sandwiches**2 + 18*bars**2 >= 42, "c4")
    m.addConstr(8*pizza + 18*bars >= 37, "c5")
    m.addConstr(8*pizza + 15*pies >= 21, "c6")
    m.addConstr(8*pizza + 15*pies + 10*sandwiches + 18*bars >= 21, "c7")
    m.addConstr(6*pizza + 5*pies >= 30, "c8")
    m.addConstr(6*pizza**2 + 24*bars**2 >= 50, "c9")
    m.addConstr(14*sandwiches + 24*bars >= 41, "c10")
    m.addConstr(6*pizza + 14*sandwiches >= 49, "c11")
    m.addConstr(6*pizza + 5*pies + 14*sandwiches + 24*bars >= 49, "c12")
    m.addConstr(3*pizza**2 + sandwiches**2 >= 19, "c13")
    m.addConstr(3*pizza + 8*pies >= 15, "c14")
    m.addConstr(8*pies**2 + 15*bars**2 >= 22, "c15")
    m.addConstr(3*pizza + 8*pies + sandwiches + 15*bars >= 22, "c16")
    m.addConstr(4*pizza**2 - 7*sandwiches**2 >= 0, "c17")
    m.addConstr(15*pies + 18*bars <= 223, "c18")
    m.addConstr(8*pizza + 18*bars <= 182, "c19")
    m.addConstr(8*pizza**2 + 10*sandwiches**2 <= 85, "c20")
    m.addConstr(10*sandwiches**2 + 18*bars**2 <= 189, "c21")
    m.addConstr(15*pies**2 + 10*sandwiches**2 <= 159, "c22")
    m.addConstr(8*pizza + 15*pies <= 140, "c23")
    m.addConstr(8*pizza + 10*sandwiches + 18*bars <= 241, "c24")
    m.addConstr(15*pies + 10*sandwiches + 18*bars <= 130, "c25")
    m.addConstr(8*pizza + 15*pies + 18*bars <= 231, "c26")
    m.addConstr(8*pizza + 15*pies + 10*sandwiches <= 216, "c27")
    m.addConstr(6*pizza + 14*sandwiches <= 139, "c28")
    m.addConstr(6*pizza + 5*pies <= 110, "c29")
    m.addConstr(5*pies**2 + 14*sandwiches**2 <= 200, "c30")
    m.addConstr(6*pizza + 24*bars <= 239, "c31")
    m.addConstr(6*pizza + 5*pies + 24*bars <= 156, "c32")
    m.addConstr(8*pies + 15*bars <= 86, "c33")


    # Optimize model
    m.optimize()

    if m.status == gp.GRB.OPTIMAL:
        print('Obj: %g' % m.objVal)
        print('pizza:', pizza.x)
        print('pies:', pies.x)
        print('sandwiches:', sandwiches.x)
        print('bars:', bars.x)
    elif m.status == gp.GRB.INFEASIBLE:
        print('Optimization problem is infeasible.')


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

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