```json
{
  "sym_variables": [
    ("x0", "peanutbutter sandwiches"),
    ("x1", "bagged salads"),
    ("x2", "granola bars"),
    ("x3", "blueberry pies"),
    ("x4", "oranges"),
    ("x5", "apple pies")
  ],
  "objective_function": "4*x0**2 + 4*x0*x4 + 8*x1**2 + 7*x1*x5 + 4*x2**2 + 4*x2*x4 + 3*x2*x5 + 4*x3*x4 + 6*x4**2 + 2*x5**2 + 9*x2 + 2*x3 + 9*x4",
  "constraints": [
    "5*x0 + 15*x1 + 3*x2 + 8*x3 + 15*x4 + 13*x5 <= 520",
    "5*x0 + 8*x1 + 3*x2 + 8*x3 + 13*x4 + 16*x5 <= 212",
    "14*x0 + 16*x1 + 7*x2 + 9*x3 + 1*x4 + 1*x5 <= 554",
    "8*x3 + 15*x4 >= 76",
    "3*x2 + 15*x4 >= 31",
    "15*x4 + 13*x5 >= 49",
    "3*x2**2 + 8*x3**2 >= 50",
    "3*x2 + 13*x5 >= 34",
    "5*x0**2 + 15*x1**2 >= 44",
    "5*x0 + 3*x2 >= 48",
    "15*x1 + 8*x3 >= 43",
    "5*x0 + 3*x2 + 13*x5 >= 54",
    "5*x0 + 15*x1 + 15*x4 >= 54",
    "5*x0 + 15*x1 + 13*x5 >= 54",
    "5*x0 + 15*x4 + 13*x5 >= 54",
    "5*x0 + 15*x1 + 8*x3 >= 54",
    "5*x0**2 + 3*x2**2 + 13*x5**2 >= 43",
    "5*x0 + 15*x1 + 15*x4 >= 43",
    "5*x0**2 + 15*x1**2 + 13*x5**2 >= 43",
    "5*x0 + 15*x4 + 13*x5 >= 43",
    "5*x0 + 15*x1 + 8*x3 >= 43",
    "5*x0 + 3*x2 + 13*x5 >= 83",
    "5*x0**2 + 15*x1**2 + 15*x4**2 >= 83",
    "5*x0 + 15*x1 + 13*x5 >= 83",
    "5*x0 + 15*x4 + 13*x5 >= 83",
    "5*x0**2 + 15*x1**2 + 8*x3**2 >= 83",
    "5*x0 + 3*x2 + 13*x5 >= 65",
    "5*x0 + 15*x1 + 15*x4 >= 65",
    "5*x0 + 15*x1 + 13*x5 >= 65",
    "5*x0 + 15*x4 + 13*x5 >= 65",
    "5*x0 + 15*x1 + 8*x3 >= 65",
    "5*x0 + 3*x2 + 13*x5 >= 77",
    "5*x0 + 15*x1 + 15*x4 >= 77",
    "5*x0 + 15*x1 + 13*x5 >= 77",
    "5*x0 + 15*x4 + 13*x5 >= 77",
    "5*x0 + 15*x1 + 8*x3 >= 77",
    "5*x0 + 15*x1 + 3*x2 + 8*x3 + 15*x4 + 13*x5 >= 77",
    "8*x1 + 16*x5 >= 29",
    "3*x2 + 16*x5 >= 28",
    "3*x2**2 + 8*x3**2 >= 18",
    "8*x3 + 16*x5 >= 27",
    "5*x0 + 8*x3 >= 13",
    "8*x3**2 + 13*x4**2 >= 15",
    "8*x1 + 8*x3 + 16*x5 >= 23",
    "5*x0 + 8*x1 + 3*x2 + 8*x3 + 13*x4 + 16*x5 >= 23",
    "7*x2**2 + 1*x4**2 >= 41",
    "14*x0 + 1*x5 >= 69",
    "9*x3 + 1*x5 >= 52",
    "9*x3 + 1*x4 >= 62",
    "14*x0 + 16*x1 >= 46",
    "14*x0**2 + 7*x2**2 >= 33",
    "14*x0 + 9*x3 >= 82",
    "14*x0 + 16*x1 + 7*x2 + 9*x3 + 1*x4 + 1*x5 >= 82",
    "-9*x0 + 5*x5 >= 0",
    "-3*x1**2 + 7*x2**2 >= 0",
    "15*x4**2 + 13*x5**2 <= 237",
    "15*x1 + 3*x2 <= 179",
    "5*x0 + 15*x1 <= 205",
    "3*x2**2 + 8*x3**2 <= 132",
    "5*x0**2 + 15*x1**2 + 8*x3**2 <= 150",
    "3*x2 + 8*x3 + 13*x5 <= 465",
    "15*x1 + 3*x2 + 8*x3 <= 126",
    "15*x1**2 + 8*x3**2 + 15*x4**2 <= 467",
    "15*x1 + 15*x4 + 13*x5 <= 502",
    "8*x3 + 15*x4 + 13*x5 <= 315",
    "3*x2**2 + 8*x3**2 + 15*x4**2 <= 373",
    "5*x0**2 + 15*x1**2 + 3*x2**2 <= 440",
    "3*x2**2 + 15*x4**2 + 13*x5**2 <= 519",
    "3*x2 + 16*x5 <= 75",
    "5*x0 + 13*x4 <= 81",
    "8*x1**2 + 13*x4**2 <= 99",
    "8*x3 + 13*x4 <= 192",
    "13*x4 + 16*x5 <= 170",
    "5*x0 + 8*x3 <= 169",
    "3*x2**2 + 13*x4**2 <= 99",
    "3*x2 + 8*x3 <= 149",
    "8*x1 + 8*x3 <= 69",
    "8*x3 + 16*x5 <= 204",
    "8*x1 + 16*x5 <= 169",
    "5*x0**2 + 3*x2**2 + 13*x4**2 <= 55",
    "8*x1 + 8*x3 + 13*x4 <= 209",
    "9*x3 + 1*x5 <= 309",
    "16*x1 + 1*x5 <= 504",
    "1*x4 + 1*x5 <= 168",
    "7*x2 + 1*x4 <= 119",
    "x0 == int",
    "x1 == int",
    "x2 == int",
    "x3 == int",
    "x4 == int",
    "x5 == int"

  ]
}
```

```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="peanutbutter sandwiches")
x1 = m.addVar(vtype=GRB.INTEGER, name="bagged salads")
x2 = m.addVar(vtype=GRB.INTEGER, name="granola bars")
x3 = m.addVar(vtype=GRB.INTEGER, name="blueberry pies")
x4 = m.addVar(vtype=GRB.INTEGER, name="oranges")
x5 = m.addVar(vtype=GRB.INTEGER, name="apple pies")


# Set objective function
m.setObjective(4*x0**2 + 4*x0*x4 + 8*x1**2 + 7*x1*x5 + 4*x2**2 + 4*x2*x4 + 3*x2*x5 + 4*x3*x4 + 6*x4**2 + 2*x5**2 + 9*x2 + 2*x3 + 9*x4, GRB.MINIMIZE)

# Add constraints
m.addConstr(5*x0 + 15*x1 + 3*x2 + 8*x3 + 15*x4 + 13*x5 <= 520, "r0")
m.addConstr(5*x0 + 8*x1 + 3*x2 + 8*x3 + 13*x4 + 16*x5 <= 212, "r1")
m.addConstr(14*x0 + 16*x1 + 7*x2 + 9*x3 + 1*x4 + 1*x5 <= 554, "r2")
m.addConstr(8*x3 + 15*x4 >= 76, "c3")
m.addConstr(3*x2 + 15*x4 >= 31, "c4")
m.addConstr(15*x4 + 13*x5 >= 49, "c5")
m.addConstr(3*x2**2 + 8*x3**2 >= 50, "c6")
# ... (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('Optimization problem is infeasible.')
else:
    print('Optimization ended with status %d' % m.status)

```