```json
{
  "sym_variables": [
    ("x0", "green beans"),
    ("x1", "oranges"),
    ("x2", "slices of pizza")
  ],
  "objective_function": "3.42 * x0 * x1 + 7.77 * x1 * x2 + 6.09 * x2**2 + 3.32 * x0 + 2.66 * x1",
  "constraints": [
    "4 * x0 + 16 * x1 + 20 * x2 <= 107",
    "5 * x0 + 16 * x1 + 7 * x2 <= 113",
    "x0**2 + x2**2 >= 21",
    "x1**2 + x2**2 >= 23",
    "4 * x0 + 16 * x1 >= 11",
    "4 * x0 + 16 * x1 + 20 * x2 >= 23",
    "5 * x0 + 16 * x1 >= 37",
    "16 * x1 + 7 * x2 >= 20",
    "5 * x0 + 16 * x1 + 7 * x2 >= 25",
    "2 * x0 - 10 * x2 >= 0",
    "5 * x0 + 7 * x2 <= 68",
    "16**2 * x1**2 + 7**2 * x2**2 <= 99",
    "x0 is integer",
    "x2 is integer"

  ]
}
```

```python
import gurobipy as gp

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

# Create variables
green_beans = m.addVar(vtype=gp.GRB.INTEGER, name="green_beans")
oranges = m.addVar(vtype=gp.GRB.CONTINUOUS, name="oranges")
slices_pizza = m.addVar(vtype=gp.GRB.INTEGER, name="slices_pizza")


# Set objective function
m.setObjective(3.42 * green_beans * oranges + 7.77 * oranges * slices_pizza + 6.09 * slices_pizza**2 + 3.32 * green_beans + 2.66 * oranges, gp.GRB.MINIMIZE)

# Add constraints
m.addConstr(4 * green_beans + 16 * oranges + 20 * slices_pizza <= 107, "dollar_cost")
m.addConstr(5 * green_beans + 16 * oranges + 7 * slices_pizza <= 113, "tastiness_rating")
m.addConstr(green_beans**2 + slices_pizza**2 >= 21, "c1")
m.addConstr(oranges**2 + slices_pizza**2 >= 23, "c2")
m.addConstr(4 * green_beans + 16 * oranges >= 11, "c3")
m.addConstr(4 * green_beans + 16 * oranges + 20 * slices_pizza >= 23, "c4")
m.addConstr(5 * green_beans + 16 * oranges >= 37, "c5")
m.addConstr(16 * oranges + 7 * slices_pizza >= 20, "c6")
m.addConstr(5 * green_beans + 16 * oranges + 7 * slices_pizza >= 25, "c7")
m.addConstr(2 * green_beans - 10 * slices_pizza >= 0, "c8")
m.addConstr(5 * green_beans + 7 * slices_pizza <= 68, "c9")
m.addConstr((16*oranges)**2 + (7*slices_pizza)**2 <= 99, "c10")


# Optimize model
m.optimize()

# Print results
if m.status == gp.GRB.OPTIMAL:
    print('Obj: %g' % m.objVal)
    print('green_beans:', green_beans.x)
    print('oranges:', oranges.x)
    print('slices_pizza:', slices_pizza.x)
elif m.status == gp.GRB.INFEASIBLE:
    print('The model is infeasible.')
else:
    print('Optimization ended with status %d' % m.status)

```