```json
{
  "sym_variables": [
    ("x0", "cantaloupes"),
    ("x1", "chicken drumsticks"),
    ("x2", "apple pies"),
    ("x3", "bowls of pasta")
  ],
  "objective_function": "3.28*x0**2 + 6.66*x0*x2 + 1.42*x0*x3 + 6.84*x1**2 + 9.64*x1*x3 + 3.22*x2**2 + 4.23*x2*x3 + 2.46*x1",
  "constraints": [
    "6*x0 + 15*x1 + 18*x2 + 21*x3 <= 263",
    "6*x0**2 + 21*x3**2 >= 44",
    "18*x2**2 + 21*x3**2 >= 64",
    "15*x1 + 18*x2 + 21*x3 >= 35",
    "6*x0 + 15*x1 + 21*x3 >= 35",
    "15*x1 + 18*x2 + 21*x3 >= 61",
    "6*x0 + 15*x1 + 21*x3 >= 61",
    "6*x0 + 15*x1 + 18*x2 + 21*x3 >= 61",
    "-3*x2**2 + 2*x3**2 >= 0",
    "6*x0 + 15*x1 <= 175",
    "6*x0**2 + 15*x1**2 + 21*x3**2 <= 215"
  ]
}
```

```python
import gurobipy as gp

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

    # Create variables
    cantaloupes = m.addVar(vtype=gp.GRB.INTEGER, name="cantaloupes")
    chicken_drumsticks = m.addVar(vtype=gp.GRB.INTEGER, name="chicken_drumsticks")
    apple_pies = m.addVar(vtype=gp.GRB.INTEGER, name="apple_pies")
    bowls_of_pasta = m.addVar(vtype=gp.GRB.INTEGER, name="bowls_of_pasta")

    # Set objective function
    m.setObjective(3.28*cantaloupes**2 + 6.66*cantaloupes*apple_pies + 1.42*cantaloupes*bowls_of_pasta + 6.84*chicken_drumsticks**2 + 9.64*chicken_drumsticks*bowls_of_pasta + 3.22*apple_pies**2 + 4.23*apple_pies*bowls_of_pasta + 2.46*chicken_drumsticks, gp.GRB.MINIMIZE)

    # Add constraints
    m.addConstr(6*cantaloupes + 15*chicken_drumsticks + 18*apple_pies + 21*bowls_of_pasta <= 263, "calcium_upper_bound")
    m.addConstr(6*cantaloupes**2 + 21*bowls_of_pasta**2 >= 44, "calcium_constraint1")
    m.addConstr(18*apple_pies**2 + 21*bowls_of_pasta**2 >= 64, "calcium_constraint2")
    m.addConstr(15*chicken_drumsticks + 18*apple_pies + 21*bowls_of_pasta >= 35, "calcium_constraint3")
    m.addConstr(6*cantaloupes + 15*chicken_drumsticks + 21*bowls_of_pasta >= 35, "calcium_constraint4")
    m.addConstr(15*chicken_drumsticks + 18*apple_pies + 21*bowls_of_pasta >= 61, "calcium_constraint5")
    m.addConstr(6*cantaloupes + 15*chicken_drumsticks + 21*bowls_of_pasta >= 61, "calcium_constraint6")
    m.addConstr(6*cantaloupes + 15*chicken_drumsticks + 18*apple_pies + 21*bowls_of_pasta >= 61, "calcium_constraint7")
    m.addConstr(-3*apple_pies**2 + 2*bowls_of_pasta**2 >= 0, "constraint8")
    m.addConstr(6*cantaloupes + 15*chicken_drumsticks <= 175, "constraint9")
    m.addConstr(6*cantaloupes**2 + 15*chicken_drumsticks**2 + 21*bowls_of_pasta**2 <= 215, "constraint10")


    # Optimize model
    m.optimize()

    if m.status == gp.GRB.OPTIMAL:
        print('Obj: %g' % m.objVal)
        for v in m.getVars():
            print('%s %g' % (v.varName, v.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')
```