```json
{
  "sym_variables": [
    ("x0", "ham sandwiches"),
    ("x1", "bowls of cereal"),
    ("x2", "black beans")
  ],
  "objective_function": "7.18 * x0 * x1 + 6.24 * x1**2 + 6.71 * x1 * x2",
  "constraints": [
    "8 * x0 + 10 * x1 >= 26",
    "8 * x0 + 13 * x2 >= 26",
    "10 * x1 + 13 * x2 >= 34",
    "8 * x0 + 10 * x1 + 13 * x2 >= 34",
    "4 * x0 - 3 * x2 >= 0",
    "10 * x1 + 13 * x2 <= 97",
    "8 * x0 + 10 * x1 <= 78",
    "8 * x0 + 10 * x1 + 13 * x2 <= 117"
  ]
}
```

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

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

    # Create variables
    ham_sandwiches = m.addVar(vtype=GRB.INTEGER, name="ham_sandwiches")
    bowls_of_cereal = m.addVar(vtype=GRB.INTEGER, name="bowls_of_cereal")
    black_beans = m.addVar(vtype=GRB.INTEGER, name="black_beans")

    # Set objective function
    m.setObjective(7.18 * ham_sandwiches * bowls_of_cereal + 6.24 * bowls_of_cereal**2 + 6.71 * bowls_of_cereal * black_beans, GRB.MINIMIZE)

    # Add constraints
    m.addConstr(8 * ham_sandwiches + 10 * bowls_of_cereal >= 26, "protein_constraint1")
    m.addConstr(8 * ham_sandwiches + 13 * black_beans >= 26, "protein_constraint2")
    m.addConstr(10 * bowls_of_cereal + 13 * black_beans >= 34, "protein_constraint3")
    m.addConstr(8 * ham_sandwiches + 10 * bowls_of_cereal + 13 * black_beans >= 34, "protein_constraint4")
    m.addConstr(4 * ham_sandwiches - 3 * black_beans >= 0, "constraint5")
    m.addConstr(10 * bowls_of_cereal + 13 * black_beans <= 97, "protein_constraint6")
    m.addConstr(8 * ham_sandwiches + 10 * bowls_of_cereal <= 78, "protein_constraint7")
    m.addConstr(8 * ham_sandwiches + 10 * bowls_of_cereal + 13 * black_beans <= 117, "protein_constraint8")


    # Optimize model
    m.optimize()

    if m.status == GRB.OPTIMAL:
        print('Obj: %g' % m.objVal)
        print('ham_sandwiches:', ham_sandwiches.x)
        print('bowls_of_cereal:', bowls_of_cereal.x)
        print('black_beans:', black_beans.x)
    elif m.status == GRB.INFEASIBLE:
        print('The model is infeasible.')
    else:
        print('Optimization ended with status %d' % m.status)


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

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