```json
{
  "sym_variables": [
    ("x0", "SOC operators"),
    ("x1", "network administrators")
  ],
  "objective_function": "9*x0**2 + 6*x1**2",
  "constraints": [
    "0.86*x0 + 0.09*x1 >= 20",
    "0.64*x0**2 + 0.79*x1**2 >= 13",
    "0.64*x0 + 0.79*x1 >= 13",
    "0.34*x0 + 0.12*x1 >= 23",
    "7*x0**2 - 6*x1**2 >= 0",
    "0.86*x0**2 + 0.09*x1**2 <= 76",
    "0.64*x0**2 + 0.79*x1**2 <= 32",
    "0.34*x0**2 + 0.12*x1**2 <= 68"
  ]
}
```

```python
import gurobipy as gp

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

    # Create variables
    x0 = model.addVar(vtype=gp.GRB.INTEGER, name="SOC_operators")
    x1 = model.addVar(vtype=gp.GRB.INTEGER, name="network_administrators")


    # Set objective function
    model.setObjective(9*x0**2 + 6*x1**2, gp.GRB.MINIMIZE)

    # Add constraints
    model.addConstr(0.86*x0 + 0.09*x1 >= 20, "c1")
    model.addConstr(0.64*x0**2 + 0.79*x1**2 >= 13, "c2")
    model.addConstr(0.64*x0 + 0.79*x1 >= 13, "c3")
    model.addConstr(0.34*x0 + 0.12*x1 >= 23, "c4")
    model.addConstr(7*x0**2 - 6*x1**2 >= 0, "c5")
    model.addConstr(0.86*x0**2 + 0.09*x1**2 <= 76, "c6")
    model.addConstr(0.64*x0**2 + 0.79*x1**2 <= 32, "c7")
    model.addConstr(0.34*x0**2 + 0.12*x1**2 <= 68, "c8")



    # Optimize model
    model.optimize()

    # Check for infeasibility
    if model.status == gp.GRB.INFEASIBLE:
        print("The model is infeasible.")
    else:
        # Print optimal solution
        print("Optimal solution found:")
        print(f"SOC operators: {x0.x}")
        print(f"network administrators: {x1.x}")
        print(f"Objective value: {model.objVal}")

except gp.GurobiError as e:
    print(f"Gurobi error: {e}")

except AttributeError:
    print("Encountered an attribute error. Check variable definitions and constraint formulations.")

```
