## Symbolic Representation

To solve this problem, we first need to convert the natural language description into a symbolic representation.

Let's define the variables:
- $x_1$ = number of ordinary bags
- $x_2$ = number of special bags

The objective is to minimize the cost, which is $10x_1 + 12x_2$.

The constraints based on the requirements are:
- Sesame seeds: $5x_1 + 10x_2 \geq 50$
- Onion powder: $8x_1 + 6x_2 \geq 60$
- Garlic powder: $7x_1 + 8x_2 \geq 65$
- Non-negativity: $x_1 \geq 0, x_2 \geq 0$

## Symbolic Representation in JSON Format

```json
{
    'sym_variables': [('x1', 'ordinary bags'), ('x2', 'special bags')],
    'objective_function': '10*x1 + 12*x2',
    'constraints': [
        '5*x1 + 10*x2 >= 50',
        '8*x1 + 6*x2 >= 60',
        '7*x1 + 8*x2 >= 65',
        'x1 >= 0',
        'x2 >= 0'
    ]
}
```

## Gurobi Code in Python

```python
import gurobi

def solve_bagel_mix_problem():
    # Create a new model
    model = gurobi.Model()

    # Define the variables
    x1 = model.addVar(name="ordinary_bags", lb=0, vtype=gurobi.GRB.CONTINUOUS)
    x2 = model.addVar(name="special_bags", lb=0, vtype=gurobi.GRB.CONTINUOUS)

    # Define the objective function
    model.setObjective(10*x1 + 12*x2, gurobi.GRB.MINIMIZE)

    # Define the constraints
    model.addConstr(5*x1 + 10*x2 >= 50, name="sesame_seeds")
    model.addConstr(8*x1 + 6*x2 >= 60, name="onion_powder")
    model.addConstr(7*x1 + 8*x2 >= 65, name="garlic_powder")

    # Optimize the model
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.OPTIMAL:
        print("Optimal solution found.")
        print(f"Number of ordinary bags: {x1.varValue}")
        print(f"Number of special bags: {x2.varValue}")
        print(f"Minimum cost: {model.objVal}")
    else:
        print("No optimal solution found.")

solve_bagel_mix_problem()
```