To solve the given optimization problem, we first need to convert the natural language description into a symbolic representation. This involves defining variables and formulating the objective function and constraints algebraically.

Let's define:
- $x_1$ as the number of ordinary bags used.
- $x_2$ as the number of special bags used.

The objective is to minimize the total cost, which can be represented by the objective function: 
\[ \text{Minimize} \quad 10x_1 + 12x_2 \]

The constraints based on the requirements for sesame seeds, onion powder, and garlic powder are:
- For sesame seeds: $5x_1 + 10x_2 \geq 50$
- For onion powder: $8x_1 + 6x_2 \geq 60$
- For garlic powder: $7x_1 + 8x_2 \geq 65$

Additionally, since the company cannot use a negative number of bags, we have:
- $x_1 \geq 0$
- $x_2 \geq 0$

Thus, the symbolic representation of the problem is:

```json
{
    'sym_variables': [('x1', 'number of ordinary bags'), ('x2', 'number of 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']
}
```

To solve this problem using Gurobi in Python, we can use the following code:

```python
from gurobipy import *

# Create a new model
m = Model("bagel_mix")

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

# Set the objective function
m.setObjective(10*x1 + 12*x2, GRB.MINIMIZE)

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

# Optimize the model
m.optimize()

# Print the solution
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Ordinary bags: {x1.x}")
    print(f"Special bags: {x2.x}")
    print(f"Total cost: {m.objVal}")
else:
    print("No optimal solution found")
```