## Problem Description and Formulation

The problem is a classic example of a linear programming problem. The bagel company wants to mix two types of bags of everything seasoning, ordinary and special, to create a house mix that meets certain requirements at minimum cost.

Let's define the decision variables:

- $x$: the number of ordinary bags
- $y$: the number of special bags

The objective is to minimize the total cost, which is $10x + 12y$.

The constraints are:

- The house mix must contain at least 50 grams of sesame seeds: $5x + 10y \geq 50$
- The house mix must contain at least 60 grams of onion powder: $8x + 6y \geq 60$
- The house mix must contain at least 65 grams of garlic powder: $7x + 8y \geq 65$
- $x \geq 0$ and $y \geq 0$, since the number of bags cannot be negative.

## Gurobi Code

```python
import gurobi

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

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

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

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

    # Optimize the model
    model.optimize()

    # Print the results
    if model.status == gurobi.GRB.OPTIMAL:
        print(f"Optimal solution: x = {x.varValue}, y = {y.varValue}")
        print(f"Minimum cost: ${model.objVal:.2f}")
    else:
        print("No optimal solution found")

solve_bagel_mix_problem()
```

This code defines the problem using Gurobi's Python interface, solves it, and prints the optimal solution and minimum cost. Note that the `vtype` parameter is set to `gurobi.GRB.CONTINUOUS` to allow for fractional numbers of bags, which may not be practical in reality. If you want to restrict the decision variables to integers, you can change `vtype` to `gurobi.GRB.INTEGER`.