## Problem Description and Formulation

The problem is an optimization problem with two variables: `cheeseburgers` and `hot dogs`. The objective is to minimize the function `3 * cheeseburgers + 6 * hot dogs` subject to several constraints.

### Constraints

1. **Fat Content Constraints**
   - Each cheeseburger contains 5 grams of fat.
   - Each hot dog contains 4 grams of fat.
   - At least 11 grams of fat must come from cheeseburgers and hot dogs.
   - No more than 43 grams of fat can come from cheeseburgers and hot dogs.

2. **Calcium Content Constraints**
   - Each cheeseburger contains 2 milligrams of calcium.
   - Each hot dog contains 3 milligrams of calcium.
   - At least 8 milligrams of calcium must come from cheeseburgers and hot dogs.
   - No more than 25 milligrams of calcium can come from cheeseburgers and hot dogs.

3. **Variable Constraints**
   - `cheeseburgers` can be a fractional number.
   - `hot dogs` must be a whole number.

4. **Additional Constraints**
   - $10 \cdot cheeseburgers - 3 \cdot hot dogs \geq 0$

### Gurobi Code Formulation

```python
import gurobi

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

    # Define variables
    cheeseburgers = model.addVar(lb=0, name="cheeseburgers", vtype=gurobi.GRB.CONTINUOUS)
    hot_dogs = model.addVar(lb=0, name="hot_dogs", vtype=gurobi.GRB.INTEGER)

    # Objective function: Minimize 3 * cheeseburgers + 6 * hot_dogs
    model.setObjective(3 * cheeseburgers + 6 * hot_dogs, gurobi.GRB.MINIMIZE)

    # Constraints
    # At least 11 grams of fat
    model.addConstraint(5 * cheeseburgers + 4 * hot_dogs >= 11, name="fat_min")
    # No more than 43 grams of fat
    model.addConstraint(5 * cheeseburgers + 4 * hot_dogs <= 43, name="fat_max")
    # At least 8 milligrams of calcium
    model.addConstraint(2 * cheeseburgers + 3 * hot_dogs >= 8, name="calcium_min")
    # No more than 25 milligrams of calcium
    model.addConstraint(2 * cheeseburgers + 3 * hot_dogs <= 25, name="calcium_max")
    # Additional constraint: 10 * cheeseburgers - 3 * hot_dogs >= 0
    model.addConstraint(10 * cheeseburgers - 3 * hot_dogs >= 0, name="additional_constraint")

    # Solve the model
    model.optimize()

    # Print solution
    if model.status == gurobi.GRB.OPTIMAL:
        print("Optimal Solution:")
        print(f"Cheeseburgers: {cheeseburgers.varValue}")
        print(f"Hot Dogs: {hot_dogs.varValue}")
        print(f"Objective: {model.objVal}")
    else:
        print("No optimal solution found.")

optimization_problem()
```