To solve the given optimization problem using Gurobi, we first need to understand and possibly simplify or clarify the constraints provided:

1. The objective function to minimize is: $3 \times \text{cheeseburgers} + 6 \times \text{hot dogs}$.
2. Constraints:
   - Each cheeseburger contains 5 grams of fat and 2 milligrams of calcium.
   - Each hot dog contains 4 grams of fat and 3 milligrams of calcium.
   - The total fat from cheeseburgers and hot dogs must be at least 11 grams.
   - The total calcium from cheeseburgers and hot dogs must be at least 8 milligrams.
   - The expression $10 \times \text{cheeseburgers} - 3 \times \text{hot dogs} \geq 0$ must hold.
   - The total fat from cheeseburgers and hot dogs must not exceed 43 grams (as per the resource 'r0' description, noting a discrepancy with "40 grams" in the text, we'll use 43 as it matches the provided data).
   - The total calcium from cheeseburgers and hot dogs must not exceed 25 milligrams (as per the resource 'r1' description, noting a discrepancy with "13 milligrams" in the text, we'll use 25 as it matches the provided data).
   - Cheeseburgers can be fractional, but hot dogs must be whole numbers.

Given these points, let's formulate the problem in Gurobi. Note that there seems to be some inconsistency in the constraints regarding the upper bounds of fat and calcium intake. We will proceed with the values provided in the resource descriptions ('r0' and 'r1') for upper bounds.

```python
from gurobipy import *

# Create a model
m = Model("Optimization_Problem")

# Define variables
cheeseburgers = m.addVar(vtype=GRB.CONTINUOUS, name="cheeseburgers")
hot_dogs = m.addVar(vtype=GRB.INTEGER, name="hot_dogs")

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

# Constraints
# Total fat at least 11 grams
m.addConstr(5*cheeseburgers + 4*hot_dogs >= 11, name="fat_min")

# Total calcium at least 8 milligrams
m.addConstr(2*cheeseburgers + 3*hot_dogs >= 8, name="calcium_min")

# Expression constraint: 10*cheeseburgers - 3*hot_dogs >= 0
m.addConstr(10*cheeseburgers - 3*hot_dogs >= 0, name="expression_constraint")

# Total fat not exceeding 43 grams (using the upper bound from 'r0')
m.addConstr(5*cheeseburgers + 4*hot_dogs <= 43, name="fat_max")

# Total calcium not exceeding 25 milligrams (using the upper bound from 'r1')
m.addConstr(2*cheeseburgers + 3*hot_dogs <= 25, name="calcium_max")

# Optimize
m.optimize()

# Print results
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Cheeseburgers: {cheeseburgers.x}")
    print(f"Hot Dogs: {hot_dogs.x}")
    print(f"Objective Function Value: {m.objVal}")
else:
    print("No optimal solution found")
```