Here's the formulation and the Gurobi code:

**Decision Variables:**

* `x_alpha`: Number of hours plant Alpha operates daily.
* `x_beta`: Number of hours plant Beta operates daily.

**Objective Function:**

Minimize the total daily operating cost:

```
Minimize: 40 * x_alpha + 100 * x_beta
```

**Constraints:**

* **Cement Production:**  The total cement produced must be at least 100 tons.
   ```
   3 * x_alpha + 5 * x_beta >= 100
   ```

* **Stucco Production:** The total stucco produced must be at least 80 tons.
   ```
   2 * x_alpha + 4 * x_beta >= 80
   ```

* **Non-negativity:** The operating hours cannot be negative.
   ```
   x_alpha >= 0
   x_beta >= 0
   ```

```python
import gurobipy as gp
from gurobipy import GRB

# Create a new model
model = gp.Model("YoungBucksProduction")

# Create decision variables
x_alpha = model.addVar(lb=0, name="x_alpha")
x_beta = model.addVar(lb=0, name="x_beta")

# Set objective function
model.setObjective(40 * x_alpha + 100 * x_beta, GRB.MINIMIZE)

# Add constraints
model.addConstr(3 * x_alpha + 5 * x_beta >= 100, "CementProduction")
model.addConstr(2 * x_alpha + 4 * x_beta >= 80, "StuccoProduction")

# Optimize the model
model.optimize()

# Print the results
if model.status == GRB.OPTIMAL:
    print(f"Optimal Cost: ${model.objVal}")
    print(f"Alpha Operating Hours: {x_alpha.x}")
    print(f"Beta Operating Hours: {x_beta.x}")
elif model.status == GRB.INFEASIBLE:
    print("The model is infeasible.")
else:
    print(f"Optimization terminated with status: {model.status}")

```
