Here's the formulation of the linear program and the Gurobi code to solve it:

**Decision Variables:**

*  `x`: Number of premium sandwiches produced.
*  `y`: Number of regular sandwiches produced.

**Objective Function:**

Maximize profit: `5x + 1y`

**Constraints:**

* **Preparation Time:** `6x + 4y <= 400` (minutes)
* **Meat:** `5x + 1y <= 100` (slices)
* **Non-negativity:** `x >= 0`, `y >= 0`


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

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

# Create decision variables
x = model.addVar(vtype=GRB.INTEGER, name="premium_sandwiches")
y = model.addVar(vtype=GRB.INTEGER, name="regular_sandwiches")

# Set objective function
model.setObjective(5*x + 1*y, GRB.MAXIMIZE)

# Add constraints
model.addConstr(6*x + 4*y <= 400, "prep_time")
model.addConstr(5*x + 1*y <= 100, "meat")

# Optimize model
model.optimize()

# Print results
if model.status == GRB.OPTIMAL:
    print(f"Optimal Solution Found:")
    print(f"Premium Sandwiches: {x.x}")
    print(f"Regular Sandwiches: {y.x}")
    print(f"Maximum Profit: ${model.objVal}")
elif model.status == GRB.INFEASIBLE:
    print("Model is infeasible. No solution exists.")
else:
    print(f"Optimization terminated with status: {model.status}")

```
