## Problem Description and Formulation

The problem is a classic example of a linear programming problem. The goal is to minimize the cost of mixing pork and chicken to create sausages while meeting the requirements for protein and fat.

Let's define the variables:

- \(x\): kilograms of pork
- \(y\): kilograms of chicken

The objective function to minimize is the total cost:
\[ \text{Minimize:} \quad 40x + 50y \]

Subject to the constraints:
1. Protein requirement: \(2x + 3y \geq 10\)
2. Fat requirement: \(4x + 2y \geq 15\)
3. Non-negativity: \(x \geq 0, y \geq 0\)

## Gurobi Code

To solve this problem using Gurobi in Python, we will first install the gurobi package if it's not already installed. You can install it via pip:

```bash
pip install gurobi
```

Now, let's write the Gurobi code:

```python
import gurobi as gp

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

# Define variables
x = model.addVar(name="pork", lb=0)  # Kilograms of pork
y = model.addVar(name="chicken", lb=0)  # Kilograms of chicken

# Objective function: Minimize cost
model.setObjective(40*x + 50*y, gp.GRB.MINIMIZE)

# Constraints
model.addConstr(2*x + 3*y >= 10, name="protein_requirement")
model.addConstr(4*x + 2*y >= 15, name="fat_requirement")

# Optimize the model
model.optimize()

# Print the status
if model.status == gp.GRB.Status.OPTIMAL:
    print("Optimal solution found.")
    print(f"Optimal cost: ${model.objval:.2f}")
    print(f"Pork: {x.varValue:.2f} kg")
    print(f"Chicken: {y.varValue:.2f} kg")
else:
    print("No optimal solution found.")
```

This code sets up the linear programming problem as described, solves it using Gurobi, and prints out the optimal mixture and the minimum cost if an optimal solution exists. If no optimal solution is found (e.g., if the problem is infeasible), it will indicate that as well.