To solve this optimization problem, we first need to define the decision variables and the objective function. Let's denote the amount of shrimp used in kilograms as \(x_s\) and the amount of beef used in kilograms as \(x_b\). The objective is to minimize the total cost of the mixture, which can be represented as \(36x_s + 40x_b\), given that shrimp costs $36 per kg and beef costs $40 per kg.

The constraints are:
1. The mixture needs to contain at least 20 units of protein.
2. The mixture needs to contain at least 25 units of fat.

Given the protein and fat content per kilogram of each ingredient, we can formulate these constraints as follows:
1. Protein constraint: \(2.5x_s + 4x_b \geq 20\)
2. Fat constraint: \(3x_s + 2.5x_b \geq 25\)

Additionally, since we cannot use negative amounts of ingredients, we have non-negativity constraints:
- \(x_s \geq 0\)
- \(x_b \geq 0\)

Now, let's translate this problem into Gurobi code in Python:

```python
from gurobipy import *

# Create a new model
m = Model("Sausage_Mixture")

# Define the decision variables
x_s = m.addVar(lb=0, name="shrimp")  # Amount of shrimp in kg
x_b = m.addVar(lb=0, name="beef")    # Amount of beef in kg

# Define the objective function: Minimize total cost
m.setObjective(36*x_s + 40*x_b, GRB.MINIMIZE)

# Add constraints
m.addConstr(2.5*x_s + 4*x_b >= 20, name="protein_constraint")
m.addConstr(3*x_s + 2.5*x_b >= 25, name="fat_constraint")

# Optimize the model
m.optimize()

# Print the solution
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Shrimp (kg): {x_s.x}")
    print(f"Beef (kg): {x_b.x}")
    print(f"Total Cost: ${m.objVal:.2f}")
else:
    print("No optimal solution found")
```