To solve this optimization problem, we first need to define the variables, objective function, and constraints using Gurobi's Python interface.

## Step 1: Define the Variables
We have four variables: `cornichons`, `apple_pies`, `strips_of_bacon`, and `cheeseburgers`. These are the quantities we want to optimize.

## Step 2: Define the Objective Function
The objective function to maximize is: $2.18 \times cornichons + 4.04 \times apple\_pies + 4.38 \times strips\_of\_bacon + 6.25 \times cheeseburgers$.

## 3: Define the Constraints
We have the following constraints:

1. $5 \times cornichons + 25 \times apple\_pies + 26 \times strips\_of\_bacon + 11 \times cheeseburgers \leq 692$ (total fat)
2. $21 \times cornichons + 32 \times apple\_pies + 13 \times strips\_of\_bacon + 4 \times cheeseburgers \leq 239$ (total protein)
3. $25 \times apple\_pies + 11 \times cheeseburgers \geq 102$ (fat from apple pies and cheeseburgers)
4. $5 \times cornichons + 11 \times cheeseburgers \geq 136$ (fat from cornichons and cheeseburgers)
5. $5 \times cornichons + 26 \times strips\_of\_bacon \geq 98$ (fat from cornichons and strips of bacon)
6. $25 \times apple\_pies + 26 \times strips\_of\_bacon \geq 102$ (fat from apple pies and strips of bacon)
7. $5 \times cornichons + 26 \times strips\_of\_bacon + 11 \times cheeseburgers \geq 121$ (fat from cornichons, strips of bacon, and cheeseburgers)
8. $32 \times apple\_pies + 4 \times cheeseburgers \geq 59$ (protein from apple pies and cheeseburgers)
9. $13 \times strips\_of\_bacon + 4 \times cheeseburgers \geq 46$ (protein from strips of bacon and cheeseburgers)
10. $21 \times cornichons + 32 \times apple\_pies \geq 46$ (protein from cornichons and apple pies)
11. $21 \times cornichons + 4 \times cheeseburgers \geq 50$ (protein from cornichons and cheeseburgers)
12. $21 \times cornichons + 13 \times strips\_of\_bacon + 4 \times cheeseburgers \geq 41$ (protein from cornichons, strips of bacon, and cheeseburgers)
13. $6 \times strips\_of\_bacon - 9 \times cheeseburgers \geq 0$ (relationship between strips of bacon and cheeseburgers)
14. $5 \times cornichons + 11 \times cheeseburgers \leq 403$ (fat limit from cornichons and cheeseburgers)
15. $25 \times apple\_pies + 26 \times strips\_of\_bacon \leq 553$ (fat limit from apple pies and strips of bacon)
16. $5 \times cornichons + 25 \times apple\_pies \leq 377$ (fat limit from cornichons and apple pies)
17. $25 \times apple\_pies + 11 \times cheeseburgers \leq 459$ (fat limit from apple pies and cheeseburgers)
18. $26 \times strips\_of\_bacon + 11 \times cheeseburgers \leq 358$ (fat limit from strips of bacon and cheeseburgers)
19. $25 \times apple\_pies + 26 \times strips\_of\_bacon + 11 \times cheeseburgers \leq 537$ (fat limit from apple pies, strips of bacon, and cheeseburgers)
20. $5 \times cornichons + 25 \times apple\_pies + 26 \times strips\_of\_bacon + 11 \times cheeseburgers \leq 537$ (total fat limit)
21. $21 \times cornichons + 32 \times apple\_pies \leq 182$ (protein limit from cornichons and apple pies)
22. $13 \times strips\_of\_bacon + 4 \times cheeseburgers \leq 218$ (protein limit from strips of bacon and cheeseburgers)
23. $21 \times cornichons + 32 \times apple\_pies + 13 \times strips\_of\_bacon + 4 \times cheeseburgers \leq 218$ (total protein limit)

## 4: Implement in Gurobi
Now, let's implement this problem in Gurobi:

```python
import gurobi

def solve_optimization_problem():
    # Create a new Gurobi model
    model = gurobi.Model()

    # Define the variables
    cornichons = model.addVar(lb=0, name="cornichons", vtype=gurobi.GRB.CONTINUOUS)
    apple_pies = model.addVar(lb=0, name="apple_pies", vtype=gurobi.GRB.CONTINUOUS)
    strips_of_bacon = model.addVar(lb=0, name="strips_of_bacon", vtype=gurobi.GRB.CONTINUOUS)
    cheeseburgers = model.addVar(lb=0, name="cheeseburgers", vtype=gurobi.GRB.CONTINUOUS)

    # Define the objective function
    model.setObjective(2.18 * cornichons + 4.04 * apple_pies + 4.38 * strips_of_bacon + 6.25 * cheeseburgers, gurobi.GRB.MAXIMIZE)

    # Add constraints
    model.addConstr(5 * cornichons + 25 * apple_pies + 26 * strips_of_bacon + 11 * cheeseburgers <= 692)
    model.addConstr(21 * cornichons + 32 * apple_pies + 13 * strips_of_bacon + 4 * cheeseburgers <= 239)
    model.addConstr(25 * apple_pies + 11 * cheeseburgers >= 102)
    model.addConstr(5 * cornichons + 11 * cheeseburgers >= 136)
    model.addConstr(5 * cornichons + 26 * strips_of_bacon >= 98)
    model.addConstr(25 * apple_pies + 26 * strips_of_bacon >= 102)
    model.addConstr(5 * cornichons + 26 * strips_of_bacon + 11 * cheeseburgers >= 121)
    model.addConstr(32 * apple_pies + 4 * cheeseburgers >= 59)
    model.addConstr(13 * strips_of_bacon + 4 * cheeseburgers >= 46)
    model.addConstr(21 * cornichons + 32 * apple_pies >= 46)
    model.addConstr(21 * cornichons + 4 * cheeseburgers >= 50)
    model.addConstr(21 * cornichons + 13 * strips_of_bacon + 4 * cheeseburgers >= 41)
    model.addConstr(6 * strips_of_bacon - 9 * cheeseburgers >= 0)
    model.addConstr(5 * cornichons + 11 * cheeseburgers <= 403)
    model.addConstr(25 * apple_pies + 26 * strips_of_bacon <= 553)
    model.addConstr(5 * cornichons + 25 * apple_pies <= 377)
    model.addConstr(25 * apple_pies + 11 * cheeseburgers <= 459)
    model.addConstr(26 * strips_of_bacon + 11 * cheeseburgers <= 358)
    model.addConstr(25 * apple_pies + 26 * strips_of_bacon + 11 * cheeseburgers <= 537)
    model.addConstr(5 * cornichons + 25 * apple_pies + 26 * strips_of_bacon + 11 * cheeseburgers <= 537)
    model.addConstr(21 * cornichons + 32 * apple_pies <= 182)
    model.addConstr(13 * strips_of_bacon + 4 * cheeseburgers <= 218)
    model.addConstr(21 * cornichons + 32 * apple_pies + 13 * strips_of_bacon + 4 * cheeseburgers <= 218)

    # Optimize the model
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.OPTIMAL:
        print("Objective: ", model.objval)
        print("cornichons: ", cornichons.varValue)
        print("apple_pies: ", apple_pies.varValue)
        print("strips_of_bacon: ", strips_of_bacon.varValue)
        print("cheeseburgers: ", cheeseburgers.varValue)
    else:
        print("The model is infeasible")

solve_optimization_problem()
```