## Problem Description and Formulation

The problem is an optimization problem with two variables: 'black beans' and 'cornichons'. The objective is to maximize the function 2 * 'black beans' + 5 * 'cornichons' subject to several constraints.

### Variables and Parameters

- Variables: 
  - 'black beans' (continuous)
  - 'cornichons' (integer)

- Parameters:
  - 'r0' or 'tastiness rating': 
    - 'black beans': 20
    - 'cornichons': 13
    - Upper bound: 290
  - 'r1' or 'sourness index': 
    - 'black beans': 25
    - 'cornichons': 13
    - Upper bound: 288

### Constraints

1. The tastiness rating of black beans is 20 (implicit, as it's a parameter).
2. The sourness index of black beans is 25 (implicit, as it's a parameter).
3. The tastiness rating of cornichons is 13 (implicit, as it's a parameter).
4. Cornichons have a sourness index of 13 (implicit, as it's a parameter).
5. The total combined tastiness rating from black beans and cornichons must be 102 or more: \(20x_0 + 13x_1 \geq 102\).
6. The total combined sourness index from black beans and cornichons must be greater than or equal to 69: \(25x_0 + 13x_1 \geq 69\).
7. \(4x_0 - 4x_1 \geq 0\).
8. The total combined tastiness rating from black beans and cornichons should be 152 at a maximum: \(20x_0 + 13x_1 \leq 152\).
9. The total combined sourness index from black beans and cornichons must be 240 at a maximum: \(25x_0 + 13x_1 \leq 240\).

### Gurobi Code

```python
import gurobi

def optimization_problem():
    # Create a new model
    m = gurobi.Model()

    # Define variables
    black_beans = m.addVar(name="black_beans", lb=0, ub=None)  # Continuous
    cornichons = m.addVar(name="cornichons", lb=0, integer=True)  # Integer

    # Objective function: Maximize 2 * black_beans + 5 * cornichons
    m.setObjective(2 * black_beans + 5 * cornichons, gurobi.GRB.MAXIMIZE)

    # Constraints
    m.addConstr(20 * black_beans + 13 * cornichons >= 102, name="tastiness_rating_min")
    m.addConstr(25 * black_beans + 13 * cornichons >= 69, name="sourness_index_min")
    m.addConstr(4 * black_beans - 4 * cornichons >= 0, name="balance_constraint")
    m.addConstr(20 * black_beans + 13 * cornichons <= 152, name="tastiness_rating_max")
    m.addConstr(25 * black_beans + 13 * cornichons <= 240, name="sourness_index_max")

    # Optimize
    m.optimize()

    # Print solution
    if m.status == gurobi.GRB.OPTIMAL:
        print("Optimal solution found.")
        print(f"Black beans: {black_beans.varValue}")
        print(f"Cornichons: {cornichons.varValue}")
        print(f"Objective: {m.objVal}")
    else:
        print("No optimal solution found.")

optimization_problem()
```