## Step 1: Define the symbolic representation of the variables
The variables are 'black beans' and 'cornichons', which we can denote as $x_1$ and $x_2$ respectively.

## Step 2: Define the objective function in symbolic notation
The objective function to maximize is $2x_1 + 5x_2$.

## Step 3: Define the constraints in symbolic notation
The constraints are:
- $20x_1 \geq 20$ (tastiness rating of black beans, but this seems to be an equality or a given parameter, not a constraint in the traditional sense),
- $25x_1 \geq 25$ (sourness index of black beans, similarly),
- $13x_2 \geq 13$ (tastiness rating of cornichons),
- $13x_2 \geq 13$ (sourness index of cornichons),
- $20x_1 + 13x_2 \geq 102$ (total combined tastiness rating),
- $25x_1 + 13x_2 \geq 69$ (total combined sourness index),
- $4x_1 - 4x_2 \geq 0$ (relationship between black beans and cornichons),
- $20x_1 + 13x_2 \leq 152$ (maximum total combined tastiness rating),
- $25x_1 + 13x_2 \leq 240$ (maximum total combined sourness index).

However, upon closer inspection, the first four "constraints" seem to be characteristics of the items rather than constraints on the optimization problem. The actual constraints from the problem statement are:
- $20x_1 + 13x_2 \geq 102$,
- $25x_1 + 13x_2 \geq 69$,
- $4x_1 - 4x_2 \geq 0$,
- $20x_1 + 13x_2 \leq 152$,
- $25x_1 + 13x_2 \leq 240$.

## 4: Correct and clarify the constraints and variables' properties
- $x_1$ can be a non-integer,
- $x_2$ must be an integer.

## 5: Formulate the problem in Gurobi
We need to maximize $2x_1 + 5x_2$ subject to the given constraints.

## 6: Write down the symbolic representation
```json
{
'sym_variables': [('x1', 'black beans'), ('x2', 'cornichons')],
'objective_function': '2*x1 + 5*x2',
'constraints': [
    '20*x1 + 13*x2 >= 102',
    '25*x1 + 13*x2 >= 69',
    '4*x1 - 4*x2 >= 0',
    '20*x1 + 13*x2 <= 152',
    '25*x1 + 13*x2 <= 240'
]
}
```

## 7: Implement the problem in Gurobi Python
```python
import gurobi

def solve_optimization_problem():
    model = gurobi.Model()
    
    # Define variables
    x1 = model.addVar(name="black_beans", lb=0)  # No lower bound specified, assuming 0
    x2 = model.addVar(name="cornichons", lb=0, integrality=gurobi.GRB.INTEGER)  # Must be integer
    
    # Objective function
    model.setObjective(2*x1 + 5*x2, gurobi.GRB.MAXIMIZE)
    
    # Constraints
    model.addConstr(20*x1 + 13*x2 >= 102)
    model.addConstr(25*x1 + 13*x2 >= 69)
    model.addConstr(4*x1 - 4*x2 >= 0)
    model.addConstr(20*x1 + 13*x2 <= 152)
    model.addConstr(25*x1 + 13*x2 <= 240)
    
    # Solve the model
    model.optimize()
    
    if model.status == gurobi.GRB.Status.OPTIMAL:
        print("Optimal solution found.")
        print(f"Black beans: {x1.varValue}")
        print(f"Cornichons: {x2.varValue}")
        print(f"Objective: {model.objVal}")
    elif model.status == gurobi.GRB.Status.INFEASIBLE:
        print("The model is infeasible.")
    else:
        print("The model has a non-optimal status.")

solve_optimization_problem()
```