## Step 1: Define the symbolic representation of the variables
The variables are ['protein bars', 'cornichons', 'chicken thighs', 'chicken breasts'] which can be represented symbolically as ['x0', 'x1', 'x2', 'x3'].

## Step 2: Create a dictionary mapping symbolic variables to their natural language counterparts
The symbolic variables and their corresponding natural language objects are:
- 'x0': 'protein bars'
- 'x1': 'cornichons'
- 'x2': 'chicken thighs'
- 'x3': 'chicken breasts'

## 3: Define the objective function in symbolic notation
The objective function to minimize is $2x_0 + 8x_1 + 5x_2 + 7x_3$.

## 4: List all the constraints in symbolic notation
Constraints:
1. $4x_0 + 3x_1 \geq 18$
2. $4x_0 + 11x_2 + 10x_3 \geq 35$
3. $3x_1 + 11x_2 + 10x_3 \geq 35$
4. $4x_0 + 3x_1 + 11x_2 \geq 35$
5. $4x_0 + 11x_2 + 10x_3 \geq 36$
6. $3x_1 + 11x_2 + 10x_3 \geq 36$
7. $4x_0 + 3x_1 + 11x_2 \geq 36$
8. $4x_0 + 11x_2 + 10x_3 \geq 31$
9. $3x_1 + 11x_2 + 10x_3 \geq 31$
10. $4x_0 + 3x_1 + 11x_2 \geq 31$
11. $4x_0 + 3x_1 + 11x_2 + 10x_3 \geq 31$
12. $5x_2 + 11x_3 \geq 104$
13. $10x_0 + 12x_1 \geq 53$
14. $12x_1 + 11x_3 \geq 80$
15. $10x_0 + 12x_1 + 5x_2 \geq 64$
16. $12x_1 + 5x_2 + 11x_3 \geq 64$
17. $10x_0 + 12x_1 + 11x_3 \geq 64$
18. $10x_0 + 12x_1 + 5x_2 \geq 58$
19. $12x_1 + 5x_2 + 11x_3 \geq 58$
20. $10x_0 + 12x_1 + 11x_3 \geq 58$
21. $10x_0 + 12x_1 + 5x_2 \geq 97$
22. $12x_1 + 5x_2 + 11x_3 \geq 97$
23. $10x_0 + 12x_1 + 11x_3 \geq 97$
24. $10x_0 + 12x_1 + 5x_2 + 11x_3 \geq 97$
25. $5x_0 - 5x_2 \geq 0$
26. $x_0 - 3x_1 \geq 0$
27. $4x_0 + 3x_1 \leq 83$
28. $4x_0 + 10x_3 \leq 141$
29. $3x_1 + 11x_2 \leq 54$
30. $11x_2 + 10x_3 \leq 148$
31. $4x_0 + 11x_2 \leq 96$
32. $10x_0 + 12x_1 + 11x_3 \leq 284$
33. $10x_0 + 12x_1 + 5x_2 \leq 264$

## 5: Define the symbolic representation of the problem
```json
{
    'sym_variables': [
        ('x0', 'protein bars'),
        ('x1', 'cornichons'),
        ('x2', 'chicken thighs'),
        ('x3', 'chicken breasts')
    ],
    'objective_function': '2*x0 + 8*x1 + 5*x2 + 7*x3',
    'constraints': [
        '4*x0 + 3*x1 >= 18',
        '4*x0 + 11*x2 + 10*x3 >= 35',
        '3*x1 + 11*x2 + 10*x3 >= 35',
        '4*x0 + 3*x1 + 11*x2 >= 35',
        '4*x0 + 11*x2 + 10*x3 >= 36',
        '3*x1 + 11*x2 + 10*x3 >= 36',
        '4*x0 + 3*x1 + 11*x2 >= 36',
        '4*x0 + 11*x2 + 10*x3 >= 31',
        '3*x1 + 11*x2 + 10*x3 >= 31',
        '4*x0 + 3*x1 + 11*x2 >= 31',
        '4*x0 + 3*x1 + 11*x2 + 10*x3 >= 31',
        '5*x2 + 11*x3 >= 104',
        '10*x0 + 12*x1 >= 53',
        '12*x1 + 11*x3 >= 80',
        '10*x0 + 12*x1 + 5*x2 >= 64',
        '12*x1 + 5*x2 + 11*x3 >= 64',
        '10*x0 + 12*x1 + 11*x3 >= 64',
        '10*x0 + 12*x1 + 5*x2 >= 58',
        '12*x1 + 5*x2 + 11*x3 >= 58',
        '10*x0 + 12*x1 + 11*x3 >= 58',
        '10*x0 + 12*x1 + 5*x2 >= 97',
        '12*x1 + 5*x2 + 11*x3 >= 97',
        '10*x0 + 12*x1 + 11*x3 >= 97',
        '10*x0 + 12*x1 + 5*x2 + 11*x3 >= 97',
        '5*x0 - 5*x2 >= 0',
        'x0 - 3*x1 >= 0',
        '4*x0 + 3*x1 <= 83',
        '4*x0 + 10*x3 <= 141',
        '3*x1 + 11*x2 <= 54',
        '11*x2 + 10*x3 <= 148',
        '4*x0 + 11*x2 <= 96',
        '10*x0 + 12*x1 + 11*x3 <= 284',
        '10*x0 + 12*x1 + 5*x2 <= 264'
    ]
}
```

## 6: Implement the optimization problem using Gurobi
```python
import gurobi

def solve_optimization_problem():
    model = gurobi.Model()

    # Define variables
    x0 = model.addVar(name="protein_bars", lb=-gurobi.GRB.INFINITY)
    x1 = model.addVar(name="cornichons", lb=-gurobi.GRB.INFINITY)
    x2 = model.addVar(name="chicken_thighs", lb=-gurobi.GRB.INFINITY)
    x3 = model.addVar(name="chicken_breasts", lb=-gurobi.GRB.INFINITY)

    # Objective function
    model.setObjective(2*x0 + 8*x1 + 5*x2 + 7*x3, gurobi.GRB.MINIMIZE)

    # Constraints
    model.addConstr(4*x0 + 3*x1 >= 18)
    model.addConstr(4*x0 + 11*x2 + 10*x3 >= 35)
    model.addConstr(3*x1 + 11*x2 + 10*x3 >= 35)
    model.addConstr(4*x0 + 3*x1 + 11*x2 >= 35)
    model.addConstr(4*x0 + 11*x2 + 10*x3 >= 36)
    model.addConstr(3*x1 + 11*x2 + 10*x3 >= 36)
    model.addConstr(4*x0 + 3*x1 + 11*x2 >= 36)
    model.addConstr(4*x0 + 11*x2 + 10*x3 >= 31)
    model.addConstr(3*x1 + 11*x2 + 10*x3 >= 31)
    model.addConstr(4*x0 + 3*x1 + 11*x2 >= 31)
    model.addConstr(4*x0 + 3*x1 + 11*x2 + 10*x3 >= 31)
    model.addConstr(5*x2 + 11*x3 >= 104)
    model.addConstr(10*x0 + 12*x1 >= 53)
    model.addConstr(12*x1 + 11*x3 >= 80)
    model.addConstr(10*x0 + 12*x1 + 5*x2 >= 64)
    model.addConstr(12*x1 + 5*x2 + 11*x3 >= 64)
    model.addConstr(10*x0 + 12*x1 + 11*x3 >= 64)
    model.addConstr(10*x0 + 12*x1 + 5*x2 >= 58)
    model.addConstr(12*x1 + 5*x2 + 11*x3 >= 58)
    model.addConstr(10*x0 + 12*x1 + 11*x3 >= 58)
    model.addConstr(10*x0 + 12*x1 + 5*x2 >= 97)
    model.addConstr(12*x1 + 5*x2 + 11*x3 >= 97)
    model.addConstr(10*x0 + 12*x1 + 11*x3 >= 97)
    model.addConstr(10*x0 + 12*x1 + 5*x2 + 11*x3 >= 97)
    model.addConstr(5*x0 - 5*x2 >= 0)
    model.addConstr(x0 - 3*x1 >= 0)
    model.addConstr(4*x0 + 3*x1 <= 83)
    model.addConstr(4*x0 + 10*x3 <= 141)
    model.addConstr(3*x1 + 11*x2 <= 54)
    model.addConstr(11*x2 + 10*x3 <= 148)
    model.addConstr(4*x0 + 11*x2 <= 96)
    model.addConstr(10*x0 + 12*x1 + 11*x3 <= 284)
    model.addConstr(10*x0 + 12*x1 + 5*x2 <= 264)

    # Solve the model
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.OPTIMAL:
        print("Optimal solution found.")
        print(f"Objective: {model.objval}")
        print(f"Protein bars: {x0.x}")
        print(f"Cornichons: {x1.x}")
        print(f"Chicken thighs: {x2.x}")
        print(f"Chicken breasts: {x3.x}")
    else:
        print("No optimal solution found.")

solve_optimization_problem()
```