## Step 1: Define the symbolic representation of the variables
The variables are 'hamburgers', 'eggs', 'protein bars', and 'pickles', which can be represented symbolically as $x_0$, $x_1$, $x_2$, and $x_3$ respectively.

## Step 2: Convert the natural language description into a symbolic representation
The symbolic representation of the variables is:
- $x_0$ : hamburgers
- $x_1$ : eggs
- $x_2$ : protein bars
- $x_3$ : pickles

## Step 3: Define the objective function in symbolic notation
The objective function to maximize is $5x_0 + x_1 + 7x_2 + 6x_3$.

## Step 4: List the constraints in symbolic notation
Constraints:
1. $11x_0 \leq 159$
2. $8x_0 + 14x_1 + x_2 + 4x_3 \leq 87$
3. $5x_0 + 11x_1 + 10x_2 + 7x_3 \leq 132$
4. $7x_1 + x_3 \geq 14$
5. $7x_1 + 7x_2 \geq 34$
6. $11x_0 + 7x_1 \geq 22$
7. $x_2 + 4x_3 \geq 20$
8. $14x_1 + x_2 \geq 14$
9. $8x_0 + 4x_3 \geq 9$
10. $14x_1 + x_2 + 4x_3 \geq 21$
11. $8x_0 + x_2 + 4x_3 \geq 21$
12. $8x_0 + 14x_1 + x_2 \geq 21$
13. $8x_0 + 14x_1 + 4x_3 \geq 21$
14. $14x_1 + x_2 + 4x_3 \geq 10$
15. $8x_0 + x_2 + 4x_3 \geq 10$
16. $8x_0 + 14x_1 + x_2 \geq 10$
17. $8x_0 + 14x_1 + 4x_3 \geq 10$
18. $14x_1 + x_2 + 4x_3 \geq 15$
19. $8x_0 + x_2 + 4x_3 \geq 15$
20. $8x_0 + 14x_1 + x_2 \geq 15$
21. $8x_0 + 14x_1 + 4x_3 \geq 15$
22. $14x_1 + x_2 + 4x_3 \geq 15$
23. $8x_0 + x_2 + 4x_3 \geq 15$
24. $8x_0 + 14x_1 + x_2 \geq 15$
25. $8x_0 + 14x_1 + 4x_3 \geq 15$
26. $11x_1 + 7x_3 \geq 28$
27. $5x_0 + 10x_2 \geq 17$
28. $5x_0 + 7x_3 \geq 28$
29. $11x_0 + x_3 \leq 68$
30. $7x_1 + x_3 \leq 46$
31. $11x_0 + 7x_2 + x_3 \leq 61$
32. $11x_0 + 7x_1 + 7x_2 \leq 39$
33. $11x_0 + 7x_1 + 7x_2 + x_3 \leq 39$
34. $14x_1 + x_2 \leq 41$
35. $8x_0 + x_2 \leq 31$
36. $x_2 + 4x_3 \leq 56$
37. $8x_0 + 14x_1 \leq 40$
38. $8x_0 + 14x_1 + x_2 \leq 41$
39. $8x_0 + 14x_1 + x_2 + 4x_3 \leq 41$
40. $5x_0 + 11x_1 \leq 55$
41. $5x_0 + 10x_2 + 7x_3 \leq 99$
42. $5x_0 + 11x_1 + 7x_3 \leq 101$
43. $5x_0 + 11x_1 + 10x_2 + 7x_3 \leq 101$

## 5: Create the Gurobi model and variables
```python
import gurobi

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

# Define the variables
x0 = model.addVar(name="hamburgers", lb=0)
x1 = model.addVar(name="eggs", lb=0)
x2 = model.addVar(name="protein_bars", lb=0)
x3 = model.addVar(name="pickles", lb=0)

# Objective function
model.setObjective(5 * x0 + x1 + 7 * x2 + 6 * x3, gurobi.GRB.MAXIMIZE)

# Constraints
# ... adding all constraints here ...
```

## 6: Add constraints to the Gurobi model
Due to the large number of constraints and for brevity, we will directly implement the model with constraints in the final code block.

```python
import gurobi

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

    x0 = model.addVar(name="hamburgers", lb=0)
    x1 = model.addVar(name="eggs", lb=0)
    x2 = model.addVar(name="protein_bars", lb=0)
    x3 = model.addVar(name="pickles", lb=0)

    model.setObjective(5 * x0 + x1 + 7 * x2 + 6 * x3, gurobi.GRB.MAXIMIZE)

    # Constraints
    model.addConstr(11 * x0 <= 159)
    model.addConstr(8 * x0 + 14 * x1 + x2 + 4 * x3 <= 87)
    model.addConstr(5 * x0 + 11 * x1 + 10 * x2 + 7 * x3 <= 132)
    model.addConstr(7 * x1 + x3 >= 14)
    model.addConstr(7 * x1 + 7 * x2 >= 34)
    model.addConstr(11 * x0 + 7 * x1 >= 22)
    model.addConstr(x2 + 4 * x3 >= 20)
    model.addConstr(14 * x1 + x2 >= 14)
    model.addConstr(8 * x0 + 4 * x3 >= 9)
    model.addConstr(14 * x1 + x2 + 4 * x3 >= 21)
    model.addConstr(8 * x0 + x2 + 4 * x3 >= 21)
    model.addConstr(8 * x0 + 14 * x1 + x2 >= 21)
    model.addConstr(8 * x0 + 14 * x1 + 4 * x3 >= 21)
    model.addConstr(14 * x1 + x2 + 4 * x3 >= 10)
    model.addConstr(8 * x0 + x2 + 4 * x3 >= 10)
    model.addConstr(8 * x0 + 14 * x1 + x2 >= 10)
    model.addConstr(8 * x0 + 14 * x1 + 4 * x3 >= 10)
    model.addConstr(14 * x1 + x2 + 4 * x3 >= 15)
    model.addConstr(8 * x0 + x2 + 4 * x3 >= 15)
    model.addConstr(8 * x0 + 14 * x1 + x2 >= 15)
    model.addConstr(8 * x0 + 14 * x1 + 4 * x3 >= 15)
    model.addConstr(14 * x1 + x2 + 4 * x3 >= 15)
    model.addConstr(8 * x0 + x2 + 4 * x3 >= 15)
    model.addConstr(8 * x0 + 14 * x1 + x2 >= 15)
    model.addConstr(8 * x0 + 14 * x1 + 4 * x3 >= 15)
    model.addConstr(11 * x1 + 7 * x3 >= 28)
    model.addConstr(5 * x0 + 10 * x2 >= 17)
    model.addConstr(5 * x0 + 7 * x3 >= 28)
    model.addConstr(11 * x0 + x3 <= 68)
    model.addConstr(7 * x1 + x3 <= 46)
    model.addConstr(11 * x0 + 7 * x2 + x3 <= 61)
    model.addConstr(11 * x0 + 7 * x1 + 7 * x2 <= 39)
    model.addConstr(11 * x0 + 7 * x1 + 7 * x2 + x3 <= 39)
    model.addConstr(14 * x1 + x2 <= 41)
    model.addConstr(8 * x0 + x2 <= 31)
    model.addConstr(x2 + 4 * x3 <= 56)
    model.addConstr(8 * x0 + 14 * x1 <= 40)
    model.addConstr(8 * x0 + 14 * x1 + x2 <= 41)
    model.addConstr(8 * x0 + 14 * x1 + x2 + 4 * x3 <= 41)
    model.addConstr(5 * x0 + 11 * x1 <= 55)
    model.addConstr(5 * x0 + 10 * x2 + 7 * x3 <= 99)
    model.addConstr(5 * x0 + 11 * x1 + 7 * x3 <= 101)
    model.addConstr(5 * x0 + 11 * x1 + 10 * x2 + 7 * x3 <= 101)

    model.optimize()

    if model.status == gurobi.GRB.OPTIMAL:
        print("Objective: ", model.objVal)
        print("hamburgers: ", x0.varValue)
        print("eggs: ", x1.varValue)
        print("protein_bars: ", x2.varValue)
        print("pickles: ", x3.varValue)
    else:
        print("No optimal solution found")

create_and_solve_model()
```

The final answer is: 
```json
{
    'sym_variables': [
        ('x0', 'hamburgers'), 
        ('x1', 'eggs'), 
        ('x2', 'protein bars'), 
        ('x3', 'pickles')
    ], 
    'objective_function': '5*x0 + x1 + 7*x2 + 6*x3', 
    'constraints': [
        '11*x0 <= 159', 
        '8*x0 + 14*x1 + x2 + 4*x3 <= 87', 
        '5*x0 + 11*x1 + 10*x2 + 7*x3 <= 132', 
        '7*x1 + x3 >= 14', 
        '7*x1 + 7*x2 >= 34', 
        '11*x0 + 7*x1 >= 22', 
        'x2 + 4*x3 >= 20', 
        '14*x1 + x2 >= 14', 
        '8*x0 + 4*x3 >= 9', 
        '14*x1 + x2 + 4*x3 >= 21', 
        '8*x0 + x2 + 4*x3 >= 21', 
        '8*x0 + 14*x1 + x2 >= 21', 
        '8*x0 + 14*x1 + 4*x3 >= 21', 
        '14*x1 + x2 + 4*x3 >= 10', 
        '8*x0 + x2 + 4*x3 >= 10', 
        '8*x0 + 14*x1 + x2 >= 10', 
        '8*x0 + 14*x1 + 4*x3 >= 10', 
        '14*x1 + x2 + 4*x3 >= 15', 
        '8*x0 + x2 + 4*x3 >= 15', 
        '8*x0 + 14*x1 + x2 >= 15', 
        '8*x0 + 14*x1 + 4*x3 >= 15', 
        '14*x1 + x2 + 4*x3 >= 15', 
        '8*x0 + x2 + 4*x3 >= 15', 
        '8*x0 + 14*x1 + x2 >= 15', 
        '8*x0 + 14*x1 + 4*x3 >= 15', 
        '11*x1 + 7*x3 >= 28', 
        '5*x0 + 10*x2 >= 17', 
        '5*x0 + 7*x3 >= 28', 
        '11*x0 + x3 <= 68', 
        '7*x1 + x3 <= 46', 
        '11*x0 + 7*x2 + x3 <= 61', 
        '11*x0 + 7*x1 + 7*x2 <= 39', 
        '11*x0 + 7*x1 + 7*x2 + x3 <= 39', 
        '14*x1 + x2 <= 41', 
        '8*x0 + x2 <= 31', 
        'x2 + 4*x3 <= 56', 
        '8*x0 + 14*x1 <= 40', 
        '8*x0 + 14*x1 + x2 <= 41', 
        '8*x0 + 14*x1 + x2 + 4*x3 <= 41', 
        '5*x0 + 11*x1 <= 55', 
        '5*x0 + 10*x2 + 7*x3 <= 99', 
        '5*x0 + 11*x1 + 7*x3 <= 101', 
        '5*x0 + 11*x1 + 10*x2 + 7*x3 <= 101'
    ]
}
```