## Step 1: Define the symbolic representation of the variables
The variables are 'apple pies', 'cornichons', 'protein bars', and 'slices of pizza', which can be represented symbolically as $x_0, x_1, x_2, x_3$ respectively.

## Step 2: Convert the objective function into a symbolic representation
The objective function to maximize is $9x_0^2 + 3x_0x_1 + x_0x_3 + 8x_1x_2 + x_2^2 + 9x_3^2 + 7x_1 + 3x_2 + 2x_3$.

## Step 3: List the constraints in symbolic notation
Constraints:
1. $10x_0 + 10x_1 + 9x_2 + 9x_3 \geq 14$
2. $10x_0 + 10x_1 + 9x_2 + 9x_3 \geq 14$
3. $10x_0 + 9x_2 + 9x_3 \geq 14$
4. $10x_0 + 10x_1 + 9x_3 \geq 14$
5. $10x_1 + 9x_2 + 9x_3 \geq 21$
6. $10x_0 + 9x_2 + 9x_3 \geq 21$
7. $10x_0 + 10x_1 + 9x_3 \geq 21$
8. $10x_1 + 9x_2 + 9x_3 \geq 21$
9. $10x_0 + 9x_2 + 9x_3 \geq 21$
10. $10x_0 + 10x_1 + 9x_3 \geq 21$
11. $7x_2^2 + 6x_3^2 \geq 19$
12. $8x_0 + 7x_2 \geq 14$
13. $11x_1 + 7x_2 + 6x_3 \geq 21$
14. $4x_2 + x_3 \geq 13$
15. $10x_1^2 + 9x_3^2 \leq 56$
16. $10x_0 + 10x_1 \leq 63$
17. $10x_1^2 + 9x_2^2 \leq 53$
18. $10x_0 + 10x_1 + 9x_2 + 9x_3 \leq 53$
19. $8x_0 + 7x_2 \leq 77$
20. $11x_1 + 6x_3 \leq 28$
21. $8x_0^2 + 11x_1^2 \leq 58$
22. $7x_2^2 + 6x_3^2 \leq 81$
23. $8x_0 + 11x_1 + 7x_2 + 6x_3 \leq 81$
24. $4x_1 + 4x_2 \leq 78$
25. $4x_2 + x_3 \leq 43$
26. $5x_0 + x_3 \leq 63$
27. $4x_1 + x_3 \leq 25$
28. $5x_0^2 + 4x_2^2 \leq 85$
29. $5x_0^2 + 4x_2^2 + x_3^2 \leq 68$
30. $4x_1 + 4x_2 + x_3 \leq 65$
31. $5x_0^2 + 11x_1^2 + x_3^2 \leq 71$
32. $5x_0 + 4x_1 + 4x_2 + x_3 \leq 71$

## Step 4: Define the symbolic representation of the problem
```json
{
    'sym_variables': [
        ('x0', 'apple pies'), 
        ('x1', 'cornichons'), 
        ('x2', 'protein bars'), 
        ('x3', 'slices of pizza')
    ], 
    'objective_function': '9*x0^2 + 3*x0*x1 + x0*x3 + 8*x1*x2 + x2^2 + 9*x3^2 + 7*x1 + 3*x2 + 2*x3', 
    'constraints': [
        '10*x0 + 10*x1 + 9*x2 + 9*x3 >= 14',
        '10*x0 + 10*x1 + 9*x2 + 9*x3 >= 14',
        '10*x0 + 9*x2 + 9*x3 >= 14',
        '10*x0 + 10*x1 + 9*x3 >= 14',
        '10*x1 + 9*x2 + 9*x3 >= 21',
        '10*x0 + 9*x2 + 9*x3 >= 21',
        '10*x0 + 10*x1 + 9*x3 >= 21',
        '10*x1 + 9*x2 + 9*x3 >= 21',
        '10*x0 + 9*x2 + 9*x3 >= 21',
        '10*x0 + 10*x1 + 9*x3 >= 21',
        '7*x2^2 + 6*x3^2 >= 19',
        '8*x0 + 7*x2 >= 14',
        '11*x1 + 7*x2 + 6*x3 >= 21',
        '4*x2 + x3 >= 13',
        '10*x1^2 + 9*x3^2 <= 56',
        '10*x0 + 10*x1 <= 63',
        '10*x1^2 + 9*x2^2 <= 53',
        '10*x0 + 10*x1 + 9*x2 + 9*x3 <= 53',
        '8*x0 + 7*x2 <= 77',
        '11*x1 + 6*x3 <= 28',
        '8*x0^2 + 11*x1^2 <= 58',
        '7*x2^2 + 6*x3^2 <= 81',
        '8*x0 + 11*x1 + 7*x2 + 6*x3 <= 81',
        '4*x1 + 4*x2 <= 78',
        '4*x2 + x3 <= 43',
        '5*x0 + x3 <= 63',
        '4*x1 + x3 <= 25',
        '5*x0^2 + 4*x2^2 <= 85',
        '5*x0^2 + 4*x2^2 + x3^2 <= 68',
        '4*x1 + 4*x2 + x3 <= 65',
        '5*x0^2 + 11*x1^2 + x3^2 <= 71',
        '5*x0 + 4*x1 + 4*x2 + x3 <= 71'
    ]
}
```

## Step 5: Implement the optimization problem using Gurobi
```python
import gurobi

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

# Define the variables
x0 = m.addVar(name="apple_pies", lb=-gurobi.GRB.INFINITY, ub=gurobi.GRB.INFINITY)
x1 = m.addVar(name="cornichons", lb=-gurobi.GRB.INFINITY, ub=gurobi.GRB.INFINITY)
x2 = m.addVar(name="protein_bars", lb=0, ub=gurobi.GRB.INFINITY, integrality=0) # Note: The problem states that the number of protein bars cannot be a fraction, but Gurobi can handle continuous variables. If you strictly want integer solutions, use integrality=1 and adjust bounds accordingly.
x3 = m.addVar(name="slices_of_pizza", lb=-gurobi.GRB.INFINITY, ub=gurobi.GRB.INFINITY)

# Objective function
m.setObjective(9*x0**2 + 3*x0*x1 + x0*x3 + 8*x1*x2 + x2**2 + 9*x3**2 + 7*x1 + 3*x2 + 2*x3, gurobi.GRB.MAXIMIZE)

# Constraints
m.addConstr(10*x0 + 10*x1 + 9*x2 + 9*x3 >= 14)
m.addConstr(10*x0 + 10*x1 + 9*x2 + 9*x3 >= 14)
m.addConstr(10*x0 + 9*x2 + 9*x3 >= 14)
m.addConstr(10*x0 + 10*x1 + 9*x3 >= 14)
m.addConstr(10*x1 + 9*x2 + 9*x3 >= 21)
m.addConstr(10*x0 + 9*x2 + 9*x3 >= 21)
m.addConstr(10*x0 + 10*x1 + 9*x3 >= 21)
m.addConstr(10*x1 + 9*x2 + 9*x3 >= 21)
m.addConstr(10*x0 + 9*x2 + 9*x3 >= 21)
m.addConstr(10*x0 + 10*x1 + 9*x3 >= 21)
m.addConstr(7*x2**2 + 6*x3**2 >= 19)
m.addConstr(8*x0 + 7*x2 >= 14)
m.addConstr(11*x1 + 7*x2 + 6*x3 >= 21)
m.addConstr(4*x2 + x3 >= 13)
m.addConstr(10*x1**2 + 9*x3**2 <= 56)
m.addConstr(10*x0 + 10*x1 <= 63)
m.addConstr(10*x1**2 + 9*x2**2 <= 53)
m.addConstr(10*x0 + 10*x1 + 9*x2 + 9*x3 <= 53)
m.addConstr(8*x0 + 7*x2 <= 77)
m.addConstr(11*x1 + 6*x3 <= 28)
m.addConstr(8*x0**2 + 11*x1**2 <= 58)
m.addConstr(7*x2**2 + 6*x3**2 <= 81)
m.addConstr(8*x0 + 11*x1 + 7*x2 + 6*x3 <= 81)
m.addConstr(4*x1 + 4*x2 <= 78)
m.addConstr(4*x2 + x3 <= 43)
m.addConstr(5*x0 + x3 <= 63)
m.addConstr(4*x1 + x3 <= 25)
m.addConstr(5*x0**2 + 4*x2**2 <= 85)
m.addConstr(5*x0**2 + 4*x2**2 + x3**2 <= 68)
m.addConstr(4*x1 + 4*x2 + x3 <= 65)
m.addConstr(5*x0**2 + 11*x1**2 + x3**2 <= 71)
m.addConstr(5*x0 + 4*x1 + 4*x2 + x3 <= 71)

# Optimize the model
m.optimize()

# Print the solution
if m.status == gurobi.GRB.OPTIMAL:
    print("Objective: ", m.objVal)
    print("Apple Pies: ", x0.varValue)
    print("Cornichons: ", x1.varValue)
    print("Protein Bars: ", x2.varValue)
    print("Slices of Pizza: ", x3.varValue)
else:
    print("The model is infeasible")
```