## Step 1: Define the symbolic representation of the variables
The variables are ['cherry pies', 'sashimi', 'knishes', 'black beans']. Let's denote them 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 $7.88x_0^2 + 2.33x_0x_2 + 2.88x_0x_3 + 3.07x_1^2 + 9.16x_1x_2 + 5.11x_1x_3 + 4.09x_0$.

## Step 3: List all the constraints in symbolic notation
Constraints:
1. $8x_0 \leq 103$
2. $12x_0 \leq 210$
3. $3x_1 \leq 103$
4. $6x_1 \leq 210$
5. $12x_2 \leq 103$
6. $9x_2 \leq 210$
7. $11x_3 \leq 103$
8. $11x_3 \leq 210$
9. $x_0^2 + x_1^2 + x_2^2 \geq 14$
10. $x_1 + x_2 + x_3 \geq 14$
11. $x_0 + x_1 + x_3 \geq 14$
12. $x_0 + x_2 + x_3 \geq 14$
13. $x_0 + x_1 + x_2 \geq 25$
14. $x_1 + x_2 + x_3 \geq 25$
15. $x_0 + x_1 + x_3 \geq 25$
16. $x_0 + x_2 + x_3 \geq 25$
17. $x_0 + x_1 + x_2 \geq 16$
18. $x_1^2 + x_2^2 + x_3^2 \geq 16$
19. $x_0^2 + x_1^2 + x_3^2 \geq 16$
20. $x_0^2 + x_1^2 + x_2^2 \geq 16$
21. $x_0 + x_2 + x_3 \geq 16$
22. $x_0 + x_1 + x_2 \geq 16$
23. $x_1 + x_2 + x_3 \geq 16$
24. $x_0^2, x_1^2, x_3^2 \geq 16$ is not directly given, but $x_0^2 + x_1^2 + x_3^2 \geq 16$ is
25. $x_0 + x_2 + x_3 \geq 16$
26. $12x_0 + 6x_1 \geq 36$
27. $9x_2^2 + 11x_3^2 \geq 17$
28. $12x_0^2 + 9x_2^2 \geq 46$
29. $6x_1 + 9x_2 \geq 47$
30. $12x_0^2 + 11x_3^2 \geq 31$
31. $6x_1^2 + 11x_3^2 \geq 19$
32. $12x_0^2 + 6x_1^2 + 9x_2^2 \geq 27$
33. $12x_0^2 + 9x_2^2 + 11x_3^2 \geq 27$
34. $12x_0 + 6x_1 + 9x_2 \geq 49$
35. $12x_0 + 9x_2 + 11x_3 \geq 49$
36. $5x_0 - 9x_1 - 2x_3 \geq 0$
37. $12x_2^2 + 11x_3^2 \leq 65$
38. $8x_0^2 + 3x_1^2 \leq 31$
39. $3x_1^2 + 12x_2^2 \leq 68$
40. $8x_0 + 3x_1 + 11x_3 \leq 89$
41. $3x_1 + 9x_2 + 11x_3 \leq 66$
42. $8x_0^2 + 12x_2^2 + 11x_3^2 \leq 75$
43. $8x_0 + 3x_1 + 12x_2 + 11x_3 \leq 75$
44. $6x_1 + 11x_3 \leq 123$
45. $9x_2 + 11x_3 \leq 62$
46. $12x_0 + 6x_1 \leq 89$
47. $6x_1^2 + 9x_2^2 \leq 111$
48. $12x_0 + 9x_2 \leq 62$
49. $12x_0^2 + 6x_1^2 + 9x_2^2 \leq 196$
50. $12x_0 + 9x_2 + 11x_3 \leq 63$
51. $6x_1^2 + 9x_2^2 + 11x_3^2 \leq 95$
52. $12x_0 + 6x_1 + 9x_2 + 11x_3 \leq 95$

## Step 4: Define the symbolic representation of the problem
```json
{
    'sym_variables': [
        ('x0', 'cherry pies'),
        ('x1', 'sashimi'),
        ('x2', 'knishes'),
        ('x3', 'black beans')
    ],
    'objective_function': '7.88*x0^2 + 2.33*x0*x2 + 2.88*x0*x3 + 3.07*x1^2 + 9.16*x1*x2 + 5.11*x1*x3 + 4.09*x0',
    'constraints': [
        '8*x0 <= 103',
        '12*x0 <= 210',
        '3*x1 <= 103',
        '6*x1 <= 210',
        '12*x2 <= 103',
        '9*x2 <= 210',
        '11*x3 <= 103',
        '11*x3 <= 210',
        'x0^2 + x1^2 + x2^2 >= 14',
        'x1 + x2 + x3 >= 14',
        'x0 + x1 + x3 >= 14',
        'x0 + x2 + x3 >= 14',
        'x0 + x1 + x2 >= 25',
        'x1 + x2 + x3 >= 25',
        'x0 + x1 + x3 >= 25',
        'x0 + x2 + x3 >= 25',
        'x0 + x1 + x2 >= 16',
        'x1^2 + x2^2 + x3^2 >= 16',
        'x0^2 + x1^2 + x3^2 >= 16',
        'x0^2 + x1^2 + x2^2 >= 16',
        'x0 + x2 + x3 >= 16',
        'x0 + x1 + x2 >= 16',
        'x1 + x2 + x3 >= 16',
        '12*x0 + 6*x1 >= 36',
        '9*x2^2 + 11*x3^2 >= 17',
        '12*x0^2 + 9*x2^2 >= 46',
        '6*x1 + 9*x2 >= 47',
        '12*x0^2 + 11*x3^2 >= 31',
        '6*x1^2 + 11*x3^2 >= 19',
        '12*x0^2 + 6*x1^2 + 9*x2^2 >= 27',
        '12*x0^2 + 9*x2^2 + 11*x3^2 >= 27',
        '12*x0 + 6*x1 + 9*x2 >= 49',
        '12*x0 + 9*x2 + 11*x3 >= 49',
        '5*x0 - 9*x1 - 2*x3 >= 0',
        '12*x2^2 + 11*x3^2 <= 65',
        '8*x0^2 + 3*x1^2 <= 31',
        '3*x1^2 + 12*x2^2 <= 68',
        '8*x0 + 3*x1 + 11*x3 <= 89',
        '3*x1 + 9*x2 + 11*x3 <= 66',
        '8*x0^2 + 12*x2^2 + 11*x3^2 <= 75',
        '8*x0 + 3*x1 + 12*x2 + 11*x3 <= 75',
        '6*x1 + 11*x3 <= 123',
        '9*x2 + 11*x3 <= 62',
        '12*x0 + 6*x1 <= 89',
        '6*x1^2 + 9*x2^2 <= 111',
        '12*x0 + 9*x2 <= 62',
        '12*x0^2 + 6*x1^2 + 9*x2^2 <= 196',
        '12*x0 + 9*x2 + 11*x3 <= 63',
        '6*x1^2 + 9*x2^2 + 11*x3^2 <= 95',
        '12*x0 + 6*x1 + 9*x2 + 11*x3 <= 95'
    ]
}
```

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

# Define the model
m = gp.Model()

# Define the variables
x0 = m.addVar(name="cherry_pies", vtype=gp.GRB.INTEGER)  # integer
x1 = m.addVar(name="sashimi")  # continuous
x2 = m.addVar(name="knishes")  # continuous
x3 = m.addVar(name="black_beans", vtype=gp.GRB.INTEGER)  # integer

# Define the objective function
m.setObjective(7.88 * x0**2 + 2.33 * x0 * x2 + 2.88 * x0 * x3 + 3.07 * x1**2 + 9.16 * x1 * x2 + 5.11 * x1 * x3 + 4.09 * x0, gp.GRB.MAXIMIZE)

# Add constraints
m.addConstr(8 * x0 <= 103)
m.addConstr(12 * x0 <= 210)
m.addConstr(3 * x1 <= 103)
m.addConstr(6 * x1 <= 210)
m.addConstr(12 * x2 <= 103)
m.addConstr(9 * x2 <= 210)
m.addConstr(11 * x3 <= 103)
m.addConstr(11 * x3 <= 210)

m.addConstr(x0**2 + x1**2 + x2**2 >= 14)
m.addConstr(x1 + x2 + x3 >= 14)
m.addConstr(x0 + x1 + x3 >= 14)
m.addConstr(x0 + x2 + x3 >= 14)
m.addConstr(x0 + x1 + x2 >= 25)
m.addConstr(x1 + x2 + x3 >= 25)
m.addConstr(x0 + x1 + x3 >= 25)
m.addConstr(x0 + x2 + x3 >= 25)
m.addConstr(x0 + x1 + x2 >= 16)
m.addConstr(x1**2 + x2**2 + x3**2 >= 16)
m.addConstr(x0**2 + x1**2 + x3**2 >= 16)
m.addConstr(x0**2 + x1**2 + x2**2 >= 16)
m.addConstr(x0 + x2 + x3 >= 16)
m.addConstr(x0 + x1 + x2 >= 16)
m.addConstr(x1 + x2 + x3 >= 16)

m.addConstr(12 * x0 + 6 * x1 >= 36)
m.addConstr(9 * x2**2 + 11 * x3**2 >= 17)
m.addConstr(12 * x0**2 + 9 * x2**2 >= 46)
m.addConstr(6 * x1 + 9 * x2 >= 47)
m.addConstr(12 * x0**2 + 11 * x3**2 >= 31)
m.addConstr(6 * x1**2 + 11 * x3**2 >= 19)
m.addConstr(12 * x0**2 + 6 * x1**2 + 9 * x2**2 >= 27)
m.addConstr(12 * x0**2 + 9 * x2**2 + 11 * x3**2 >= 27)
m.addConstr(12 * x0 + 6 * x1 + 9 * x2 >= 49)
m.addConstr(12 * x0 + 9 * x2 + 11 * x3 >= 49)
m.addConstr(5 * x0 - 9 * x1 - 2 * x3 >= 0)
m.addConstr(12 * x2**2 + 11 * x3**2 <= 65)
m.addConstr(8 * x0**2 + 3 * x1**2 <= 31)
m.addConstr(3 * x1**2 + 12 * x2**2 <= 68)
m.addConstr(8 * x0 + 3 * x1 + 11 * x3 <= 89)
m.addConstr(3 * x1 + 9 * x2 + 11 * x3 <= 66)
m.addConstr(8 * x0**2 + 12 * x2**2 + 11 * x3**2 <= 75)
m.addConstr(8 * x0 + 3 * x1 + 12 * x2 + 11 * x3 <= 75)
m.addConstr(6 * x1 + 11 * x3 <= 123)
m.addConstr(9 * x2 + 11 * x3 <= 62)
m.addConstr(12 * x0 + 6 * x1 <= 89)
m.addConstr(6 * x1**2 + 9 * x2**2 <= 111)
m.addConstr(12 * x0 + 9 * x2 <= 62)
m.addConstr(12 * x0**2 + 6 * x1**2 + 9 * x2**2 <= 196)
m.addConstr(12 * x0 + 9 * x2 + 11 * x3 <= 63)
m.addConstr(6 * x1**2 + 9 * x2**2 + 11 * x3**2 <= 95)
m.addConstr(12 * x0 + 6 * x1 + 9 * x2 + 11 * x3 <= 95)

# Solve the model
m.optimize()

# Print the solution
if m.status == gp.GRB.OPTIMAL:
    print("Objective: ", m.objVal)
    print("x0: ", x0.varValue)
    print("x1: ", x1.varValue)
    print("x2: ", x2.varValue)
    print("x3: ", x3.varValue)
else:
    print("The model is infeasible")
```