## Step 1: Define the symbolic representation of the variables
The variables are 'slices of pizza', 'cherry pies', 'peanutbutter sandwiches', and 'protein bars'. Let's denote them as $x_0$, $x_1$, $x_2$, and $x_3$ respectively.

## Step 2: Convert the objective function into symbolic notation
The objective function to minimize is $8x_0x_1 + 8x_1^2 + 9x_2^2 + x_2$.

## 3: List all the constraints in symbolic notation
1. $8x_0 \leq 255$
2. $6x_0 + 5x_1 + 14x_2 + 24x_3 \leq 271$
3. $3x_0 + 8x_1 + x_2 + 15x_3 \leq 146$
4. $10x_2^2 + 18x_3^2 \geq 42$
5. $8x_0 + 18x_3 \geq 37$
6. $8x_0 + 15x_1 \geq 21$
7. $8x_0 + 15x_1 + 10x_2 + 18x_3 \geq 21$
8. $6x_0 + 5x_1 \geq 30$
9. $6^2x_0^2 + 24^2x_3^2 \geq 50$
10. $14x_2 + 24x_3 \geq 41$
11. $6x_0 + 14x_2 \geq 49$
12. $6x_0 + 5x_1 + 14x_2 + 24x_3 \geq 49$
13. $3^2x_0^2 + x_2^2 \geq 19$
14. $3x_0 + 8x_1 \geq 15$
15. $8^2x_1^2 + 15^2x_3^2 \geq 22$
16. $3x_0 + 8x_1 + x_2 + 15x_3 \geq 22$
17. $4x_0^2 - 7x_2^2 \geq 0$
18. $15x_1 + 18x_3 \leq 223$
19. $8x_0 + 18x_3 \leq 182$
20. $8^2x_0^2 + 10^2x_2^2 \leq 85$
21. $10^2x_2^2 + 18^2x_3^2 \leq 189$
22. $15^2x_1^2 + 10^2x_2^2 \leq 159$
23. $8x_0 + 15x_1 \leq 140$
24. $8x_0 + 10x_2 + 18x_3 \leq 241$
25. $15x_1 + 10x_2 + 18x_3 \leq 130$
26. $8x_0 + 15x_1 + 18x_3 \leq 231$
27. $8x_0 + 15x_1 + 10x_2 \leq 216$
28. $6x_0 + 14x_2 \leq 139$
29. $6x_0 + 5x_1 \leq 110$
30. $5^2x_1^2 + 14^2x_2^2 \leq 200$
31. $6x_0 + 24x_3 \leq 239$
32. $6x_0 + 5x_1 + 24x_3 \leq 156$
33. $8x_1 + 15x_3 \leq 86$
34. $x_2 \in \mathbb{Z}$
35. $x_3 \in \mathbb{Z}$

## 4: Provide the symbolic representation of the problem
```json
{
'sym_variables': [
    ('x0', 'slices of pizza'), 
    ('x1', 'cherry pies'), 
    ('x2', 'peanutbutter sandwiches'), 
    ('x3', 'protein bars')
],
'objective_function': '8*x0*x1 + 8*x1^2 + 9*x2^2 + x2',
'constraints': [
    '8*x0 <= 255',
    '6*x0 + 5*x1 + 14*x2 + 24*x3 <= 271',
    '3*x0 + 8*x1 + x2 + 15*x3 <= 146',
    '10*x2^2 + 18*x3^2 >= 42',
    '8*x0 + 18*x3 >= 37',
    '8*x0 + 15*x1 >= 21',
    '8*x0 + 15*x1 + 10*x2 + 18*x3 >= 21',
    '6*x0 + 5*x1 >= 30',
    '36*x0^2 + 576*x3^2 >= 50',
    '14*x2 + 24*x3 >= 41',
    '6*x0 + 14*x2 >= 49',
    '6*x0 + 5*x1 + 14*x2 + 24*x3 >= 49',
    '9*x0^2 + x2^2 >= 19',
    '3*x0 + 8*x1 >= 15',
    '64*x1^2 + 225*x3^2 >= 22',
    '3*x0 + 8*x1 + x2 + 15*x3 >= 22',
    '4*x0^2 - 7*x2^2 >= 0',
    '15*x1 + 18*x3 <= 223',
    '8*x0 + 18*x3 <= 182',
    '64*x0^2 + 100*x2^2 <= 85',
    '100*x2^2 + 324*x3^2 <= 189',
    '225*x1^2 + 100*x2^2 <= 159',
    '8*x0 + 15*x1 <= 140',
    '8*x0 + 10*x2 + 18*x3 <= 241',
    '15*x1 + 10*x2 + 18*x3 <= 130',
    '8*x0 + 15*x1 + 18*x3 <= 231',
    '8*x0 + 15*x1 + 10*x2 <= 216',
    '6*x0 + 14*x2 <= 139',
    '6*x0 + 5*x1 <= 110',
    '25*x1^2 + 196*x2^2 <= 200',
    '6*x0 + 24*x3 <= 239',
    '6*x0 + 5*x1 + 24*x3 <= 156',
    '8*x1 + 15*x3 <= 86'
]
}
```

## 5: Write the Gurobi code
```python
import gurobi

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

# Define the variables
x0 = m.addVar(name="x0", lb=0)  # slices of pizza
x1 = m.addVar(name="x1", lb=0)  # cherry pies
x2 = m.addVar(name="x2", lb=0, integrality=gurobi.GRB.INTEGER)  # peanutbutter sandwiches
x3 = m.addVar(name="x3", lb=0, integrality=gurobi.GRB.INTEGER)  # protein bars

# Objective function
m.setObjective(8 * x0 * x1 + 8 * x1 ** 2 + 9 * x2 ** 2 + x2, gurobi.GRB.MINIMIZE)

# Constraints
m.addConstr(8 * x0 <= 255)
m.addConstr(6 * x0 + 5 * x1 + 14 * x2 + 24 * x3 <= 271)
m.addConstr(3 * x0 + 8 * x1 + x2 + 15 * x3 <= 146)
m.addConstr(10 * x2 ** 2 + 18 * x3 ** 2 >= 42)
m.addConstr(8 * x0 + 18 * x3 >= 37)
m.addConstr(8 * x0 + 15 * x1 >= 21)
m.addConstr(8 * x0 + 15 * x1 + 10 * x2 + 18 * x3 >= 21)
m.addConstr(6 * x0 + 5 * x1 >= 30)
m.addConstr(36 * x0 ** 2 + 576 * x3 ** 2 >= 50)
m.addConstr(14 * x2 + 24 * x3 >= 41)
m.addConstr(6 * x0 + 14 * x2 >= 49)
m.addConstr(6 * x0 + 5 * x1 + 14 * x2 + 24 * x3 >= 49)
m.addConstr(9 * x0 ** 2 + x2 ** 2 >= 19)
m.addConstr(3 * x0 + 8 * x1 >= 15)
m.addConstr(64 * x1 ** 2 + 225 * x3 ** 2 >= 22)
m.addConstr(3 * x0 + 8 * x1 + x2 + 15 * x3 >= 22)
m.addConstr(4 * x0 ** 2 - 7 * x2 ** 2 >= 0)
m.addConstr(15 * x1 + 18 * x3 <= 223)
m.addConstr(8 * x0 + 18 * x3 <= 182)
m.addConstr(64 * x0 ** 2 + 100 * x2 ** 2 <= 85)
m.addConstr(100 * x2 ** 2 + 324 * x3 ** 2 <= 189)
m.addConstr(225 * x1 ** 2 + 100 * x2 ** 2 <= 159)
m.addConstr(8 * x0 + 15 * x1 <= 140)
m.addConstr(8 * x0 + 10 * x2 + 18 * x3 <= 241)
m.addConstr(15 * x1 + 10 * x2 + 18 * x3 <= 130)
m.addConstr(8 * x0 + 15 * x1 + 18 * x3 <= 231)
m.addConstr(8 * x0 + 15 * x1 + 10 * x2 <= 216)
m.addConstr(6 * x0 + 14 * x2 <= 139)
m.addConstr(6 * x0 + 5 * x1 <= 110)
m.addConstr(25 * x1 ** 2 + 196 * x2 ** 2 <= 200)
m.addConstr(6 * x0 + 24 * x3 <= 239)
m.addConstr(6 * x0 + 5 * x1 + 24 * x3 <= 156)
m.addConstr(8 * x1 + 15 * x3 <= 86)

# Solve the model
m.optimize()

# Print the solution
if m.status == gurobi.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")
```