## Step 1: Define the symbolic representation of the problem
The problem involves maximizing an objective function subject to several constraints. The variables are 'strips of bacon', 'tomatoes', 'peanutbutter sandwiches', and 'bowls of cereal', which we can denote as $x_0, x_1, x_2, x_3$ respectively.

## Step 2: Translate the objective function into symbolic notation
The objective function to maximize is $2.44x_0^2 + 4.98x_0x_1 + 8.8x_0x_2 + 6.8x_1x_3$.

## 3: List the constraints in symbolic notation
Constraints:
1. $16x_0 + 8x_1 + 14x_2 + 10x_3 \leq 214$ (calcium constraint)
2. $18x_0 + 10x_1 + 9x_2 + 21x_3 \leq 259$ (sourness index constraint)
3. $16x_0 + 8x_1 \geq 17$ (calcium from bacon and tomatoes)
4. $8x_1 + 14x_2 + 10x_3 \geq 32$ (calcium from tomatoes, peanutbutter sandwiches, and bowls of cereal)
5. $16x_0 + 8x_1 + 10x_3 \geq 32$ (calcium from bacon, tomatoes, and bowls of cereal)
6. $8x_1^2 + 14x_2^2 + 10x_3^2 \geq 36$ (calcium from squares of tomatoes, peanutbutter sandwiches, and bowls of cereal)
7. $16x_0 + 8x_1 + 10x_3 \geq 36$ (calcium from bacon, tomatoes, and bowls of cereal)
8. $10x_1^2 + 21x_3^2 \geq 49$ (sourness from tomatoes and bowls of cereal)
9. $10x_1^2 + 9x_2^2 \geq 49$ (sourness from tomatoes and peanutbutter sandwiches)
10. $18x_0 + 10x_1 \geq 34$ (sourness from bacon and tomatoes)
11. $18^2x_0^2 + 10^2x_1^2 + 21^2x_3^2 \geq 40$ (sourness from squares of bacon, tomatoes, and bowls of cereal)
12. $10x_1^2 + 9x_2^2 + 21x_3^2 \geq 40$ (sourness from squares of tomatoes, peanutbutter sandwiches, and bowls of cereal)
13. $18^2x_0^2 + 9^2x_2^2 + 21^2x_3^2 \geq 40$ (sourness from squares of bacon, peanutbutter sandwiches, and bowls of cereal)
14. $18x_0 + 10x_1 + 21x_3 \geq 45$ (sourness from bacon, tomatoes, and bowls of cereal)
15. $10x_1^2 + 9x_2^2 + 21x_3^2 \geq 45$ (sourness from squares of tomatoes, peanutbutter sandwiches, and bowls of cereal)
16. $18x_0 + 9x_2 + 21x_3 \geq 45$ (sourness from bacon, peanutbutter sandwiches, and bowls of cereal)
17. $18x_0 + 10x_1 + 21x_3 \geq 55$ (sourness from bacon, tomatoes, and bowls of cereal)
18. $10x_1^2 + 9x_2^2 + 21x_3^2 \geq 55$ (sourness from squares of tomatoes, peanutbutter sandwiches, and bowls of cereal)
19. $18x_0 + 9x_2 + 21x_3 \geq 55$ (sourness from bacon, peanutbutter sandwiches, and bowls of cereal)
20. $14x_2 + 10x_3 \leq 91$ (calcium from peanutbutter sandwiches and bowls of cereal)
21. $8x_1 + 14x_2 \leq 68$ (calcium from tomatoes and peanutbutter sandwiches)
22. $16x_0 + 8x_1 \leq 137$ (calcium from bacon and tomatoes)
23. $8x_1 + 10x_3 \leq 186$ (calcium from tomatoes and bowls of cereal)
24. $16x_0 + 10x_3 \leq 190$ (calcium from bacon and bowls of cereal)
25. $16x_0 + 14x_2 + 10x_3 \leq 57$ (calcium from bacon, peanutbutter sandwiches, and bowls of cereal)
26. $16x_0 + 8x_1 + 14x_2 + 10x_3 \leq 57$ (calcium from all sources)
27. $9x_2 + 21x_3 \leq 228$ (sourness from peanutbutter sandwiches and bowls of cereal)
28. $18x_0 + 9x_2 \leq 245$ (sourness from bacon and peanutbutter sandwiches)
29. $18^2x_0^2 + 10^2x_1^2 \leq 109$ (sourness from squares of bacon and tomatoes)
30. $18x_0 + 10x_1 + 9x_2 \leq 147$ (sourness from bacon, tomatoes, and peanutbutter sandwiches)
31. $10x_1 + 9x_2 + 21x_3 \leq 150$ (sourness from tomatoes, peanutbutter sandwiches, and bowls of cereal)
32. $18x_0 + 10x_1 + 9x_2 + 21x_3 \leq 150$ (sourness from all sources)

## 4: Define the symbolic variables
The symbolic variables are:
- $x_0$ for 'strips of bacon'
- $x_1$ for 'tomatoes'
- $x_2$ for 'peanutbutter sandwiches'
- $x_3$ for 'bowls of cereal'

## 5: Output the symbolic representation of the problem
```json
{
    'sym_variables': [('x0', 'strips of bacon'), ('x1', 'tomatoes'), ('x2', 'peanutbutter sandwiches'), ('x3', 'bowls of cereal')],
    'objective_function': '2.44*x0^2 + 4.98*x0*x1 + 8.8*x0*x2 + 6.8*x1*x3',
    'constraints': [
        '16*x0 + 8*x1 + 14*x2 + 10*x3 <= 214',
        '18*x0 + 10*x1 + 9*x2 + 21*x3 <= 259',
        '16*x0 + 8*x1 >= 17',
        '8*x1 + 14*x2 + 10*x3 >= 32',
        '16*x0 + 8*x1 + 10*x3 >= 32',
        '8*x1^2 + 14*x2^2 + 10*x3^2 >= 36',
        '16*x0 + 8*x1 + 10*x3 >= 36',
        '10*x1^2 + 21*x3^2 >= 49',
        '10*x1^2 + 9*x2^2 >= 49',
        '18*x0 + 10*x1 >= 34',
        '18^2*x0^2 + 10^2*x1^2 + 21^2*x3^2 >= 40',
        '10*x1^2 + 9*x2^2 + 21*x3^2 >= 40',
        '18^2*x0^2 + 9^2*x2^2 + 21^2*x3^2 >= 40',
        '18*x0 + 10*x1 + 21*x3 >= 45',
        '10*x1^2 + 9*x2^2 + 21*x3^2 >= 45',
        '18*x0 + 9*x2 + 21*x3 >= 45',
        '18*x0 + 10*x1 + 21*x3 >= 55',
        '10*x1^2 + 9*x2^2 + 21*x3^2 >= 55',
        '18*x0 + 9*x2 + 21*x3 >= 55',
        '14*x2 + 10*x3 <= 91',
        '8*x1 + 14*x2 <= 68',
        '16*x0 + 8*x1 <= 137',
        '8*x1 + 10*x3 <= 186',
        '16*x0 + 10*x3 <= 190',
        '16*x0 + 14*x2 + 10*x3 <= 57',
        '16*x0 + 8*x1 + 14*x2 + 10*x3 <= 57',
        '9*x2 + 21*x3 <= 228',
        '18*x0 + 9*x2 <= 245',
        '18^2*x0^2 + 10^2*x1^2 <= 109',
        '18*x0 + 10*x1 + 9*x2 <= 147',
        '10*x1 + 9*x2 + 21*x3 <= 150',
        '18*x0 + 10*x1 + 9*x2 + 21*x3 <= 150'
    ]
}
```

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

# Define the model
m = gurobi.Model()

# Define the variables
x0 = m.addVar(name="x0", lb=-gurobi.GRB.INFINITY)  # strips of bacon
x1 = m.addVar(name="x1", lb=-gurobi.GRB.INFINITY)  # tomatoes
x2 = m.addVar(name="x2", lb=-gurobi.GRB.INFINITY)  # peanutbutter sandwiches
x3 = m.addVar(name="x3", lb=0, type=gurobi.GRB.INTEGER)  # bowls of cereal

# Objective function
m.setObjective(2.44*x0**2 + 4.98*x0*x1 + 8.8*x0*x2 + 6.8*x1*x3, gurobi.GRB.MAXIMIZE)

# Constraints
m.addConstr(16*x0 + 8*x1 + 14*x2 + 10*x3 <= 214)
m.addConstr(18*x0 + 10*x1 + 9*x2 + 21*x3 <= 259)
m.addConstr(16*x0 + 8*x1 >= 17)
m.addConstr(8*x1 + 14*x2 + 10*x3 >= 32)
m.addConstr(16*x0 + 8*x1 + 10*x3 >= 32)
m.addConstr(8*x1**2 + 14*x2**2 + 10*x3**2 >= 36)
m.addConstr(16*x0 + 8*x1 + 10*x3 >= 36)
m.addConstr(10*x1**2 + 21*x3**2 >= 49)
m.addConstr(10*x1**2 + 9*x2**2 >= 49)
m.addConstr(18*x0 + 10*x1 >= 34)
m.addConstr((18*x0)**2 + (10*x1)**2 + (21*x3)**2 >= 40)
m.addConstr(10*x1**2 + 9*x2**2 + 21*x3**2 >= 40)
m.addConstr((18*x0)**2 + (9*x2)**2 + (21*x3)**2 >= 40)
m.addConstr(18*x0 + 10*x1 + 21*x3 >= 45)
m.addConstr(10*x1**2 + 9*x2**2 + 21*x3**2 >= 45)
m.addConstr(18*x0 + 9*x2 + 21*x3 >= 45)
m.addConstr(18*x0 + 10*x1 + 21*x3 >= 55)
m.addConstr(10*x1**2 + 9*x2**2 + 21*x3**2 >= 55)
m.addConstr(18*x0 + 9*x2 + 21*x3 >= 55)
m.addConstr(14*x2 + 10*x3 <= 91)
m.addConstr(8*x1 + 14*x2 <= 68)
m.addConstr(16*x0 + 8*x1 <= 137)
m.addConstr(8*x1 + 10*x3 <= 186)
m.addConstr(16*x0 + 10*x3 <= 190)
m.addConstr(16*x0 + 14*x2 + 10*x3 <= 57)
m.addConstr(16*x0 + 8*x1 + 14*x2 + 10*x3 <= 57)
m.addConstr(9*x2 + 21*x3 <= 228)
m.addConstr(18*x0 + 9*x2 <= 245)
m.addConstr((18*x0)**2 + (10*x1)**2 <= 109)
m.addConstr(18*x0 + 10*x1 + 9*x2 <= 147)
m.addConstr(10*x1 + 9*x2 + 21*x3 <= 150)
m.addConstr(18*x0 + 10*x1 + 9*x2 + 21*x3 <= 150)

# 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")
```