## Step 1: Define the symbolic representation of the variables
The variables are 'apple pies', 'lemons', and 'bowls of cereal', which we will denote as $x_1$, $x_2$, and $x_3$ respectively.

## Step 2: Convert the objective function into a symbolic representation
The objective function to minimize is $7.06 \cdot x_1 \cdot x_2 + 9.79 \cdot x_2^2 + 8.75 \cdot x_2 \cdot x_3 + 8.31 \cdot x_3$.

## 3: List the constraints with symbolic variables
The constraints are:
1. $12.53x_1 + 10.8x_2 + 12.65x_3 \leq 143$ (milligrams of iron)
2. $7.39x_1 + 12.51x_2 + 5.63x_3 \leq 198$ (sourness index)
3. $7.25x_1 + 0.15x_2 + 3.3x_3 \leq 127$ (grams of carbohydrates)
4. $12.53x_1^2 + 12.65x_3^2 \geq 38$ (iron from apple pies and bowls of cereal)
5. $12.53x_1^2 + 10.8x_2^2 + 12.65x_3^2 \geq 28$ (iron from all sources squared)
6. $12.53x_1 + 10.8x_2 + 12.65x_3 \geq 28$ (total iron)
7. $7.39x_1 + 5.63x_3 \geq 42$ (sourness index from apple pies and bowls of cereal)
8. $12.51x_2 + 5.63x_3 \geq 32$ (sourness index from lemons and bowls of cereal)
9. $7.39x_1 + 12.51x_2 + 5.63x_3 \geq 32$ (total sourness index)
10. $7.25x_1 + 3.3x_3 \geq 23$ (carbohydrates from apple pies and bowls of cereal)
11. $0.15x_2^2 + 3.3x_3^2 \geq 36$ (carbohydrates from lemons and bowls of cereal squared)
12. $7.25x_1 + 0.15x_2 + 3.3x_3 \geq 39$ (total carbohydrates)
13. $7.25x_1 + 0.15x_2 + 3.3x_3 \geq 39$ (duplicate of total carbohydrates)
14. $12.53x_1^2 + 12.65x_3^2 \leq 114$ (upper limit on iron from apple pies and bowls of cereal squared)
15. $10.8x_2 + 12.65x_3 \leq 114$ (upper limit on iron from lemons and bowls of cereal)
16. $0.15x_2 + 3.3x_3 \leq 112$ (upper limit on carbohydrates from lemons and bowls of cereal)
17. $7.25x_1^2 + 3.3x_3^2 \leq 79$ (upper limit on carbohydrates from apple pies and bowls of cereal squared)
18. $x_1, x_2, x_3 \in \mathbb{Z}$ (integer constraints)

## Step 4: Create the symbolic representation dictionary
```json
{
    'sym_variables': [
        ('x1', 'apple pies'), 
        ('x2', 'lemons'), 
        ('x3', 'bowls of cereal')
    ], 
    'objective_function': '7.06 * x1 * x2 + 9.79 * x2^2 + 8.75 * x2 * x3 + 8.31 * x3', 
    'constraints': [
        '12.53 * x1 + 10.8 * x2 + 12.65 * x3 <= 143',
        '7.39 * x1 + 12.51 * x2 + 5.63 * x3 <= 198',
        '7.25 * x1 + 0.15 * x2 + 3.3 * x3 <= 127',
        '12.53 * x1^2 + 12.65 * x3^2 >= 38',
        '12.53 * x1^2 + 10.8 * x2^2 + 12.65 * x3^2 >= 28',
        '12.53 * x1 + 10.8 * x2 + 12.65 * x3 >= 28',
        '7.39 * x1 + 5.63 * x3 >= 42',
        '12.51 * x2 + 5.63 * x3 >= 32',
        '7.39 * x1 + 12.51 * x2 + 5.63 * x3 >= 32',
        '7.25 * x1 + 3.3 * x3 >= 23',
        '0.15 * x2^2 + 3.3 * x3^2 >= 36',
        '7.25 * x1 + 0.15 * x2 + 3.3 * x3 >= 39',
        '7.25 * x1 + 0.15 * x2 + 3.3 * x3 >= 39',
        '12.53 * x1^2 + 12.65 * x3^2 <= 114',
        '10.8 * x2 + 12.65 * x3 <= 114',
        '0.15 * x2 + 3.3 * x3 <= 112',
        '7.25 * x1^2 + 3.3 * x3^2 <= 79'
    ]
}
```

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

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

# Define the variables
x1 = m.addVar(name='apple_pies', vtype=gurobi.GRB.INTEGER)
x2 = m.addVar(name='lemons', vtype=gurobi.GRB.INTEGER)
x3 = m.addVar(name='bowls_of_cereal', vtype=gurobi.GRB.INTEGER)

# Objective function
m.setObjective(7.06 * x1 * x2 + 9.79 * x2**2 + 8.75 * x2 * x3 + 8.31 * x3, gurobi.GRB.MINIMIZE)

# Constraints
m.addConstr(12.53 * x1 + 10.8 * x2 + 12.65 * x3 <= 143)
m.addConstr(7.39 * x1 + 12.51 * x2 + 5.63 * x3 <= 198)
m.addConstr(7.25 * x1 + 0.15 * x2 + 3.3 * x3 <= 127)
m.addConstr(12.53 * x1**2 + 12.65 * x3**2 >= 38)
m.addConstr(12.53 * x1**2 + 10.8 * x2**2 + 12.65 * x3**2 >= 28)
m.addConstr(12.53 * x1 + 10.8 * x2 + 12.65 * x3 >= 28)
m.addConstr(7.39 * x1 + 5.63 * x3 >= 42)
m.addConstr(12.51 * x2 + 5.63 * x3 >= 32)
m.addConstr(7.39 * x1 + 12.51 * x2 + 5.63 * x3 >= 32)
m.addConstr(7.25 * x1 + 3.3 * x3 >= 23)
m.addConstr(0.15 * x2**2 + 3.3 * x3**2 >= 36)
m.addConstr(7.25 * x1 + 0.15 * x2 + 3.3 * x3 >= 39)
m.addConstr(7.25 * x1 + 0.15 * x2 + 3.3 * x3 >= 39)
m.addConstr(12.53 * x1**2 + 12.65 * x3**2 <= 114)
m.addConstr(10.8 * x2 + 12.65 * x3 <= 114)
m.addConstr(0.15 * x2 + 3.3 * x3 <= 112)
m.addConstr(7.25 * x1**2 + 3.3 * x3**2 <= 79)

# Optimize the model
m.optimize()

# Print the solution
if m.status == gurobi.GRB.OPTIMAL:
    print('Objective: ', m.objVal)
    print('Apple pies: ', x1.varValue)
    print('Lemons: ', x2.varValue)
    print('Bowls of cereal: ', x3.varValue)
else:
    print('The model is infeasible')
```