## Step 1: Define the symbolic representation of the variables
The variables are 'apple pies', 'bowls of pasta', 'bowls of cereal', and 'ham sandwiches'. Let's denote them as $x_0, x_1, x_2, x_3$ respectively.

## Step 2: Convert the natural language objects into symbolic notation
The symbolic representation of the variables is:
- $x_0$ : 'apple pies'
- $x_1$ : 'bowls of pasta'
- $x_2$ : 'bowls of cereal'
- $x_3$ : 'ham sandwiches'

## 3: Define the objective function in symbolic notation
The objective function to maximize is $5.64x_0 + 5.52x_1 + 2.47x_2 + 8.43x_3$.

## 4: List the constraints in symbolic notation
The constraints are:
- $28x_0 \geq 116$ (minimum tastiness rating from apple pies and bowls of cereal, but it should be $28x_0 + 24x_2 \geq 116$)
- $24x_2 + 14x_3 \leq 387$ (tastiness rating from bowls of cereal and ham sandwiches)
- $28x_0 + 24x_2 \leq 192$ (maximum tastiness rating from apple pies and bowls of cereal)
- $28x_0 + 24x_1 \leq 179$ (tastiness rating from apple pies and bowls of pasta)
- $24x_1 + 24x_2 \leq 480$ (tastiness rating from bowls of pasta and bowls of cereal)
- $28x_0 + 24x_1 + 24x_2 + 14x_3 \leq 480$ (maximum total tastiness rating)
- $23x_1 + 4x_2 \leq 68$ (cost of bowls of pasta and bowls of cereal)
- $27x_0 + 23x_1 \leq 132$ (cost of apple pies and bowls of pasta)
- $27x_0 + 2x_3 \leq 133$ (cost of apple pies and ham sandwiches)
- $23x_1 + 2x_3 \leq 80$ (cost of bowls of pasta and ham sandwiches)
- $23x_1 + 4x_2 + 2x_3 \leq 139$ (cost of bowls of pasta, bowls of cereal, and ham sandwiches)
- $27x_0 + 23x_1 + 4x_2 + 2x_3 \leq 139$ (total cost)

## 5: Correct the constraints based on the problem description
Correcting and listing all constraints properly:
- $28x_0 + 24x_2 \geq 116$
- $24x_2 + 14x_3 \leq 387$
- $28x_0 + 24x_2 \leq 192$
- $28x_0 + 24x_1 \leq 179$
- $24x_1 + 24x_2 \leq 480$
- $28x_0 + 24x_1 + 24x_2 + 14x_3 \leq 480$
- $23x_1 + 4x_2 \leq 68$
- $27x_0 + 23x_1 \leq 132$
- $27x_0 + 2x_3 \leq 133$
- $23x_1 + 2x_3 \leq 80$
- $23x_1 + 4x_2 + 2x_3 \leq 139$
- $27x_0 + 23x_1 + 4x_2 + 2x_3 \leq 139$

## 6: Provide the symbolic representation in JSON format
```json
{
    'sym_variables': [
        ['x0', 'apple pies'],
        ['x1', 'bowls of pasta'],
        ['x2', 'bowls of cereal'],
        ['x3', 'ham sandwiches']
    ],
    'objective_function': '5.64*x0 + 5.52*x1 + 2.47*x2 + 8.43*x3',
    'constraints': [
        '28*x0 + 24*x2 >= 116',
        '24*x2 + 14*x3 <= 387',
        '28*x0 + 24*x2 <= 192',
        '28*x0 + 24*x1 <= 179',
        '24*x1 + 24*x2 <= 480',
        '28*x0 + 24*x1 + 24*x2 + 14*x3 <= 480',
        '23*x1 + 4*x2 <= 68',
        '27*x0 + 23*x1 <= 132',
        '27*x0 + 2*x3 <= 133',
        '23*x1 + 2*x3 <= 80',
        '23*x1 + 4*x2 + 2*x3 <= 139',
        '27*x0 + 23*x1 + 4*x2 + 2*x3 <= 139'
    ]
}
```

## 7: Write the Gurobi code in Python
```python
import gurobi

def solve_optimization_problem():
    # Create a new model
    model = gurobi.Model()

    # Define the variables
    x0 = model.addVar(name='apple_pies', lb=0)  # No lower bound specified, assuming 0
    x1 = model.addVar(name='bowls_of_pasta', lb=0)  # No lower bound specified, assuming 0
    x2 = model.addVar(name='bowls_of_cereal', lb=0)  # No lower bound specified, assuming 0
    x3 = model.addVar(name='ham_sandwiches', lb=0, integrality=gurobi.GRB.INTEGER)  # Restricted to integer

    # Objective function
    model.setObjective(5.64*x0 + 5.52*x1 + 2.47*x2 + 8.43*x3, gurobi.GRB.MAXIMIZE)

    # Constraints
    model.addConstr(28*x0 + 24*x2 >= 116)
    model.addConstr(24*x2 + 14*x3 <= 387)
    model.addConstr(28*x0 + 24*x2 <= 192)
    model.addConstr(28*x0 + 24*x1 <= 179)
    model.addConstr(24*x1 + 24*x2 <= 480)
    model.addConstr(28*x0 + 24*x1 + 24*x2 + 14*x3 <= 480)
    model.addConstr(23*x1 + 4*x2 <= 68)
    model.addConstr(27*x0 + 23*x1 <= 132)
    model.addConstr(27*x0 + 2*x3 <= 133)
    model.addConstr(23*x1 + 2*x3 <= 80)
    model.addConstr(23*x1 + 4*x2 + 2*x3 <= 139)
    model.addConstr(27*x0 + 23*x1 + 4*x2 + 2*x3 <= 139)

    # Optimize the model
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.OPTIMAL:
        print('Objective: ', model.objval)
        print('Apple pies: ', x0.varValue)
        print('Bowls of pasta: ', x1.varValue)
        print('Bowls of cereal: ', x2.varValue)
        print('Ham sandwiches: ', x3.varValue)
    else:
        print('No optimal solution found')

solve_optimization_problem()
```