## Step 1: Define the symbolic representation of the problem
The problem involves maximizing an objective function subject to several constraints. The variables are ['milkshakes', 'oreos', 'bowls of pasta', 'apple pies'], which we can represent symbolically 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 $9 \times \text{milkshakes} + 4 \times \text{oreos} + 9 \times \text{bowls of pasta} + 5 \times \text{apple pies}$, which in symbolic notation is $9x_0 + 4x_1 + 9x_2 + 5x_3$.

## 3: List the constraints in symbolic notation
The constraints given are:
1. $20.74x_2 + 14.49x_3 \geq 87$ (at least 87 milligrams of calcium from bowls of pasta and apple pies)
2. $13.58x_1 + 14.49x_3 \geq 68$ (at least 68 milligrams of calcium from oreos and apple pies)
3. $23.23x_0 + 20.74x_2 \geq 104$ (at least 104 milligrams of calcium from milkshakes and bowls of pasta)
4. $23.23x_0 + 13.58x_1 + 14.49x_3 \geq 69$ (at least 69 milligrams of calcium from milkshakes, oreos, and apple pies)
5. $10.41x_2 + 23.66x_3 \geq 16$ (total combined sourness index from bowls of pasta and apple pies)
6. $13.58x_1 + 20.74x_2 \leq 277$ (up to 277 milligrams of calcium from oreos and bowls of pasta)
7. $23.23x_0 + 13.58x_1 \leq 387$ (up to 387 milligrams of calcium from milkshakes and oreos)
8. $23.23x_0 + 20.74x_2 \leq 295$ (up to 295 milligrams of calcium from milkshakes and bowls of pasta)
9. $20.74x_2 + 14.49x_3 \leq 137$ (at most 137 milligrams of calcium from bowls of pasta and apple pies)
10. $23.23x_0 + 13.58x_1 + 14.49x_3 \leq 331$ (at most 331 milligrams of calcium from milkshakes, oreos, and apple pies)
11. $23.23x_0 + 13.58x_1 + 20.74x_2 \leq 256$ (up to 256 milligrams of calcium from milkshakes, oreos, and bowls of pasta)
12. $23.23x_0 + 13.58x_1 + 20.74x_2 + 14.49x_3 \leq 256$ (up to 256 milligrams of calcium from all)
13. $20.53x_0 + 10.41x_2 \leq 68$ (total combined sourness index from milkshakes and bowls of pasta)
14. $11.23x_1 + 23.66x_3 \leq 107$ (total combined sourness index from oreos and apple pies)
15. $10.41x_2 + 23.66x_3 \leq 50$ (total combined sourness index from bowls of pasta and apple pies)
16. $20.53x_0 + 23.66x_3 \leq 133$ (total combined sourness index from milkshakes and apple pies)
17. $11.23x_1 + 10.41x_2 + 23.66x_3 \leq 61$ (total combined sourness index from oreos, bowls of pasta, and apple pies)
18. $20.53x_0 + 11.23x_1 + 10.41x_2 \leq 143$ (total combined sourness index from milkshakes, oreos, and bowls of pasta)
19. $20.53x_0 + 11.23x_1 + 23.66x_3 \leq 157$ (total combined sourness index from milkshakes, oreos, and apple pies)
20. $20.53x_0 + 11.23x_1 + 10.41x_2 + 23.66x_3 \leq 157$ (total combined sourness index from all)

## 4: Provide the symbolic representation in JSON format
```json
{
    'sym_variables': [
        ('x0', 'milkshakes'), 
        ('x1', 'oreos'), 
        ('x2', 'bowls of pasta'), 
        ('x3', 'apple pies')
    ], 
    'objective_function': '9*x0 + 4*x1 + 9*x2 + 5*x3', 
    'constraints': [
        '20.74*x2 + 14.49*x3 >= 87',
        '13.58*x1 + 14.49*x3 >= 68',
        '23.23*x0 + 20.74*x2 >= 104',
        '23.23*x0 + 13.58*x1 + 14.49*x3 >= 69',
        '10.41*x2 + 23.66*x3 >= 16',
        '13.58*x1 + 20.74*x2 <= 277',
        '23.23*x0 + 13.58*x1 <= 387',
        '23.23*x0 + 20.74*x2 <= 295',
        '20.74*x2 + 14.49*x3 <= 137',
        '23.23*x0 + 13.58*x1 + 14.49*x3 <= 331',
        '23.23*x0 + 13.58*x1 + 20.74*x2 <= 256',
        '23.23*x0 + 13.58*x1 + 20.74*x2 + 14.49*x3 <= 256',
        '20.53*x0 + 10.41*x2 <= 68',
        '11.23*x1 + 23.66*x3 <= 107',
        '10.41*x2 + 23.66*x3 <= 50',
        '20.53*x0 + 23.66*x3 <= 133',
        '11.23*x1 + 10.41*x2 + 23.66*x3 <= 61',
        '20.53*x0 + 11.23*x1 + 10.41*x2 <= 143',
        '20.53*x0 + 11.23*x1 + 23.66*x3 <= 157',
        '20.53*x0 + 11.23*x1 + 10.41*x2 + 23.66*x3 <= 157'
    ]
}
```

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

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

# Define the variables
x0 = model.addVar(name="milkshakes", lb=0)
x1 = model.addVar(name="oreos", lb=0)
x2 = model.addVar(name="bowls of pasta", lb=0)
x3 = model.addVar(name="apple pies", lb=0)

# Define the objective function
model.setObjective(9*x0 + 4*x1 + 9*x2 + 5*x3, gurobi.GRB.MAXIMIZE)

# Add constraints
model.addConstr(20.74*x2 + 14.49*x3 >= 87)
model.addConstr(13.58*x1 + 14.49*x3 >= 68)
model.addConstr(23.23*x0 + 20.74*x2 >= 104)
model.addConstr(23.23*x0 + 13.58*x1 + 14.49*x3 >= 69)
model.addConstr(10.41*x2 + 23.66*x3 >= 16)
model.addConstr(13.58*x1 + 20.74*x2 <= 277)
model.addConstr(23.23*x0 + 13.58*x1 <= 387)
model.addConstr(23.23*x0 + 20.74*x2 <= 295)
model.addConstr(20.74*x2 + 14.49*x3 <= 137)
model.addConstr(23.23*x0 + 13.58*x1 + 14.49*x3 <= 331)
model.addConstr(23.23*x0 + 13.58*x1 + 20.74*x2 <= 256)
model.addConstr(23.23*x0 + 13.58*x1 + 20.74*x2 + 14.49*x3 <= 256)
model.addConstr(20.53*x0 + 10.41*x2 <= 68)
model.addConstr(11.23*x1 + 23.66*x3 <= 107)
model.addConstr(10.41*x2 + 23.66*x3 <= 50)
model.addConstr(20.53*x0 + 23.66*x3 <= 133)
model.addConstr(11.23*x1 + 10.41*x2 + 23.66*x3 <= 61)
model.addConstr(20.53*x0 + 11.23*x1 + 10.41*x2 <= 143)
model.addConstr(20.53*x0 + 11.23*x1 + 23.66*x3 <= 157)
model.addConstr(20.53*x0 + 11.23*x1 + 10.41*x2 + 23.66*x3 <= 157)

# Optimize the model
model.optimize()

# Print the solution
if model.status == gurobi.GRB.OPTIMAL:
    print("Objective: ", model.objVal)
    print("Milkshakes: ", x0.varValue)
    print("Oreos: ", x1.varValue)
    print("Bowls of pasta: ", x2.varValue)
    print("Apple pies: ", x3.varValue)
else:
    print("The model is infeasible")
```