## Step 1: Define the symbolic representation of the problem
The problem involves maximizing an objective function subject to several constraints. The variables are 'apple pies', 'green beans', 'granola bars', and 'oreos', which we can denote as $x_0$, $x_1$, $x_2$, and $x_3$ respectively.

## Step 2: Translate the objective function into symbolic notation
The objective function to maximize is $2x_0 + 9x_1 + 2x_2 + 4x_3$.

## 3: List the constraints in symbolic notation
Constraints:
1. $5x_0 + 9x_1 + 4x_2 + 4x_3 \leq 76$ (iron)
2. $5x_0 + 4x_1 + 6x_2 + 6x_3 \leq 81$ (fat)
3. $9x_0 + 6x_1 + 3x_2 + 7x_3 \leq 83$ (calcium)
4. $4x_2 + 4x_3 \geq 7$ (iron from granola bars and oreos)
5. $9x_1 + 4x_2 \geq 6$ (iron from green beans and granola bars)
6. $5x_0 + 6x_2 + 6x_3 \geq 14$ (fat from apple pies, granola bars, and oreos)
7. $5x_0 + 4x_1 + 6x_3 \geq 14$ (fat from apple pies, green beans, and oreos)
8. $5x_0 + 4x_1 + 6x_2 \geq 14$ (fat from apple pies, green beans, and granola bars)
9. $5x_0 + 6x_2 + 6x_3 \geq 13$ (fat from apple pies, granola bars, and oreos)
10. $5x_0 + 4x_1 + 6x_3 \geq 13$ (fat from apple pies, green beans, and oreos)
11. $5x_0 + 4x_1 + 6x_2 \geq 13$ (fat from apple pies, green beans, and granola bars)
12. $5x_0 + 6x_2 + 6x_3 \geq 11$ (fat from apple pies, granola bars, and oreos)
13. $5x_0 + 4x_1 + 6x_3 \geq 11$ (fat from apple pies, green beans, and oreos)
14. $5x_0 + 4x_1 + 6x_2 \geq 11$ (fat from apple pies, green beans, and granola bars)
15. $9x_0 + 7x_3 \geq 8$ (calcium from apple pies and oreos)
16. $6x_1 + 7x_3 \geq 17$ (calcium from green beans and oreos)
17. $6x_1 + 3x_2 \geq 10$ (calcium from green beans and granola bars)
18. $9x_0 + 3x_2 \geq 16$ (calcium from apple pies and granola bars)
19. $6x_1 - 5x_2 \geq 0$ (green beans and granola bars constraint)
20. $4x_2 + 4x_3 \leq 20$ (iron from granola bars and oreos)
21. $5x_0 + 9x_1 \leq 36$ (iron from apple pies and green beans)
22. $5x_0 + 4x_3 \leq 63$ (iron from apple pies and oreos)
23. $9x_1 + 4x_3 \leq 35$ (iron from green beans and oreos)
24. $5x_0 + 4x_2 \leq 57$ (iron from apple pies and granola bars)
25. $5x_0 + 4x_2 + 4x_3 \leq 64$ (iron from apple pies, granola bars, and oreos)
26. $5x_0 + 9x_1 + 4x_2 + 4x_3 \leq 64$ (total iron)
27. $6x_2 + 6x_3 \leq 61$ (fat from granola bars and oreos)
28. $4x_1 + 6x_3 \leq 65$ (fat from green beans and oreos)
29. $5x_0 + 6x_3 \leq 75$ (fat from apple pies and oreos)
30. $5x_0 + 4x_1 + 6x_2 + 6x_3 \leq 75$ (total fat)
31. $9x_0 + 3x_2 \leq 37$ (calcium from apple pies and granola bars)
32. $3x_2 + 7x_3 \leq 23$ (calcium from granola bars and oreos)
33. $9x_0 + 6x_1 \leq 71$ (calcium from apple pies and green beans)
34. $6x_1 + 7x_3 \leq 33$ (calcium from green beans and oreos)
35. $6x_1 + 3x_2 \leq 78$ (calcium from green beans and granola bars)
36. $9x_0 + 6x_1 + 3x_2 + 7x_3 \leq 78$ (total calcium)

## 4: Provide the symbolic representation in JSON format
```json
{
    'sym_variables': [
        ('x0', 'apple pies'),
        ('x1', 'green beans'),
        ('x2', 'granola bars'),
        ('x3', 'oreos')
    ],
    'objective_function': '2*x0 + 9*x1 + 2*x2 + 4*x3',
    'constraints': [
        '5*x0 + 9*x1 + 4*x2 + 4*x3 <= 76',
        '5*x0 + 4*x1 + 6*x2 + 6*x3 <= 81',
        '9*x0 + 6*x1 + 3*x2 + 7*x3 <= 83',
        '4*x2 + 4*x3 >= 7',
        '9*x1 + 4*x2 >= 6',
        '5*x0 + 6*x2 + 6*x3 >= 14',
        '5*x0 + 4*x1 + 6*x3 >= 14',
        '5*x0 + 4*x1 + 6*x2 >= 14',
        '5*x0 + 6*x2 + 6*x3 >= 13',
        '5*x0 + 4*x1 + 6*x3 >= 13',
        '5*x0 + 4*x1 + 6*x2 >= 13',
        '5*x0 + 6*x2 + 6*x3 >= 11',
        '5*x0 + 4*x1 + 6*x3 >= 11',
        '5*x0 + 4*x1 + 6*x2 >= 11',
        '9*x0 + 7*x3 >= 8',
        '6*x1 + 7*x3 >= 17',
        '6*x1 + 3*x2 >= 10',
        '9*x0 + 3*x2 >= 16',
        '6*x1 - 5*x2 >= 0',
        '4*x2 + 4*x3 <= 20',
        '5*x0 + 9*x1 <= 36',
        '5*x0 + 4*x3 <= 63',
        '9*x1 + 4*x3 <= 35',
        '5*x0 + 4*x2 <= 57',
        '5*x0 + 4*x2 + 4*x3 <= 64',
        '5*x0 + 9*x1 + 4*x2 + 4*x3 <= 64',
        '6*x2 + 6*x3 <= 61',
        '4*x1 + 6*x3 <= 65',
        '5*x0 + 6*x3 <= 75',
        '5*x0 + 4*x1 + 6*x2 + 6*x3 <= 75',
        '9*x0 + 3*x2 <= 37',
        '3*x2 + 7*x3 <= 23',
        '9*x0 + 6*x1 <= 71',
        '6*x1 + 7*x3 <= 33',
        '6*x1 + 3*x2 <= 78',
        '9*x0 + 6*x1 + 3*x2 + 7*x3 <= 78'
    ]
}
```

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

# Define the model
m = gp.Model()

# Define the variables
x0 = m.addVar(name="apple_pies", lb=0)
x1 = m.addVar(name="green_beans", lb=0)
x2 = m.addVar(name="granola_bars", lb=0)
x3 = m.addVar(name="oreos", lb=0)

# Define the objective function
m.setObjective(2*x0 + 9*x1 + 2*x2 + 4*x3, gp.GRB.MAXIMIZE)

# Add constraints
m.addConstr(5*x0 + 9*x1 + 4*x2 + 4*x3 <= 76)
m.addConstr(5*x0 + 4*x1 + 6*x2 + 6*x3 <= 81)
m.addConstr(9*x0 + 6*x1 + 3*x2 + 7*x3 <= 83)
m.addConstr(4*x2 + 4*x3 >= 7)
m.addConstr(9*x1 + 4*x2 >= 6)
m.addConstr(5*x0 + 6*x2 + 6*x3 >= 14)
m.addConstr(5*x0 + 4*x1 + 6*x3 >= 14)
m.addConstr(5*x0 + 4*x1 + 6*x2 >= 14)
m.addConstr(5*x0 + 6*x2 + 6*x3 >= 13)
m.addConstr(5*x0 + 4*x1 + 6*x3 >= 13)
m.addConstr(5*x0 + 4*x1 + 6*x2 >= 13)
m.addConstr(5*x0 + 6*x2 + 6*x3 >= 11)
m.addConstr(5*x0 + 4*x1 + 6*x3 >= 11)
m.addConstr(5*x0 + 4*x1 + 6*x2 >= 11)
m.addConstr(9*x0 + 7*x3 >= 8)
m.addConstr(6*x1 + 7*x3 >= 17)
m.addConstr(6*x1 + 3*x2 >= 10)
m.addConstr(9*x0 + 3*x2 >= 16)
m.addConstr(6*x1 - 5*x2 >= 0)
m.addConstr(4*x2 + 4*x3 <= 20)
m.addConstr(5*x0 + 9*x1 <= 36)
m.addConstr(5*x0 + 4*x3 <= 63)
m.addConstr(9*x1 + 4*x3 <= 35)
m.addConstr(5*x0 + 4*x2 <= 57)
m.addConstr(5*x0 + 4*x2 + 4*x3 <= 64)
m.addConstr(5*x0 + 9*x1 + 4*x2 + 4*x3 <= 64)
m.addConstr(6*x2 + 6*x3 <= 61)
m.addConstr(4*x1 + 6*x3 <= 65)
m.addConstr(5*x0 + 6*x3 <= 75)
m.addConstr(5*x0 + 4*x1 + 6*x2 + 6*x3 <= 75)
m.addConstr(9*x0 + 3*x2 <= 37)
m.addConstr(3*x2 + 7*x3 <= 23)
m.addConstr(9*x0 + 6*x1 <= 71)
m.addConstr(6*x1 + 7*x3 <= 33)
m.addConstr(6*x1 + 3*x2 <= 78)
m.addConstr(9*x0 + 6*x1 + 3*x2 + 7*x3 <= 78)

# Solve the model
m.optimize()

# Print the solution
if m.status == gp.GRB.OPTIMAL:
    print("Objective: ", m.objVal)
    print("Apple Pies: ", x0.varValue)
    print("Green Beans: ", x1.varValue)
    print("Granola Bars: ", x2.varValue)
    print("Oreos: ", x3.varValue)
else:
    print("The model is infeasible")
```