## Step 1: Define the symbolic representation of the variables
The variables are 'eggs', 'fruit salads', 'kiwis', 'apple pies' which can be represented symbolically as $x_0, x_1, x_2, x_3$ respectively.

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

## Step 3: List the constraints in symbolic notation
Constraints:
1. $28x_1 + 34x_2 \geq 67$
2. $24x_0 + 28x_1 + 14x_3 \geq 44$
3. $24x_0 + 28x_1 + 34x_2 + 14x_3 \geq 44$
4. $6x_0 + 14x_1 \geq 51$
5. $6x_0 + 20x_2 \geq 81$
6. $6x_0 + 14x_1 + 24x_3 \geq 58$
7. $6x_0 + 14x_1 + 20x_2 + 24x_3 \geq 58$
8. $32x_2 + x_3 \geq 31$
9. $6x_0 + 11x_1 + x_3 \geq 37$
10. $11x_1 + 32x_2 + x_3 \geq 37$
11. $6x_0 + 32x_2 + x_3 \geq 37$
12. $6x_0 + 11x_1 + x_3 \geq 48$
13. $11x_1 + 32x_2 + x_3 \geq 48$
14. $6x_0 + 32x_2 + x_3 \geq 48$
15. $6x_0 + 11x_1 + x_3 \geq 52$
16. $11x_1 + 32x_2 + x_3 \geq 52$
17. $6x_0 + 32x_2 + x_3 \geq 52$
18. $6x_0 + 11x_1 + 32x_2 + x_3 \geq 52$
19. $18x_0 + 23x_1 \geq 42$
20. $18x_0 + 24x_2 \geq 33$
21. $24x_2 + 26x_3 \geq 21$
22. $18x_0 + 26x_3 \geq 20$
23. $18x_0 + 24x_2 + 26x_3 \geq 29$
24. $18x_0 + 23x_1 + 24x_2 + 26x_3 \geq 29$
25. $10x_0 - 3x_3 \geq 0$
26. $2x_0 - 4x_2 \geq 0$
27. $28x_1 + 34x_2 \leq 274$
28. $20x_2 + 24x_3 \leq 265$
29. $14x_1 + 24x_3 \leq 351$
30. $6x_0 + 14x_1 \leq 240$
31. $14x_1 + 20x_2 + 24x_3 \leq 186$
32. $6x_0 + 14x_1 + 24x_3 \leq 253$
33. $6x_0 + 14x_1 + 20x_2 \leq 283$
34. $6x_0 + 11x_1 + x_3 \leq 137$
35. $11x_1 + 32x_2 + x_3 \leq 140$
36. $18x_0 + 26x_3 \leq 53$
37. $18x_0 + 24x_2 + 26x_3 \leq 84$

## Step 4: Define the resource attributes
Resource attributes:
- $r_0: 24x_0 + 28x_1 + 34x_2 + 14x_3 \leq 347$
- $r_1: 6x_0 + 14x_1 + 20x_2 + 24x_3 \leq 356$
- $r_2: 6x_0 + 11x_1 + 32x_2 + x_3 \leq 213$
- $r_3: 18x_0 + 23x_1 + 24x_2 + 26x_3 \leq 213$

## 5: Create the symbolic representation of the problem
```json
{
    'sym_variables': [
        ('x0', 'eggs'),
        ('x1', 'fruit salads'),
        ('x2', 'kiwis'),
        ('x3', 'apple pies')
    ],
    'objective_function': '4*x0 + 9*x1 + 9*x2 + 2*x3',
    'constraints': [
        '28*x1 + 34*x2 >= 67',
        '24*x0 + 28*x1 + 14*x3 >= 44',
        '24*x0 + 28*x1 + 34*x2 + 14*x3 >= 44',
        '6*x0 + 14*x1 >= 51',
        '6*x0 + 20*x2 >= 81',
        '6*x0 + 14*x1 + 24*x3 >= 58',
        '6*x0 + 14*x1 + 20*x2 + 24*x3 >= 58',
        '32*x2 + x3 >= 31',
        '6*x0 + 11*x1 + x3 >= 37',
        '11*x1 + 32*x2 + x3 >= 37',
        '6*x0 + 32*x2 + x3 >= 37',
        '6*x0 + 11*x1 + x3 >= 48',
        '11*x1 + 32*x2 + x3 >= 48',
        '6*x0 + 32*x2 + x3 >= 48',
        '6*x0 + 11*x1 + x3 >= 52',
        '11*x1 + 32*x2 + x3 >= 52',
        '6*x0 + 32*x2 + x3 >= 52',
        '6*x0 + 11*x1 + 32*x2 + x3 >= 52',
        '18*x0 + 23*x1 >= 42',
        '18*x0 + 24*x2 >= 33',
        '24*x2 + 26*x3 >= 21',
        '18*x0 + 26*x3 >= 20',
        '18*x0 + 24*x2 + 26*x3 >= 29',
        '18*x0 + 23*x1 + 24*x2 + 26*x3 >= 29',
        '10*x0 - 3*x3 >= 0',
        '2*x0 - 4*x2 >= 0',
        '28*x1 + 34*x2 <= 274',
        '20*x2 + 24*x3 <= 265',
        '14*x1 + 24*x3 <= 351',
        '6*x0 + 14*x1 <= 240',
        '14*x1 + 20*x2 + 24*x3 <= 186',
        '6*x0 + 14*x1 + 24*x3 <= 253',
        '6*x0 + 14*x1 + 20*x2 <= 283',
        '6*x0 + 11*x1 + x3 <= 137',
        '11*x1 + 32*x2 + x3 <= 140',
        '18*x0 + 26*x3 <= 53',
        '18*x0 + 24*x2 + 26*x3 <= 84',
        '24*x0 + 28*x1 + 34*x2 + 14*x3 <= 347',
        '6*x0 + 14*x1 + 20*x2 + 24*x3 <= 356',
        '6*x0 + 11*x1 + 32*x2 + x3 <= 213',
        '18*x0 + 23*x1 + 24*x2 + 26*x3 <= 213'
    ]
}
```

## 6: Implement the problem in Gurobi
```python
import gurobi

def solve_optimization_problem():
    model = gurobi.Model()

    # Define variables
    eggs = model.addVar(name="eggs", lb=0)
    fruit_salads = model.addVar(name="fruit_salads", lb=0)
    kiwis = model.addVar(name="kiwis", lb=0)
    apple_pies = model.addVar(name="apple_pies", lb=0)

    # Objective function
    model.setObjective(4 * eggs + 9 * fruit_salads + 9 * kiwis + 2 * apple_pies, gurobi.GRB.MINIMIZE)

    # Constraints
    model.addConstr(28 * fruit_salads + 34 * kiwis >= 67)
    model.addConstr(24 * eggs + 28 * fruit_salads + 14 * apple_pies >= 44)
    model.addConstr(24 * eggs + 28 * fruit_salads + 34 * kiwis + 14 * apple_pies >= 44)
    model.addConstr(6 * eggs + 14 * fruit_salads >= 51)
    model.addConstr(6 * eggs + 20 * kiwis >= 81)
    model.addConstr(6 * eggs + 14 * fruit_salads + 24 * apple_pies >= 58)
    model.addConstr(6 * eggs + 14 * fruit_salads + 20 * kiwis + 24 * apple_pies >= 58)
    model.addConstr(32 * kiwis + apple_pies >= 31)
    model.addConstr(6 * eggs + 11 * fruit_salads + apple_pies >= 37)
    model.addConstr(11 * fruit_salads + 32 * kiwis + apple_pies >= 37)
    model.addConstr(6 * eggs + 32 * kiwis + apple_pies >= 37)
    model.addConstr(6 * eggs + 11 * fruit_salads + apple_pies >= 48)
    model.addConstr(11 * fruit_salads + 32 * kiwis + apple_pies >= 48)
    model.addConstr(6 * eggs + 32 * kiwis + apple_pies >= 48)
    model.addConstr(6 * eggs + 11 * fruit_salads + apple_pies >= 52)
    model.addConstr(11 * fruit_salads + 32 * kiwis + apple_pies >= 52)
    model.addConstr(6 * eggs + 32 * kiwis + apple_pies >= 52)
    model.addConstr(6 * eggs + 11 * fruit_salads + 32 * kiwis + apple_pies >= 52)
    model.addConstr(18 * eggs + 23 * fruit_salads >= 42)
    model.addConstr(18 * eggs + 24 * kiwis >= 33)
    model.addConstr(24 * kiwis + 26 * apple_pies >= 21)
    model.addConstr(18 * eggs + 26 * apple_pies >= 20)
    model.addConstr(18 * eggs + 24 * kiwis + 26 * apple_pies >= 29)
    model.addConstr(18 * eggs + 23 * fruit_salads + 24 * kiwis + 26 * apple_pies >= 29)
    model.addConstr(10 * eggs - 3 * apple_pies >= 0)
    model.addConstr(2 * eggs - 4 * kiwis >= 0)
    model.addConstr(28 * fruit_salads + 34 * kiwis <= 274)
    model.addConstr(20 * kiwis + 24 * apple_pies <= 265)
    model.addConstr(14 * fruit_salads + 24 * apple_pies <= 351)
    model.addConstr(6 * eggs + 14 * fruit_salads <= 240)
    model.addConstr(14 * fruit_salads + 20 * kiwis + 24 * apple_pies <= 186)
    model.addConstr(6 * eggs + 14 * fruit_salads + 24 * apple_pies <= 253)
    model.addConstr(6 * eggs + 14 * fruit_salads + 20 * kiwis <= 283)
    model.addConstr(6 * eggs + 11 * fruit_salads + apple_pies <= 137)
    model.addConstr(11 * fruit_salads + 32 * kiwis + apple_pies <= 140)
    model.addConstr(18 * eggs + 26 * apple_pies <= 53)
    model.addConstr(18 * eggs + 24 * kiwis + 26 * apple_pies <= 84)
    model.addConstr(24 * eggs + 28 * fruit_salads + 34 * kiwis + 14 * apple_pies <= 347)
    model.addConstr(6 * eggs + 14 * fruit_salads + 20 * kiwis + 24 * apple_pies <= 356)
    model.addConstr(6 * eggs + 11 * fruit_salads + 32 * kiwis + apple_pies <= 213)
    model.addConstr(18 * eggs + 23 * fruit_salads + 24 * kiwis + 26 * apple_pies <= 213)

    # Solve the model
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.OPTIMAL:
        print("Objective: ", model.objval)
        print("Eggs: ", eggs.varValue)
        print("Fruit Salads: ", fruit_salads.varValue)
        print("Kiwis: ", kiwis.varValue)
        print("Apple Pies: ", apple_pies.varValue)
    else:
        print("The model is infeasible")

solve_optimization_problem()
```