## Step 1: Define the symbolic representation of the variables
The variables are defined as follows: 
- $x_0$ represents 'cheeseburgers'
- $x_1$ represents 'lemons'
- $x_2$ represents 'strips of bacon'
- $x_3$ represents 'hot dogs'

## Step 2: Define the objective function in symbolic notation
The objective function to minimize is $9.28x_0 + 9.53x_1 + 1.87x_2 + 8.04x_3$.

## Step 3: List the constraints in symbolic notation
Constraints:
1. $8x_0 + 6x_1 + 4x_2 + 3x_3 \leq 70$ (carbohydrates)
2. $x_0 + 3x_1 + 5x_2 + 3x_3 \leq 53$ (dollar cost)
3. $3x_0 + 3x_1 + 3x_2 + 7x_3 \leq 58$ (grams of fat)
4. $8x_0 + 3x_3 \geq 6$ (carbohydrates from cheeseburgers and hot dogs)
5. $6x_1 + 3x_3 \geq 10$ (carbohydrates from lemons and hot dogs)
6. $8x_0 + 6x_1 \geq 15$ (carbohydrates from cheeseburgers and lemons)
7. $8x_0 + 6x_1 + 4x_2 + 3x_3 \geq 15$ (total carbohydrates)
8. $3x_1 + 3x_3 \geq 11$ (cost from lemons and hot dogs)
9. $3x_1 + 5x_2 \geq 4$ (cost from lemons and strips of bacon)
10. $5x_2 + 3x_3 \geq 13$ (cost from strips of bacon and hot dogs)
11. $x_0 + 3x_3 \geq 7$ (cost from cheeseburgers and hot dogs)
12. $x_0 + 5x_2 + 3x_3 \geq 13$ (cost from cheeseburgers, strips of bacon, and hot dogs)
13. $x_0 + 3x_1 + 5x_2 + 3x_3 \geq 13$ (cost from all items)
14. $3x_1 + 7x_3 \geq 9$ (fat from lemons and hot dogs)
15. $3x_2 + 7x_3 \geq 11$ (fat from strips of bacon and hot dogs)
16. $3x_0 + 7x_3 \geq 5$ (fat from cheeseburgers and hot dogs)
17. $3x_0 + 3x_2 \geq 12$ (fat from cheeseburgers and strips of bacon)
18. $3x_0 + 3x_2 + 7x_3 \geq 9$ (fat from cheeseburgers, strips of bacon, and hot dogs)
19. $3x_1 + 3x_2 + 7x_3 \geq 9$ (fat from lemons, strips of bacon, and hot dogs)
20. $3x_0 + 3x_2 + 7x_3 \geq 12$ (fat from cheeseburgers, strips of bacon, and hot dogs)
21. $3x_1 + 3x_2 + 7x_3 \geq 12$ (fat from lemons, strips of bacon, and hot dogs)
22. $3x_0 + 3x_1 + 3x_2 + 7x_3 \geq 12$ (total fat)
23. $6x_2 - 6x_3 \geq 0$ (strips of bacon and hot dogs constraint)
24. $8x_0 + 6x_1 \leq 40$ (carbohydrates from cheeseburgers and lemons)
25. $6x_1 + 4x_2 \leq 32$ (carbohydrates from lemons and strips of bacon)
26. $8x_0 + 4x_2 \leq 57$ (carbohydrates from cheeseburgers and strips of bacon)
27. $8x_0 + 3x_3 \leq 52$ (carbohydrates from cheeseburgers and hot dogs)
28. $6x_1 + 3x_3 \leq 25$ (carbohydrates from lemons and hot dogs)
29. $8x_0 + 6x_1 + 4x_2 \leq 54$ (carbohydrates from cheeseburgers, lemons, and strips of bacon)
30. $8x_0 + 4x_2 + 3x_3 \leq 67$ (carbohydrates from cheeseburgers, strips of bacon, and hot dogs)
31. $8x_0 + 6x_1 + 3x_3 \leq 34$ (carbohydrates from cheeseburgers, lemons, and hot dogs)
32. $x_0 + 5x_2 + 3x_3 \leq 39$ (cost from cheeseburgers, strips of bacon, and hot dogs)
33. $3x_1 + 7x_3 \leq 18$ (fat from lemons and hot dogs)
34. $3x_0 + 3x_1 + 7x_3 \leq 38$ (fat from cheeseburgers, lemons, and hot dogs)
35. $3x_1 + 3x_2 + 7x_3 \leq 20$ (fat from lemons, strips of bacon, and hot dogs)
36. $3x_0 + 3x_2 + 7x_3 \leq 37$ (fat from cheeseburgers, strips of bacon, and hot dogs)

## Step 4: Provide the symbolic representation of the problem
```json
{
    'sym_variables': [
        ('x0', 'cheeseburgers'), 
        ('x1', 'lemons'), 
        ('x2', 'strips of bacon'), 
        ('x3', 'hot dogs')
    ], 
    'objective_function': '9.28*x0 + 9.53*x1 + 1.87*x2 + 8.04*x3', 
    'constraints': [
        '8*x0 + 6*x1 + 4*x2 + 3*x3 <= 70',
        'x0 + 3*x1 + 5*x2 + 3*x3 <= 53',
        '3*x0 + 3*x1 + 3*x2 + 7*x3 <= 58',
        '8*x0 + 3*x3 >= 6',
        '6*x1 + 3*x3 >= 10',
        '8*x0 + 6*x1 >= 15',
        '8*x0 + 6*x1 + 4*x2 + 3*x3 >= 15',
        '3*x1 + 3*x3 >= 11',
        '3*x1 + 5*x2 >= 4',
        '5*x2 + 3*x3 >= 13',
        'x0 + 3*x3 >= 7',
        'x0 + 5*x2 + 3*x3 >= 13',
        'x0 + 3*x1 + 5*x2 + 3*x3 >= 13',
        '3*x1 + 7*x3 >= 9',
        '3*x2 + 7*x3 >= 11',
        '3*x0 + 7*x3 >= 5',
        '3*x0 + 3*x2 >= 12',
        '3*x0 + 3*x2 + 7*x3 >= 9',
        '3*x1 + 3*x2 + 7*x3 >= 9',
        '3*x0 + 3*x2 + 7*x3 >= 12',
        '3*x1 + 3*x2 + 7*x3 >= 12',
        '3*x0 + 3*x1 + 3*x2 + 7*x3 >= 12',
        '6*x2 - 6*x3 >= 0',
        '8*x0 + 6*x1 <= 40',
        '6*x1 + 4*x2 <= 32',
        '8*x0 + 4*x2 <= 57',
        '8*x0 + 3*x3 <= 52',
        '6*x1 + 3*x3 <= 25',
        '8*x0 + 6*x1 + 4*x2 <= 54',
        '8*x0 + 4*x2 + 3*x3 <= 67',
        '8*x0 + 6*x1 + 3*x3 <= 34',
        'x0 + 5*x2 + 3*x3 <= 39',
        '3*x1 + 7*x3 <= 18',
        '3*x0 + 3*x1 + 7*x3 <= 38',
        '3*x1 + 3*x2 + 7*x3 <= 20',
        '3*x0 + 3*x2 + 7*x3 <= 37'
    ]
}
```

## Step 5: Output Gurobi code
```python
import gurobi

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

    # Define variables
    x0 = model.addVar(name="cheeseburgers", lb=0, ub=gurobi.GRB.INFINITY)
    x1 = model.addVar(name="lemons", lb=0, ub=gurobi.GRB.INFINITY, integrality=1)
    x2 = model.addVar(name="strips of bacon", lb=0, ub=gurobi.GRB.INFINITY, integrality=1)
    x3 = model.addVar(name="hot dogs", lb=0, ub=gurobi.GRB.INFINITY, integrality=1)

    # Objective function
    model.setObjective(9.28*x0 + 9.53*x1 + 1.87*x2 + 8.04*x3, gurobi.GRB.MINIMIZE)

    # Constraints
    model.addConstr(8*x0 + 6*x1 + 4*x2 + 3*x3 <= 70)
    model.addConstr(x0 + 3*x1 + 5*x2 + 3*x3 <= 53)
    model.addConstr(3*x0 + 3*x1 + 3*x2 + 7*x3 <= 58)
    model.addConstr(8*x0 + 3*x3 >= 6)
    model.addConstr(6*x1 + 3*x3 >= 10)
    model.addConstr(8*x0 + 6*x1 >= 15)
    model.addConstr(8*x0 + 6*x1 + 4*x2 + 3*x3 >= 15)
    model.addConstr(3*x1 + 3*x3 >= 11)
    model.addConstr(3*x1 + 5*x2 >= 4)
    model.addConstr(5*x2 + 3*x3 >= 13)
    model.addConstr(x0 + 3*x3 >= 7)
    model.addConstr(x0 + 5*x2 + 3*x3 >= 13)
    model.addConstr(x0 + 3*x1 + 5*x2 + 3*x3 >= 13)
    model.addConstr(3*x1 + 7*x3 >= 9)
    model.addConstr(3*x2 + 7*x3 >= 11)
    model.addConstr(3*x0 + 7*x3 >= 5)
    model.addConstr(3*x0 + 3*x2 >= 12)
    model.addConstr(3*x0 + 3*x2 + 7*x3 >= 9)
    model.addConstr(3*x1 + 3*x2 + 7*x3 >= 9)
    model.addConstr(3*x0 + 3*x2 + 7*x3 >= 12)
    model.addConstr(3*x1 + 3*x2 + 7*x3 >= 12)
    model.addConstr(3*x0 + 3*x1 + 3*x2 + 7*x3 >= 12)
    model.addConstr(6*x2 - 6*x3 >= 0)
    model.addConstr(8*x0 + 6*x1 <= 40)
    model.addConstr(6*x1 + 4*x2 <= 32)
    model.addConstr(8*x0 + 4*x2 <= 57)
    model.addConstr(8*x0 + 3*x3 <= 52)
    model.addConstr(6*x1 + 3*x3 <= 25)
    model.addConstr(8*x0 + 6*x1 + 4*x2 <= 54)
    model.addConstr(8*x0 + 4*x2 + 3*x3 <= 67)
    model.addConstr(8*x0 + 6*x1 + 3*x3 <= 34)
    model.addConstr(x0 + 5*x2 + 3*x3 <= 39)
    model.addConstr(3*x1 + 7*x3 <= 18)
    model.addConstr(3*x0 + 3*x1 + 7*x3 <= 38)
    model.addConstr(3*x1 + 3*x2 + 7*x3 <= 20)
    model.addConstr(3*x0 + 3*x2 + 7*x3 <= 37)

    model.optimize()

    if model.status == gurobi.GRB.OPTIMAL:
        print("Objective: ", model.objVal)
        print("Cheeseburgers: ", x0.varValue)
        print("Lemons: ", x1.varValue)
        print("Strips of bacon: ", x2.varValue)
        print("Hot dogs: ", x3.varValue)
    else:
        print("No solution found")

solve_optimization_problem()
```