## Step 1: Define the symbolic representation of the problem
The problem involves variables: steaks, bowls of pasta, hot dogs, and cheeseburgers, which can be represented symbolically as $x_0, x_1, x_2, x_3$ respectively.

## Step 2: Translate the objective function into symbolic notation
The objective function to minimize is $1 \times \text{steaks} + 3 \times \text{bowls of pasta} + 5 \times \text{hot dogs} + 3 \times \text{cheeseburgers}$, which translates to $x_0 + 3x_1 + 5x_2 + 3x_3$.

## 3: List the constraints in symbolic notation
Constraints:
1. $1x_0 \leq 567$
2. $3x_0 \leq 560$
3. $4x_1 \leq 567$
4. $18x_1 \leq 560$
5. $15x_2 \leq 567$
6. $34x_2 \leq 560$
7. $4x_3 \leq 567$
8. $22x_3 \leq 560$
9. $4x_1 + 15x_2 \geq 97$
10. $1x_0 + 4x_1 \geq 93$
11. $1x_0 + 4x_1 + 4x_3 \geq 112$
12. $1x_0 + 15x_2 + 4x_3 \geq 112$
13. $4x_1 + 15x_2 + 4x_3 \geq 112$
14. $1x_0 + 4x_1 + 15x_2 \geq 112$
15. $1x_0 + 4x_1 + 4x_3 \geq 136$
16. $1x_0 + 15x_2 + 4x_3 \geq 136$
17. $4x_1 + 15x_2 + 4x_3 \geq 136$
18. $1x_0 + 4x_1 + 15x_2 \geq 136$
19. $1x_0 + 4x_1 + 4x_3 \geq 127$
20. $1x_0 + 15x_2 + 4x_3 \geq 127$
21. $4x_1 + 15x_2 + 4x_3 \geq 127$
22. $1x_0 + 4x_1 + 15x_2 \geq 127$
23. $1x_0 + 4x_1 + 4x_3 \geq 135$
24. $1x_0 + 15x_2 + 4x_3 \geq 135$
25. $4x_1 + 15x_2 + 4x_3 \geq 135$
26. $1x_0 + 4x_1 + 15x_2 \geq 135$
27. $1x_0 + 4x_1 + 15x_2 + 4x_3 \geq 135$
28. $18x_1 + 34x_2 \geq 112$
29. $3x_0 + 34x_2 \geq 107$
30. $3x_0 + 18x_1 \geq 75$
31. $3x_0 + 18x_1 + 22x_3 \geq 103$
32. $3x_0 + 18x_1 + 34x_2 \geq 103$
33. $3x_0 + 34x_2 + 22x_3 \geq 103$
34. $3x_0 + 18x_1 + 22x_3 \geq 113$
35. $3x_0 + 18x_1 + 34x_2 \geq 113$
36. $3x_0 + 34x_2 + 22x_3 \geq 113$
37. $3x_0 + 18x_1 + 22x_3 \geq 90$
38. $3x_0 + 18x_1 + 34x_2 \geq 90$
39. $3x_0 + 34x_2 + 22x_3 \geq 90$
40. $3x_0 + 18x_1 + 34x_2 + 22x_3 \geq 90$
41. $-8x_0 + x_3 \geq 0$
42. $-8x_2 + 5x_3 \geq 0$
43. $4x_1 + 15x_2 \leq 510$
44. $1x_0 + 4x_1 \leq 369$
45. $34x_2 + 22x_3 \leq 249$
46. $3x_0 + 34x_2 \leq 417$
47. $18x_1 + 22x_3 \leq 323$

## 4: Create the Gurobi model and variables
We will now create a Gurobi model and define the variables.

## 5: Implement the objective function and constraints in Gurobi
```python
import gurobi

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

# Define the variables
x0 = model.addVar(name="steaks", lb=0, ub=None)
x1 = model.addVar(name="bowls of pasta", lb=0, ub=None)
x2 = model.addVar(name="hot dogs", lb=0, ub=None)
x3 = model.addVar(name="cheeseburgers", lb=0, ub=None)

# Objective function
model.setObjective(x0 + 3*x1 + 5*x2 + 3*x3, gurobi.GRB.MINIMIZE)

# Constraints
model.addConstr(x0 <= 567)
model.addConstr(3*x0 <= 560)
model.addConstr(4*x1 <= 567)
model.addConstr(18*x1 <= 560)
model.addConstr(15*x2 <= 567)
model.addConstr(34*x2 <= 560)
model.addConstr(4*x3 <= 567)
model.addConstr(22*x3 <= 560)
model.addConstr(4*x1 + 15*x2 >= 97)
model.addConstr(x0 + 4*x1 >= 93)
model.addConstr(x0 + 4*x1 + 4*x3 >= 112)
model.addConstr(x0 + 15*x2 + 4*x3 >= 112)
model.addConstr(4*x1 + 15*x2 + 4*x3 >= 112)
model.addConstr(x0 + 4*x1 + 15*x2 >= 112)
model.addConstr(x0 + 4*x1 + 4*x3 >= 136)
model.addConstr(x0 + 15*x2 + 4*x3 >= 136)
model.addConstr(4*x1 + 15*x2 + 4*x3 >= 136)
model.addConstr(x0 + 4*x1 + 15*x2 >= 136)
model.addConstr(x0 + 4*x1 + 4*x3 >= 127)
model.addConstr(x0 + 15*x2 + 4*x3 >= 127)
model.addConstr(4*x1 + 15*x2 + 4*x3 >= 127)
model.addConstr(x0 + 4*x1 + 15*x2 >= 127)
model.addConstr(x0 + 4*x1 + 4*x3 >= 135)
model.addConstr(x0 + 15*x2 + 4*x3 >= 135)
model.addConstr(4*x1 + 15*x2 + 4*x3 >= 135)
model.addConstr(x0 + 4*x1 + 15*x2 >= 135)
model.addConstr(x0 + 4*x1 + 15*x2 + 4*x3 >= 135)
model.addConstr(18*x1 + 34*x2 >= 112)
model.addConstr(3*x0 + 34*x2 >= 107)
model.addConstr(3*x0 + 18*x1 >= 75)
model.addConstr(3*x0 + 18*x1 + 22*x3 >= 103)
model.addConstr(3*x0 + 18*x1 + 34*x2 >= 103)
model.addConstr(3*x0 + 34*x2 + 22*x3 >= 103)
model.addConstr(3*x0 + 18*x1 + 22*x3 >= 113)
model.addConstr(3*x0 + 18*x1 + 34*x2 >= 113)
model.addConstr(3*x0 + 34*x2 + 22*x3 >= 113)
model.addConstr(3*x0 + 18*x1 + 22*x3 >= 90)
model.addConstr(3*x0 + 18*x1 + 34*x2 >= 90)
model.addConstr(3*x0 + 34*x2 + 22*x3 >= 90)
model.addConstr(3*x0 + 18*x1 + 34*x2 + 22*x3 >= 90)
model.addConstr(-8*x0 + x3 >= 0)
model.addConstr(-8*x2 + 5*x3 >= 0)
model.addConstr(4*x1 + 15*x2 <= 510)
model.addConstr(x0 + 4*x1 <= 369)
model.addConstr(34*x2 + 22*x3 <= 249)
model.addConstr(3*x0 + 34*x2 <= 417)
model.addConstr(18*x1 + 22*x3 <= 323)

# Solve the model
model.optimize()

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

```json
{
    'sym_variables': [
        ('x0', 'steaks'), 
        ('x1', 'bowls of pasta'), 
        ('x2', 'hot dogs'), 
        ('x3', 'cheeseburgers')
    ], 
    'objective_function': 'x0 + 3*x1 + 5*x2 + 3*x3', 
    'constraints': [
        'x0 <= 567',
        '3*x0 <= 560',
        '4*x1 <= 567',
        '18*x1 <= 560',
        '15*x2 <= 567',
        '34*x2 <= 560',
        '4*x3 <= 567',
        '22*x3 <= 560',
        '4*x1 + 15*x2 >= 97',
        'x0 + 4*x1 >= 93',
        'x0 + 4*x1 + 4*x3 >= 112',
        'x0 + 15*x2 + 4*x3 >= 112',
        '4*x1 + 15*x2 + 4*x3 >= 112',
        'x0 + 4*x1 + 15*x2 >= 112',
        'x0 + 4*x1 + 4*x3 >= 136',
        'x0 + 15*x2 + 4*x3 >= 136',
        '4*x1 + 15*x2 + 4*x3 >= 136',
        'x0 + 4*x1 + 15*x2 >= 136',
        'x0 + 4*x1 + 4*x3 >= 127',
        'x0 + 15*x2 + 4*x3 >= 127',
        '4*x1 + 15*x2 + 4*x3 >= 127',
        'x0 + 4*x1 + 15*x2 >= 127',
        'x0 + 4*x1 + 4*x3 >= 135',
        'x0 + 15*x2 + 4*x3 >= 135',
        '4*x1 + 15*x2 + 4*x3 >= 135',
        'x0 + 4*x1 + 15*x2 >= 135',
        'x0 + 4*x1 + 15*x2 + 4*x3 >= 135',
        '18*x1 + 34*x2 >= 112',
        '3*x0 + 34*x2 >= 107',
        '3*x0 + 18*x1 >= 75',
        '3*x0 + 18*x1 + 22*x3 >= 103',
        '3*x0 + 18*x1 + 34*x2 >= 103',
        '3*x0 + 34*x2 + 22*x3 >= 103',
        '3*x0 + 18*x1 + 22*x3 >= 113',
        '3*x0 + 18*x1 + 34*x2 >= 113',
        '3*x0 + 34*x2 + 22*x3 >= 113',
        '3*x0 + 18*x1 + 22*x3 >= 90',
        '3*x0 + 18*x1 + 34*x2 >= 90',
        '3*x0 + 34*x2 + 22*x3 >= 90',
        '3*x0 + 18*x1 + 34*x2 + 22*x3 >= 90',
        '-8*x0 + x3 >= 0',
        '-8*x2 + 5*x3 >= 0',
        '4*x1 + 15*x2 <= 510',
        'x0 + 4*x1 <= 369',
        '34*x2 + 22*x3 <= 249',
        '3*x0 + 34*x2 <= 417',
        '18*x1 + 22*x3 <= 323'
    ]
}
```