## Step 1: Define the symbolic representation of the problem
The problem involves minimizing an objective function subject to several constraints. The variables are ['potatoes', 'ham sandwiches', 'bowls of instant ramen', 'black beans'], which we can denote 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 $4.31x_0 + 8.98x_1 + 5.94x_2 + 6.61x_3$.

## 3: List the constraints in symbolic notation
The constraints are:
1. $13x_1 + 14x_3 \geq 48$ (at least 48 grams of fat from ham sandwiches and black beans)
2. $18x_0 + 28x_2 \geq 20$ (at least 20 grams of fat from potatoes and bowls of instant ramen)
3. $18x_0 + 13x_1 \geq 43$ (at least 43 grams of fat from potatoes and ham sandwiches)
4. $13x_1 + 28x_2 \geq 23$ (at least 23 grams of fat from ham sandwiches and bowls of instant ramen)
5. $18x_0 + 13x_1 + 28x_2 + 14x_3 \geq 23$ (at least 23 grams of fat from all sources)
6. $11x_0 + 15x_3 \geq 44$ (at least 44 grams of fiber from potatoes and black beans)
7. $8x_1 + 15x_3 \geq 41$ (at least 41 grams of fiber from ham sandwiches and black beans)
8. $11x_0 + 8x_1 \geq 32$ (at least 32 grams of fiber from potatoes and ham sandwiches)
9. $11x_0 + 8x_1 + 29x_2 \geq 31$ (at least 31 grams of fiber from potatoes, ham sandwiches, and bowls of instant ramen)
10. $11x_0 + 8x_1 + 15x_3 \geq 31$ (at least 31 grams of fiber from potatoes, ham sandwiches, and black beans)
11. $8x_1 + 29x_2 + 15x_3 \geq 31$ (at least 31 grams of fiber from ham sandwiches, bowls of instant ramen, and black beans)
12. $11x_0 + 8x_1 + 29x_2 \geq 44$ (at least 44 grams of fiber from potatoes, ham sandwiches, and bowls of instant ramen)
13. $11x_0 + 8x_1 + 15x_3 \geq 44$ (at least 44 grams of fiber from potatoes, ham sandwiches, and black beans)
14. $8x_1 + 29x_2 + 15x_3 \geq 44$ (at least 44 grams of fiber from ham sandwiches, bowls of instant ramen, and black beans)
15. $11x_0 + 8x_1 + 29x_2 \geq 49$ (at least 49 grams of fiber from potatoes, ham sandwiches, and bowls of instant ramen)
16. $11x_0 + 8x_1 + 15x_3 \geq 49$ (at least 49 grams of fiber from potatoes, ham sandwiches, and black beans)
17. $8x_1 + 29x_2 + 15x_3 \geq 49$ (at least 49 grams of fiber from ham sandwiches, bowls of instant ramen, and black beans)
18. $11x_0 + 8x_1 + 29x_2 + 15x_3 \geq 49$ (at least 49 grams of fiber from all sources)
19. $-5x_2 + 8x_3 \geq 0$ ( constraint involving bowls of instant ramen and black beans)
20. $18x_0 + 28x_2 + 14x_3 \leq 160$ (up to 160 grams of fat from potatoes, bowls of instant ramen, and black beans)
21. $18x_0 + 13x_1 + 28x_2 \leq 140$ (up to 140 grams of fat from potatoes, ham sandwiches, and bowls of instant ramen)
22. $11x_0 + 8x_1 + 15x_3 \leq 147$ (up to 147 grams of fiber from potatoes, ham sandwiches, and black beans)
23. $11x_0 + 29x_2 + 15x_3 \leq 198$ (up to 198 grams of fiber from potatoes, bowls of instant ramen, and black beans)

## 4: Define the symbolic variables
The symbolic variables are:
- $x_0$ for 'potatoes'
- $x_1$ for 'ham sandwiches'
- $x_2$ for 'bowls of instant ramen'
- $x_3$ for 'black beans'

## 5: Write down the problem in a structured format
```json
{
    'sym_variables': [
        ('x0', 'potatoes'), 
        ('x1', 'ham sandwiches'), 
        ('x2', 'bowls of instant ramen'), 
        ('x3', 'black beans')
    ], 
    'objective_function': '4.31*x0 + 8.98*x1 + 5.94*x2 + 6.61*x3', 
    'constraints': [
        '13*x1 + 14*x3 >= 48',
        '18*x0 + 28*x2 >= 20',
        '18*x0 + 13*x1 >= 43',
        '13*x1 + 28*x2 >= 23',
        '18*x0 + 13*x1 + 28*x2 + 14*x3 >= 23',
        '11*x0 + 15*x3 >= 44',
        '8*x1 + 15*x3 >= 41',
        '11*x0 + 8*x1 >= 32',
        '11*x0 + 8*x1 + 29*x2 >= 31',
        '11*x0 + 8*x1 + 15*x3 >= 31',
        '8*x1 + 29*x2 + 15*x3 >= 31',
        '11*x0 + 8*x1 + 29*x2 >= 44',
        '11*x0 + 8*x1 + 15*x3 >= 44',
        '8*x1 + 29*x2 + 15*x3 >= 44',
        '11*x0 + 8*x1 + 29*x2 >= 49',
        '11*x0 + 8*x1 + 15*x3 >= 49',
        '8*x1 + 29*x2 + 15*x3 >= 49',
        '11*x0 + 8*x1 + 29*x2 + 15*x3 >= 49',
        '-5*x2 + 8*x3 >= 0',
        '18*x0 + 28*x2 + 14*x3 <= 160',
        '18*x0 + 13*x1 + 28*x2 <= 140',
        '11*x0 + 8*x1 + 15*x3 <= 147',
        '11*x0 + 29*x2 + 15*x3 <= 198'
    ]
}
```

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

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

    # Define the variables
    x0 = model.addVar(name="x0", lb=0)  # potatoes
    x1 = model.addVar(name="x1", lb=0)  # ham sandwiches
    x2 = model.addVar(name="x2", lb=0)  # bowls of instant ramen
    x3 = model.addVar(name="x3", lb=0)  # black beans

    # Define the objective function
    model.setObjective(4.31 * x0 + 8.98 * x1 + 5.94 * x2 + 6.61 * x3, gurobi.GRB.MINIMIZE)

    # Add constraints
    model.addConstr(13 * x1 + 14 * x3 >= 48)
    model.addConstr(18 * x0 + 28 * x2 >= 20)
    model.addConstr(18 * x0 + 13 * x1 >= 43)
    model.addConstr(13 * x1 + 28 * x2 >= 23)
    model.addConstr(18 * x0 + 13 * x1 + 28 * x2 + 14 * x3 >= 23)
    model.addConstr(11 * x0 + 15 * x3 >= 44)
    model.addConstr(8 * x1 + 15 * x3 >= 41)
    model.addConstr(11 * x0 + 8 * x1 >= 32)
    model.addConstr(11 * x0 + 8 * x1 + 29 * x2 >= 31)
    model.addConstr(11 * x0 + 8 * x1 + 15 * x3 >= 31)
    model.addConstr(8 * x1 + 29 * x2 + 15 * x3 >= 31)
    model.addConstr(11 * x0 + 8 * x1 + 29 * x2 >= 44)
    model.addConstr(11 * x0 + 8 * x1 + 15 * x3 >= 44)
    model.addConstr(8 * x1 + 29 * x2 + 15 * x3 >= 44)
    model.addConstr(11 * x0 + 8 * x1 + 29 * x2 >= 49)
    model.addConstr(11 * x0 + 8 * x1 + 15 * x3 >= 49)
    model.addConstr(8 * x1 + 29 * x2 + 15 * x3 >= 49)
    model.addConstr(11 * x0 + 8 * x1 + 29 * x2 + 15 * x3 >= 49)
    model.addConstr(-5 * x2 + 8 * x3 >= 0)
    model.addConstr(18 * x0 + 28 * x2 + 14 * x3 <= 160)
    model.addConstr(18 * x0 + 13 * x1 + 28 * x2 <= 140)
    model.addConstr(11 * x0 + 8 * x1 + 15 * x3 <= 147)
    model.addConstr(11 * x0 + 29 * x2 + 15 * x3 <= 198)

    # Optimize the model
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.OPTIMAL:
        print("Objective: ", model.objval)
        print("Potatoes: ", x0.varValue)
        print("Ham sandwiches: ", x1.varValue)
        print("Bowls of instant ramen: ", x2.varValue)
        print("Black beans: ", x3.varValue)
    else:
        print("The model is infeasible")

solve_optimization_problem()
```