## Step 1: Define the symbolic representation of the variables
The variables are 'bananas', 'bowls of pasta', 'potatoes', 'hamburgers' 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 $8.09x_0 + 5.1x_1 + 8.86x_2 + 4.19x_3$.

## Step 3: List all constraints in symbolic notation
1. $0.31x_1 + 1.51x_2 \geq 67$
2. $3.93x_0 + 1.57x_3 \geq 77$
3. $0.31x_1 + 1.57x_3 \geq 63$
4. $1.51x_2 + 1.57x_3 \geq 32$
5. $3.93x_0 + 0.31x_1 \geq 60$
6. $3.93x_0 + 1.51x_2 + 1.57x_3 \geq 60$
7. $3.93x_0 + 0.31x_1 + 1.57x_3 \geq 60$
8. $3.93x_0 + 1.51x_2 + 1.57x_3 \geq 68$
9. $3.93x_0 + 0.31x_1 + 1.57x_3 \geq 68$
10. $3.93x_0 + 0.31x_1 + 1.51x_2 + 1.57x_3 \geq 68$
11. $4.86x_1 + 2.44x_2 \geq 106$
12. $2.44x_2 + 1.43x_3 \geq 41$
13. $1.31x_0 + 2.44x_2 \geq 64$
14. $1.31x_0 + 4.86x_1 \geq 46$
15. $1.31x_0 + 1.43x_3 \geq 61$
16. $4.86x_1 + 1.43x_3 \geq 102$
17. $1.31x_0 + 4.86x_1 + 2.44x_2 + 1.43x_3 \geq 102$
18. $-5x_1 + 5x_3 \geq 0$
19. $2x_1 - 7x_2 \geq 0$
20. $-x_2 + 4x_3 \geq 0$
21. $3.93x_0 + 0.31x_1 + 1.57x_3 \leq 212$
22. $3.93x_0 + 0.31x_1 + 1.51x_2 \leq 188$
23. $4.86x_1 + 1.43x_3 \leq 431$
24. $1.31x_0 + 1.43x_3 \leq 113$
25. $1.31x_0 + 4.86x_1 \leq 136$
26. $2.44x_2 + 1.43x_3 \leq 185$
27. $1.31x_0 + 2.44x_2 \leq 418$
28. $1.31x_0 + 2.44x_2 + 1.43x_3 \leq 127$
29. $1.31x_0 + 4.86x_1 + 2.44x_2 \leq 260$

## Step 4: Define the symbolic representation of the problem
```json
{
    'sym_variables': [
        ('x0', 'bananas'), 
        ('x1', 'bowls of pasta'), 
        ('x2', 'potatoes'), 
        ('x3', 'hamburgers')
    ], 
    'objective_function': '8.09x0 + 5.1x1 + 8.86x2 + 4.19x3', 
    'constraints': [
        '0.31x1 + 1.51x2 >= 67',
        '3.93x0 + 1.57x3 >= 77',
        '0.31x1 + 1.57x3 >= 63',
        '1.51x2 + 1.57x3 >= 32',
        '3.93x0 + 0.31x1 >= 60',
        '3.93x0 + 1.51x2 + 1.57x3 >= 60',
        '3.93x0 + 0.31x1 + 1.57x3 >= 60',
        '3.93x0 + 1.51x2 + 1.57x3 >= 68',
        '3.93x0 + 0.31x1 + 1.57x3 >= 68',
        '3.93x0 + 0.31x1 + 1.51x2 + 1.57x3 >= 68',
        '4.86x1 + 2.44x2 >= 106',
        '2.44x2 + 1.43x3 >= 41',
        '1.31x0 + 2.44x2 >= 64',
        '1.31x0 + 4.86x1 >= 46',
        '1.31x0 + 1.43x3 >= 61',
        '4.86x1 + 1.43x3 >= 102',
        '1.31x0 + 4.86x1 + 2.44x2 + 1.43x3 >= 102',
        '-5x1 + 5x3 >= 0',
        '2x1 - 7x2 >= 0',
        '-x2 + 4x3 >= 0',
        '3.93x0 + 0.31x1 + 1.57x3 <= 212',
        '3.93x0 + 0.31x1 + 1.51x2 <= 188',
        '4.86x1 + 1.43x3 <= 431',
        '1.31x0 + 1.43x3 <= 113',
        '1.31x0 + 4.86x1 <= 136',
        '2.44x2 + 1.43x3 <= 185',
        '1.31x0 + 2.44x2 <= 418',
        '1.31x0 + 2.44x2 + 1.43x3 <= 127',
        '1.31x0 + 4.86x1 + 2.44x2 <= 260'
    ]
}
```

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

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

# Define the variables
x0 = m.addVar(name="bananas", lb=0)
x1 = m.addVar(name="bowls of pasta", lb=0)
x2 = m.addVar(name="potatoes", lb=0)
x3 = m.addVar(name="hamburgers", lb=0)

# Objective function
m.setObjective(8.09*x0 + 5.1*x1 + 8.86*x2 + 4.19*x3, gurobi.GRB.MINIMIZE)

# Constraints
m.addConstr(0.31*x1 + 1.51*x2 >= 67)
m.addConstr(3.93*x0 + 1.57*x3 >= 77)
m.addConstr(0.31*x1 + 1.57*x3 >= 63)
m.addConstr(1.51*x2 + 1.57*x3 >= 32)
m.addConstr(3.93*x0 + 0.31*x1 >= 60)
m.addConstr(3.93*x0 + 1.51*x2 + 1.57*x3 >= 60)
m.addConstr(3.93*x0 + 0.31*x1 + 1.57*x3 >= 60)
m.addConstr(3.93*x0 + 1.51*x2 + 1.57*x3 >= 68)
m.addConstr(3.93*x0 + 0.31*x1 + 1.57*x3 >= 68)
m.addConstr(3.93*x0 + 0.31*x1 + 1.51*x2 + 1.57*x3 >= 68)
m.addConstr(4.86*x1 + 2.44*x2 >= 106)
m.addConstr(2.44*x2 + 1.43*x3 >= 41)
m.addConstr(1.31*x0 + 2.44*x2 >= 64)
m.addConstr(1.31*x0 + 4.86*x1 >= 46)
m.addConstr(1.31*x0 + 1.43*x3 >= 61)
m.addConstr(4.86*x1 + 1.43*x3 >= 102)
m.addConstr(1.31*x0 + 4.86*x1 + 2.44*x2 + 1.43*x3 >= 102)
m.addConstr(-5*x1 + 5*x3 >= 0)
m.addConstr(2*x1 - 7*x2 >= 0)
m.addConstr(-x2 + 4*x3 >= 0)
m.addConstr(3.93*x0 + 0.31*x1 + 1.57*x3 <= 212)
m.addConstr(3.93*x0 + 0.31*x1 + 1.51*x2 <= 188)
m.addConstr(4.86*x1 + 1.43*x3 <= 431)
m.addConstr(1.31*x0 + 1.43*x3 <= 113)
m.addConstr(1.31*x0 + 4.86*x1 <= 136)
m.addConstr(2.44*x2 + 1.43*x3 <= 185)
m.addConstr(1.31*x0 + 2.44*x2 <= 418)
m.addConstr(1.31*x0 + 2.44*x2 + 1.43*x3 <= 127)
m.addConstr(1.31*x0 + 4.86*x1 + 2.44*x2 <= 260)

# Solve the model
m.optimize()

# Print the solution
if m.status == gurobi.GRB.OPTIMAL:
    print("Objective: ", m.objval)
    print("bananas: ", x0.x)
    print("bowls of pasta: ", x1.x)
    print("potatoes: ", x2.x)
    print("hamburgers: ", x3.x)
else:
    print("The model is infeasible")
```