## Step 1: Define the symbolic representation of the variables
The variables are: ['hot dogs', 'chicken thighs', 'kiwis', 'black beans', 'chicken drumsticks']. Let's denote them as $x_0, x_1, x_2, x_3, x_4$ respectively.

## Step 2: Convert the objective function into a symbolic representation
The objective function to minimize is $6.2x_0 + 1.61x_1 + 2.93x_2 + 6.29x_3 + 8.4x_4$.

## Step 3: List all the constraints in symbolic notation
1. $5x_0 \geq 5$
2. $15x_0 \geq 15$ (redundant with 1)
3. $13x_1 \geq 13$ 
4. $16x_1 \geq 16$ (redundant with 3)
5. $8x_2 \geq 8$
6. $3x_2 \geq 3$ (redundant with 5)
7. $9x_3 \geq 9$
8. $8x_3 \geq 8$ (redundant with 7)
9. $2x_4 \geq 2$
10. $3x_4 \geq 3$ (redundant with 9)
11. $8x_2 + 2x_4 \geq 10$
12. $13x_1 + 9x_3 \geq 18$
13. $9x_3 + 2x_4 \geq 15$
14. $5x_0 + 2x_4 \geq 9$
15. $8x_2 + 9x_3 \geq 15$
16. $13x_1 + 8x_2 \geq 21$
17. $5x_0 + 13x_1 \geq 18$
18. $5x_0 + 8x_2 + 9x_3 \geq 19$
19. $5x_0 + 13x_1 + 8x_2 + 9x_3 + 2x_4 \geq 19$
20. $16x_1 + 8x_3 \geq 28$
21. $16x_1 + 3x_2 \geq 26$
22. $8x_3 + 3x_4 \geq 24$
23. $15x_0 + 3x_2 \geq 39$
24. $3x_2 + 8x_3 \geq 30$
25. $15x_0 + 8x_3 + 3x_4 \geq 20$
26. $15x_0 + 16x_1 + 3x_2 + 8x_3 + 3x_4 \geq 20$
27. $-6x_0 + x_4 \geq 0$
28. $13x_1 + 2x_4 \leq 65$
29. $8x_2 + 2x_4 \leq 49$
30. $5x_0 + 9x_3 \leq 28$
31. $13x_1 + 9x_3 \leq 31$
32. $5x_0 + 8x_2 + 2x_4 \leq 53$
33. $5x_0 + 9x_3 + 2x_4 \leq 79$
34. $5x_0 + 13x_1 + 9x_3 \leq 100$
35. $3x_2 + 3x_4 \leq 99$
36. $15x_0 + 16x_1 \leq 77$
37. $8x_3 + 3x_4 \leq 65$
38. $16x_1 + 8x_3 \leq 124$
39. $16x_1 + 3x_4 \leq 85$
40. $15x_0 + 3x_2 \leq 118$
41. $15x_0 + 3x_4 \leq 100$
42. $16x_1 + 3x_2 \leq 128$

## Step 4: Define the symbolic representation of the problem
```json
{
    'sym_variables': [
        ('x0', 'hot dogs'), 
        ('x1', 'chicken thighs'), 
        ('x2', 'kiwis'), 
        ('x3', 'black beans'), 
        ('x4', 'chicken drumsticks')
    ], 
    'objective_function': '6.2*x0 + 1.61*x1 + 2.93*x2 + 6.29*x3 + 8.4*x4', 
    'constraints': [
        '5*x0 >= 5',
        '13*x1 >= 13',
        '8*x2 >= 8',
        '9*x3 >= 9',
        '2*x4 >= 2',
        '8*x2 + 2*x4 >= 10',
        '13*x1 + 9*x3 >= 18',
        '9*x3 + 2*x4 >= 15',
        '5*x0 + 2*x4 >= 9',
        '8*x2 + 9*x3 >= 15',
        '13*x1 + 8*x2 >= 21',
        '5*x0 + 13*x1 >= 18',
        '5*x0 + 8*x2 + 9*x3 >= 19',
        '5*x0 + 13*x1 + 8*x2 + 9*x3 + 2*x4 >= 19',
        '16*x1 + 8*x3 >= 28',
        '16*x1 + 3*x2 >= 26',
        '8*x3 + 3*x4 >= 24',
        '15*x0 + 3*x2 >= 39',
        '3*x2 + 8*x3 >= 30',
        '15*x0 + 8*x3 + 3*x4 >= 20',
        '15*x0 + 16*x1 + 3*x2 + 8*x3 + 3*x4 >= 20',
        '-6*x0 + x4 >= 0',
        '13*x1 + 2*x4 <= 65',
        '8*x2 + 2*x4 <= 49',
        '5*x0 + 9*x3 <= 28',
        '13*x1 + 9*x3 <= 31',
        '5*x0 + 8*x2 + 2*x4 <= 53',
        '5*x0 + 9*x3 + 2*x4 <= 79',
        '5*x0 + 13*x1 + 9*x3 <= 100',
        '3*x2 + 3*x4 <= 99',
        '15*x0 + 16*x1 <= 77',
        '8*x3 + 3*x4 <= 65',
        '16*x1 + 8*x3 <= 124',
        '16*x1 + 3*x4 <= 85',
        '15*x0 + 3*x2 <= 118',
        '15*x0 + 3*x4 <= 100',
        '16*x1 + 3*x2 <= 128'
    ]
}
```

## Step 5: Write the Gurobi code
```python
import gurobi

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

# Define the variables
x0 = m.addVar(name="hot_dogs", vtype=gurobi.GRB.INTEGER)
x1 = m.addVar(name="chicken_thighs", vtype=gurobi.GRB.INTEGER)
x2 = m.addVar(name="kiwis", vtype=gurobi.GRB.INTEGER)
x3 = m.addVar(name="black_beans", vtype=gurobi.GRB.INTEGER)
x4 = m.addVar(name="chicken_drumsticks", vtype=gurobi.GRB.INTEGER)

# Objective function
m.setObjective(6.2*x0 + 1.61*x1 + 2.93*x2 + 6.29*x3 + 8.4*x4, gurobi.GRB.MINIMIZE)

# Constraints
m.addConstr(5*x0 >= 5)
m.addConstr(13*x1 >= 13)
m.addConstr(8*x2 >= 8)
m.addConstr(9*x3 >= 9)
m.addConstr(2*x4 >= 2)
m.addConstr(8*x2 + 2*x4 >= 10)
m.addConstr(13*x1 + 9*x3 >= 18)
m.addConstr(9*x3 + 2*x4 >= 15)
m.addConstr(5*x0 + 2*x4 >= 9)
m.addConstr(8*x2 + 9*x3 >= 15)
m.addConstr(13*x1 + 8*x2 >= 21)
m.addConstr(5*x0 + 13*x1 >= 18)
m.addConstr(5*x0 + 8*x2 + 9*x3 >= 19)
m.addConstr(5*x0 + 13*x1 + 8*x2 + 9*x3 + 2*x4 >= 19)
m.addConstr(16*x1 + 8*x3 >= 28)
m.addConstr(16*x1 + 3*x2 >= 26)
m.addConstr(8*x3 + 3*x4 >= 24)
m.addConstr(15*x0 + 3*x2 >= 39)
m.addConstr(3*x2 + 8*x3 >= 30)
m.addConstr(15*x0 + 8*x3 + 3*x4 >= 20)
m.addConstr(15*x0 + 16*x1 + 3*x2 + 8*x3 + 3*x4 >= 20)
m.addConstr(-6*x0 + x4 >= 0)
m.addConstr(13*x1 + 2*x4 <= 65)
m.addConstr(8*x2 + 2*x4 <= 49)
m.addConstr(5*x0 + 9*x3 <= 28)
m.addConstr(13*x1 + 9*x3 <= 31)
m.addConstr(5*x0 + 8*x2 + 2*x4 <= 53)
m.addConstr(5*x0 + 9*x3 + 2*x4 <= 79)
m.addConstr(5*x0 + 13*x1 + 9*x3 <= 100)
m.addConstr(3*x2 + 3*x4 <= 99)
m.addConstr(15*x0 + 16*x1 <= 77)
m.addConstr(8*x3 + 3*x4 <= 65)
m.addConstr(16*x1 + 8*x3 <= 124)
m.addConstr(16*x1 + 3*x4 <= 85)
m.addConstr(15*x0 + 3*x2 <= 118)
m.addConstr(15*x0 + 3*x4 <= 100)
m.addConstr(16*x1 + 3*x2 <= 128)

# Solve the model
m.optimize()

# Print the solution
if m.status == gurobi.GRB.OPTIMAL:
    print("Objective: ", m.objval)
    print("Hot dogs: ", x0.varValue)
    print("Chicken thighs: ", x1.varValue)
    print("Kiwis: ", x2.varValue)
    print("Black beans: ", x3.varValue)
    print("Chicken drumsticks: ", x4.varValue)
else:
    print("No optimal solution found")
```