## Step 1: Define the symbolic representation of the variables
The variables are 'rotisserie chickens', 'pickles', 'apples', and 'protein bars', which we will denote as $x_0$, $x_1$, $x_2$, and $x_3$ respectively.

## Step 2: Convert the objective function into symbolic notation
The objective function to maximize is $6.22x_0 + 5.78x_1 + 6.84x_2 + 4.41x_3$.

## Step 3: List all constraints in symbolic notation
Constraints:
1. $8x_0 + 5x_1 + 4x_2 + 11x_3 \leq 116$ (total protein)
2. $9x_0 + 5x_1 + 3x_2 + 2x_3 \leq 83$ (total fat)
3. $5x_1 + 4x_2 \geq 24$ (protein from pickles and apples)
4. $8x_0 + 5x_1 + 4x_2 \geq 27$ (protein from rotisserie chickens, pickles, and apples)
5. $5x_1 + 4x_2 + 11x_3 \geq 27$ (protein from pickles, apples, and protein bars)
6. $8x_0 + 4x_2 + 11x_3 \geq 27$ (protein from rotisserie chickens, apples, and protein bars)
7. $8x_0 + 5x_1 + 4x_2 \geq 16$ (protein from rotisserie chickens, pickles, and apples)
8. $5x_1 + 4x_2 + 11x_3 \geq 16$ (protein from pickles, apples, and protein bars)
9. $8x_0 + 4x_2 + 11x_3 \geq 16$ (protein from rotisserie chickens, apples, and protein bars)
10. $5x_1 + 4x_2 \geq 16$ (protein from pickles and apples)
11. $5x_1 + 2x_3 \geq 6$ (fat from pickles and protein bars)
12. $5x_1 + 4x_2 \leq 49$ (protein from pickles and apples)
13. $4x_2 + 11x_3 \leq 35$ (protein from apples and protein bars)
14. $8x_0 + 4x_2 + 11x_3 \leq 31$ (protein from rotisserie chickens, apples, and protein bars)
15. $5x_1 + 4x_2 + 11x_3 \leq 113$ (total protein from pickles, apples, and protein bars)
16. $8x_0 + 5x_1 + 4x_2 + 11x_3 \leq 113$ (total protein)
17. $9x_0 + 2x_3 \leq 44$ (fat from rotisserie chickens and protein bars)
18. $9x_0 + 5x_1 \leq 71$ (fat from rotisserie chickens and pickles)
19. $9x_0 + 3x_2 \leq 45$ (fat from rotisserie chickens and apples)
20. $5x_1 + 3x_2 \leq 79$ (fat from pickles and apples)
21. $5x_1 + 2x_3 \leq 49$ (fat from pickles and protein bars)
22. $5x_1 + 3x_2 + 2x_3 \leq 68$ (fat from pickles, apples, and protein bars)
23. $9x_0 + 5x_1 + 3x_2 + 2x_3 \leq 68$ (total fat)
24. $x_0 \in \mathbb{Z}$ (rotisserie chickens are integers)
25. $x_1 \in \mathbb{Z}$ (pickles are integers)

## Step 4: Provide the symbolic representation of the problem
```json
{
    'sym_variables': [
        ('x0', 'rotisserie chickens'), 
        ('x1', 'pickles'), 
        ('x2', 'apples'), 
        ('x3', 'protein bars')
    ], 
    'objective_function': '6.22*x0 + 5.78*x1 + 6.84*x2 + 4.41*x3', 
    'constraints': [
        '8*x0 + 5*x1 + 4*x2 + 11*x3 <= 116',
        '9*x0 + 5*x1 + 3*x2 + 2*x3 <= 83',
        '5*x1 + 4*x2 >= 24',
        '8*x0 + 5*x1 + 4*x2 >= 27',
        '5*x1 + 4*x2 + 11*x3 >= 27',
        '8*x0 + 4*x2 + 11*x3 >= 27',
        '8*x0 + 5*x1 + 4*x2 >= 16',
        '5*x1 + 4*x2 + 11*x3 >= 16',
        '8*x0 + 4*x2 + 11*x3 >= 16',
        '5*x1 + 4*x2 >= 16',
        '5*x1 + 2*x3 >= 6',
        '5*x1 + 4*x2 <= 49',
        '4*x2 + 11*x3 <= 35',
        '8*x0 + 4*x2 + 11*x3 <= 31',
        '5*x1 + 4*x2 + 11*x3 <= 113',
        '8*x0 + 5*x1 + 4*x2 + 11*x3 <= 113',
        '9*x0 + 2*x3 <= 44',
        '9*x0 + 5*x1 <= 71',
        '9*x0 + 3*x2 <= 45',
        '5*x1 + 3*x2 <= 79',
        '5*x1 + 2*x3 <= 49',
        '5*x1 + 3*x2 + 2*x3 <= 68',
        '9*x0 + 5*x1 + 3*x2 + 2*x3 <= 68'
    ]
}
```

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

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

# Define the variables
x0 = m.addVar(name="rotisserie_chickens", vtype=gurobi.GRB.INTEGER)  # rotisserie chickens
x1 = m.addVar(name="pickles", vtype=gurobi.GRB.INTEGER)  # pickles
x2 = m.addVar(name="apples")  # apples
x3 = m.addVar(name="protein_bars")  # protein bars

# Objective function
m.setObjective(6.22*x0 + 5.78*x1 + 6.84*x2 + 4.41*x3, gurobi.GRB.MAXIMIZE)

# Constraints
m.addConstr(8*x0 + 5*x1 + 4*x2 + 11*x3 <= 116)  # total protein
m.addConstr(9*x0 + 5*x1 + 3*x2 + 2*x3 <= 83)  # total fat
m.addConstr(5*x1 + 4*x2 >= 24)  # protein from pickles and apples
m.addConstr(8*x0 + 5*x1 + 4*x2 >= 27)  # protein from rotisserie chickens, pickles, and apples
m.addConstr(5*x1 + 4*x2 + 11*x3 >= 27)  # protein from pickles, apples, and protein bars
m.addConstr(8*x0 + 4*x2 + 11*x3 >= 27)  # protein from rotisserie chickens, apples, and protein bars
m.addConstr(8*x0 + 5*x1 + 4*x2 >= 16)  # protein from rotisserie chickens, pickles, and apples
m.addConstr(5*x1 + 4*x2 + 11*x3 >= 16)  # protein from pickles, apples, and protein bars
m.addConstr(8*x0 + 4*x2 + 11*x3 >= 16)  # protein from rotisserie chickens, apples, and protein bars
m.addConstr(5*x1 + 4*x2 >= 16)  # protein from pickles and apples
m.addConstr(5*x1 + 2*x3 >= 6)  # fat from pickles and protein bars
m.addConstr(5*x1 + 4*x2 <= 49)  # protein from pickles and apples
m.addConstr(4*x2 + 11*x3 <= 35)  # protein from apples and protein bars
m.addConstr(8*x0 + 4*x2 + 11*x3 <= 31)  # protein from rotisserie chickens, apples, and protein bars
m.addConstr(5*x1 + 4*x2 + 11*x3 <= 113)  # total protein from pickles, apples, and protein bars
m.addConstr(8*x0 + 5*x1 + 4*x2 + 11*x3 <= 113)  # total protein
m.addConstr(9*x0 + 2*x3 <= 44)  # fat from rotisserie chickens and protein bars
m.addConstr(9*x0 + 5*x1 <= 71)  # fat from rotisserie chickens and pickles
m.addConstr(9*x0 + 3*x2 <= 45)  # fat from rotisserie chickens and apples
m.addConstr(5*x1 + 3*x2 <= 79)  # fat from pickles and apples
m.addConstr(5*x1 + 2*x3 <= 49)  # fat from pickles and protein bars
m.addConstr(5*x1 + 3*x2 + 2*x3 <= 68)  # fat from pickles, apples, and protein bars
m.addConstr(9*x0 + 5*x1 + 3*x2 + 2*x3 <= 68)  # total fat

# Solve the model
m.optimize()

# Print the solution
if m.status == gurobi.GRB.OPTIMAL:
    print("Objective: ", m.objVal)
    print("rotisserie chickens: ", x0.varValue)
    print("pickles: ", x1.varValue)
    print("apples: ", x2.varValue)
    print("protein bars: ", x3.varValue)
else:
    print("The model is infeasible")
```