## Step 1: Define the symbolic representation of the variables
The variables are ['chicken breasts', 'sashimi', 'chicken drumsticks', 'hamburgers']. Let's denote them as $x_1, x_2, x_3, x_4$ respectively.

## Step 2: Define the coefficients of the objective function
The objective function to maximize is $1 \cdot x_1 + 6 \cdot x_2 + 3 \cdot x_3 + 1 \cdot x_4$.

## Step 3: Define the healthiness ratings
The healthiness ratings are given as:
- $x_1$ (chicken breasts): 1.17
- $x_2$ (sashimi): 1.68
- $x_3$ (chicken drumsticks): 1.79
- $x_4$ (hamburgers): 3.04

## 4: Translate the constraints into algebraic form
Constraints:
1. $1.17x_1 + 1.79x_3 + 3.04x_4 \geq 23$
2. $1.68x_2 + 1.79x_3 + 3.04x_4 \geq 23$
3. $1.17x_1 + 1.68x_2 + 1.79x_3 \geq 23$
4. $1.17x_1 + 1.79x_3 + 3.04x_4 \geq 16$
5. $1.68x_2 + 1.79x_3 + 3.04x_4 \geq 16$
6. $1.17x_1 + 1.68x_2 + 1.79x_3 \geq 16$
7. $1.17x_1 + 1.79x_3 + 3.04x_4 \geq 26$
8. $1.68x_2 + 1.79x_3 + 3.04x_4 \geq 26$
9. $1.17x_1 + 1.68x_2 + 1.79x_3 \geq 26$
10. $1.17x_1 + 1.68x_2 \leq 34$
11. $1.79x_3 + 3.04x_4 \leq 101$
12. $1.17x_1 + 3.04x_4 \leq 122$
13. $1.68x_2 + 3.04x_4 \leq 106$
14. $1.68x_2 + 1.79x_3 + 3.04x_4 \leq 41$
15. $1.17x_1 + 1.79x_3 + 3.04x_4 \leq 67$
16. $1.17x_1 + 1.68x_2 + 3.04x_4 \leq 111$
17. $1.17x_1 + 1.68x_2 + 1.79x_3 + 3.04x_4 \leq 111$

## 5: Define the variable bounds
- $x_1$ is continuous
- $x_2$ is integer
- $x_3$ is integer
- $x_4$ is integer

## 6: Symbolic representation
```json
{
    'sym_variables': [('x1', 'chicken breasts'), ('x2', 'sashimi'), ('x3', 'chicken drumsticks'), ('x4', 'hamburgers')],
    'objective_function': '1*x1 + 6*x2 + 3*x3 + 1*x4',
    'constraints': [
        '1.17*x1 + 1.79*x3 + 3.04*x4 >= 23',
        '1.68*x2 + 1.79*x3 + 3.04*x4 >= 23',
        '1.17*x1 + 1.68*x2 + 1.79*x3 >= 23',
        '1.17*x1 + 1.79*x3 + 3.04*x4 >= 16',
        '1.68*x2 + 1.79*x3 + 3.04*x4 >= 16',
        '1.17*x1 + 1.68*x2 + 1.79*x3 >= 16',
        '1.17*x1 + 1.79*x3 + 3.04*x4 >= 26',
        '1.68*x2 + 1.79*x3 + 3.04*x4 >= 26',
        '1.17*x1 + 1.68*x2 + 1.79*x3 >= 26',
        '1.17*x1 + 1.68*x2 <= 34',
        '1.79*x3 + 3.04*x4 <= 101',
        '1.17*x1 + 3.04*x4 <= 122',
        '1.68*x2 + 3.04*x4 <= 106',
        '1.68*x2 + 1.79*x3 + 3.04*x4 <= 41',
        '1.17*x1 + 1.79*x3 + 3.04*x4 <= 67',
        '1.17*x1 + 1.68*x2 + 3.04*x4 <= 111',
        '1.17*x1 + 1.68*x2 + 1.79*x3 + 3.04*x4 <= 111'
    ]
}
```

## 7: Gurobi Code
```python
import gurobi

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

# Define the variables
x1 = m.addVar(lb=-gurobi.GRB.INFINITY, ub=gurobi.GRB.INFINITY, name='chicken breasts')
x2 = m.addVar(lb=0, ub=gurobi.GRB.INFINITY, type=gurobi.GRB.INTEGER, name='sashimi')
x3 = m.addVar(lb=0, ub=gurobi.GRB.INFINITY, type=gurobi.GRB.INTEGER, name='chicken drumsticks')
x4 = m.addVar(lb=0, ub=gurobi.GRB.INFINITY, type=gurobi.GRB.INTEGER, name='hamburgers')

# Define the objective function
m.setObjective(1 * x1 + 6 * x2 + 3 * x3 + 1 * x4, gurobi.GRB.MAXIMIZE)

# Add constraints
m.addConstr(1.17 * x1 + 1.79 * x3 + 3.04 * x4 >= 23)
m.addConstr(1.68 * x2 + 1.79 * x3 + 3.04 * x4 >= 23)
m.addConstr(1.17 * x1 + 1.68 * x2 + 1.79 * x3 >= 23)
m.addConstr(1.17 * x1 + 1.79 * x3 + 3.04 * x4 >= 16)
m.addConstr(1.68 * x2 + 1.79 * x3 + 3.04 * x4 >= 16)
m.addConstr(1.17 * x1 + 1.68 * x2 + 1.79 * x3 >= 16)
m.addConstr(1.17 * x1 + 1.79 * x3 + 3.04 * x4 >= 26)
m.addConstr(1.68 * x2 + 1.79 * x3 + 3.04 * x4 >= 26)
m.addConstr(1.17 * x1 + 1.68 * x2 + 1.79 * x3 >= 26)
m.addConstr(1.17 * x1 + 1.68 * x2 <= 34)
m.addConstr(1.79 * x3 + 3.04 * x4 <= 101)
m.addConstr(1.17 * x1 + 3.04 * x4 <= 122)
m.addConstr(1.68 * x2 + 3.04 * x4 <= 106)
m.addConstr(1.68 * x2 + 1.79 * x3 + 3.04 * x4 <= 41)
m.addConstr(1.17 * x1 + 1.79 * x3 + 3.04 * x4 <= 67)
m.addConstr(1.17 * x1 + 1.68 * x2 + 3.04 * x4 <= 111)
m.addConstr(1.17 * x1 + 1.68 * x2 + 1.79 * x3 + 3.04 * x4 <= 111)

# Solve the model
m.optimize()

# Print the solution
if m.status == gurobi.GRB.OPTIMAL:
    print('Objective: ', m.objVal)
    print('Chicken breasts: ', x1.varValue)
    print('Sashimi: ', x2.varValue)
    print('Chicken drumsticks: ', x3.varValue)
    print('Hamburgers: ', x4.varValue)
else:
    print('No solution found')
```