## Step 1: Define the symbolic variables and their corresponding natural language objects.
The symbolic variables and their corresponding natural language objects are:
- $x_0$ : rotisserie chickens
- $x_1$ : cornichons
- $x_2$ : ravioli
- $x_3$ : pickles

## Step 2: Formulate the objective function using the symbolic variables.
The objective function to minimize is $8x_0 + 3x_1 + 1x_2 + 9x_3$.

## Step 3: List all the constraints in symbolic notation.
The constraints are:
- $8x_0 + 3x_3 \geq 35$
- $8x_0 + 17x_2 \geq 35$
- $12x_1 + 17x_2 \geq 28$
- $12x_1 + 3x_3 \geq 18$
- $8x_0 + 12x_1 + 17x_2 + 3x_3 \geq 18$
- $17x_2 + 12x_3 \geq 40$
- $5x_0 + 17x_2 \geq 44$
- $5x_0 + 17x_2 + 12x_3 \geq 52$
- $5x_0 + 3x_1 + 12x_3 \geq 52$
- $3x_1 + 17x_2 + 12x_3 \geq 52$
- $5x_0 + 17x_2 + 12x_3 \geq 51$
- $5x_0 + 3x_1 + 12x_3 \geq 51$
- $3x_1 + 17x_2 + 12x_3 \geq 51$
- $5x_0 + 17x_2 + 12x_3 \geq 49$
- $5x_0 + 3x_1 + 12x_3 \geq 49$
- $3x_1 + 17x_2 + 12x_3 \geq 49$
- $5x_0 + 3x_1 + 17x_2 + 12x_3 \geq 49$
- $10x_1 - 8x_2 \geq 0$
- $x_1 - 3x_3 \geq 0$
- $-8x_0 + 9x_2 \geq 0$
- $8x_0 + 12x_1 + 3x_3 \leq 99$
- $8x_0 + 17x_2 + 3x_3 \leq 130$
- $12x_1 + 17x_2 + 3x_3 \leq 52$
- $5x_0 + 3x_1 + 12x_3 \leq 176$

## 4: Provide the symbolic representation of the problem.
```json
{
    'sym_variables': [
        ('x0', 'rotisserie chickens'),
        ('x1', 'cornichons'),
        ('x2', 'ravioli'),
        ('x3', 'pickles')
    ],
    'objective_function': '8*x0 + 3*x1 + 1*x2 + 9*x3',
    'constraints': [
        '8*x0 + 3*x3 >= 35',
        '8*x0 + 17*x2 >= 35',
        '12*x1 + 17*x2 >= 28',
        '12*x1 + 3*x3 >= 18',
        '8*x0 + 12*x1 + 17*x2 + 3*x3 >= 18',
        '17*x2 + 12*x3 >= 40',
        '5*x0 + 17*x2 >= 44',
        '5*x0 + 17*x2 + 12*x3 >= 52',
        '5*x0 + 3*x1 + 12*x3 >= 52',
        '3*x1 + 17*x2 + 12*x3 >= 52',
        '5*x0 + 17*x2 + 12*x3 >= 51',
        '5*x0 + 3*x1 + 12*x3 >= 51',
        '3*x1 + 17*x2 + 12*x3 >= 51',
        '5*x0 + 17*x2 + 12*x3 >= 49',
        '5*x0 + 3*x1 + 12*x3 >= 49',
        '3*x1 + 17*x2 + 12*x3 >= 49',
        '5*x0 + 3*x1 + 17*x2 + 12*x3 >= 49',
        '10*x1 - 8*x2 >= 0',
        'x1 - 3*x3 >= 0',
        '-8*x0 + 9*x2 >= 0',
        '8*x0 + 12*x1 + 3*x3 <= 99',
        '8*x0 + 17*x2 + 3*x3 <= 130',
        '12*x1 + 17*x2 + 3*x3 <= 52',
        '5*x0 + 3*x1 + 12*x3 <= 176'
    ]
}
```

## Step 5: Write the Gurobi code to solve the optimization problem.
```python
import gurobi

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

# Define the variables
x0 = m.addVar(name='rotisserie_chickens', lb=0)
x1 = m.addVar(name='cornichons', lb=0)
x2 = m.addVar(name='ravioli', lb=0)
x3 = m.addVar(name='pickles', lb=0)

# Set the objective function
m.setObjective(8*x0 + 3*x1 + x2 + 9*x3, gurobi.GRB.MINIMIZE)

# Add constraints
m.addConstr(8*x0 + 3*x3 >= 35)
m.addConstr(8*x0 + 17*x2 >= 35)
m.addConstr(12*x1 + 17*x2 >= 28)
m.addConstr(12*x1 + 3*x3 >= 18)
m.addConstr(8*x0 + 12*x1 + 17*x2 + 3*x3 >= 18)
m.addConstr(17*x2 + 12*x3 >= 40)
m.addConstr(5*x0 + 17*x2 >= 44)
m.addConstr(5*x0 + 17*x2 + 12*x3 >= 52)
m.addConstr(5*x0 + 3*x1 + 12*x3 >= 52)
m.addConstr(3*x1 + 17*x2 + 12*x3 >= 52)
m.addConstr(5*x0 + 17*x2 + 12*x3 >= 51)
m.addConstr(5*x0 + 3*x1 + 12*x3 >= 51)
m.addConstr(3*x1 + 17*x2 + 12*x3 >= 51)
m.addConstr(5*x0 + 17*x2 + 12*x3 >= 49)
m.addConstr(5*x0 + 3*x1 + 12*x3 >= 49)
m.addConstr(3*x1 + 17*x2 + 12*x3 >= 49)
m.addConstr(5*x0 + 3*x1 + 17*x2 + 12*x3 >= 49)
m.addConstr(10*x1 - 8*x2 >= 0)
m.addConstr(x1 - 3*x3 >= 0)
m.addConstr(-8*x0 + 9*x2 >= 0)
m.addConstr(8*x0 + 12*x1 + 3*x3 <= 99)
m.addConstr(8*x0 + 17*x2 + 3*x3 <= 130)
m.addConstr(12*x1 + 17*x2 + 3*x3 <= 52)
m.addConstr(5*x0 + 3*x1 + 12*x3 <= 176)

# Optimize the model
m.optimize()

# Print the solution
if m.status == gurobi.GRB.OPTIMAL:
    print('Objective: ', m.objVal)
    print('rotisserie chickens: ', x0.varValue)
    print('cornichons: ', x1.varValue)
    print('ravioli: ', x2.varValue)
    print('pickles: ', x3.varValue)
else:
    print('No optimal solution found')
```