## Step 1: Define the symbolic representation of the variables
The variables are 'chicken breasts', 'bananas', and 'protein bars', which we will denote as $x_0$, $x_1$, and $x_2$ respectively.

## Step 2: Convert the objective function into a symbolic representation
The objective function to minimize is $5x_0 + 3x_1 + 8x_2$.

## Step 3: Define the constraints in symbolic notation
The constraints given are:
- $10x_0 + x_1 \geq 12$
- $x_1 + 6x_2 \geq 9$
- $10x_0 + 6x_2 \geq 11$
- $10x_0 + x_1 + 6x_2 \geq 11$
- $4x_0 + x_1 \geq 9$
- $x_1 + 8x_2 \geq 8$
- $4x_0 + x_1 + 8x_2 \geq 8$
- $-5x_0 + 4x_1 \geq 0$
- $10x_0 + x_1 \leq 27$
- $4x_0 + x_1 \leq 36$
- $4x_0 + 8x_2 \leq 52$
- $4x_0 + x_1 + 8x_2 \leq 56$

## 4: Create a symbolic representation of the problem
```json
{
'sym_variables': [('x0', 'chicken breasts'), ('x1', 'bananas'), ('x2', 'protein bars')],
'objective_function': '5*x0 + 3*x1 + 8*x2',
'constraints': [
    '10*x0 + x1 >= 12',
    'x1 + 6*x2 >= 9',
    '10*x0 + 6*x2 >= 11',
    '10*x0 + x1 + 6*x2 >= 11',
    '4*x0 + x1 >= 9',
    'x1 + 8*x2 >= 8',
    '4*x0 + x1 + 8*x2 >= 8',
    '-5*x0 + 4*x1 >= 0',
    '10*x0 + x1 <= 27',
    '4*x0 + x1 <= 36',
    '4*x0 + 8*x2 <= 52',
    '4*x0 + x1 + 8*x2 <= 56'
]
}
```

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

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

# Define the variables
x0 = model.addVar(name="chicken_breasts", lb=0)
x1 = model.addVar(name="bananas", lb=0)
x2 = model.addVar(name="protein_bars", lb=0)

# Set the objective function
model.setObjective(5*x0 + 3*x1 + 8*x2, gurobi.GRB.MINIMIZE)

# Add constraints
model.addConstr(10*x0 + x1 >= 12)
model.addConstr(x1 + 6*x2 >= 9)
model.addConstr(10*x0 + 6*x2 >= 11)
model.addConstr(10*x0 + x1 + 6*x2 >= 11)
model.addConstr(4*x0 + x1 >= 9)
model.addConstr(x1 + 8*x2 >= 8)
model.addConstr(4*x0 + x1 + 8*x2 >= 8)
model.addConstr(-5*x0 + 4*x1 >= 0)
model.addConstr(10*x0 + x1 <= 27)
model.addConstr(4*x0 + x1 <= 36)
model.addConstr(4*x0 + 8*x2 <= 52)
model.addConstr(4*x0 + x1 + 8*x2 <= 56)

# Optimize the model
model.optimize()

# Print the solution
if model.status == gurobi.GRB.OPTIMAL:
    print("Objective: ", model.objval)
    print("Chicken breasts: ", x0.x)
    print("Bananas: ", x1.x)
    print("Protein bars: ", x2.x)
else:
    print("The model is infeasible")
```