## Step 1: Define the symbolic representation of the problem
First, let's define the symbolic variables and their corresponding natural language objects:
- $x_1$ represents 'rotisserie chickens'
- $x_2$ represents 'potatoes'
- $x_3$ represents 'strips of bacon'

## Step 2: Translate the objective function into algebraic terms
The objective function to maximize is $8x_1 + 1x_2 + 5x_3$.

## 3: List the constraints in semi-algebraic form
Constraints:
1. $21x_1 + 26x_2 \geq 27$
2. $27x_1 + 24x_2 + 25x_3 \geq 57$
3. $24x_2 + 25x_3 \geq 102$
4. $27x_1 + 24x_2 + 25x_3 \geq 58$
5. $32x_1 + 14x_2 + 18x_3 \geq 124$
6. $21x_1 + 26x_2 \leq 131$
7. $26x_2 + 27x_3 \leq 142$
8. $21x_1 + 26x_2 + 27x_3 \leq 142$
9. $24x_2 + 25x_3 \leq 279$
10. $27x_1 + 24x_2 + 25x_3 \leq 279$
11. $32x_1 + 18x_3 \leq 350$
12. $14x_2 + 18x_3 \leq 460$
13. $32x_1 + 14x_2 + 18x_3 \leq 460$
14. $27x_1 + 25x_2 \leq 212$
15. $27x_1 + x_3 \leq 143$
16. $27x_1 + 25x_2 + x_3 \leq 174$
17. $9x_1 + 26x_3 \leq 345$
18. $9x_1 + 31x_2 \leq 365$
19. $31x_2 + 26x_3 \leq 373$
20. $9x_1 + 31x_2 + 26x_3 \leq 314$

## 4: Provide the symbolic representation in JSON format
```json
{
    'sym_variables': [
        ('x1', 'rotisserie chickens'),
        ('x2', 'potatoes'),
        ('x3', 'strips of bacon')
    ],
    'objective_function': '8*x1 + 1*x2 + 5*x3',
    'constraints': [
        '21*x1 + 26*x2 >= 27',
        '27*x1 + 24*x2 + 25*x3 >= 57',
        '24*x2 + 25*x3 >= 102',
        '27*x1 + 24*x2 + 25*x3 >= 58',
        '32*x1 + 14*x2 + 18*x3 >= 124',
        '21*x1 + 26*x2 <= 131',
        '26*x2 + 27*x3 <= 142',
        '21*x1 + 26*x2 + 27*x3 <= 142',
        '24*x2 + 25*x3 <= 279',
        '27*x1 + 24*x2 + 25*x3 <= 279',
        '32*x1 + 18*x3 <= 350',
        '14*x2 + 18*x3 <= 460',
        '32*x1 + 14*x2 + 18*x3 <= 460',
        '27*x1 + 25*x2 <= 212',
        '27*x1 + x3 <= 143',
        '27*x1 + 25*x2 + x3 <= 174',
        '9*x1 + 26*x3 <= 345',
        '9*x1 + 31*x2 <= 365',
        '31*x2 + 26*x3 <= 373',
        '9*x1 + 31*x2 + 26*x3 <= 314'
    ]
}
```

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

def solve_optimization_problem():
    # Create a new Gurobi model
    model = gurobi.Model()

    # Define the variables
    x1 = model.addVar(name='x1', lb=-gurobi.GRB.INFINITY, ub=gurobi.GRB.INFINITY)
    x2 = model.addVar(name='x2', lb=-gurobi.GRB.INFINITY, ub=gurobi.GRB.INFINITY)
    x3 = model.addVar(name='x3', lb=-gurobi.GRB.INFINITY, ub=gurobi.GRB.INFINITY)

    # Define the objective function
    model.setObjective(8 * x1 + x2 + 5 * x3, gurobi.GRB.MAXIMIZE)

    # Add constraints
    model.addConstr(21 * x1 + 26 * x2 >= 27)
    model.addConstr(27 * x1 + 24 * x2 + 25 * x3 >= 57)
    model.addConstr(24 * x2 + 25 * x3 >= 102)
    model.addConstr(27 * x1 + 24 * x2 + 25 * x3 >= 58)
    model.addConstr(32 * x1 + 14 * x2 + 18 * x3 >= 124)
    model.addConstr(21 * x1 + 26 * x2 <= 131)
    model.addConstr(26 * x2 + 27 * x3 <= 142)
    model.addConstr(21 * x1 + 26 * x2 + 27 * x3 <= 142)
    model.addConstr(24 * x2 + 25 * x3 <= 279)
    model.addConstr(27 * x1 + 24 * x2 + 25 * x3 <= 279)
    model.addConstr(32 * x1 + 18 * x3 <= 350)
    model.addConstr(14 * x2 + 18 * x3 <= 460)
    model.addConstr(32 * x1 + 14 * x2 + 18 * x3 <= 460)
    model.addConstr(27 * x1 + 25 * x2 <= 212)
    model.addConstr(27 * x1 + x3 <= 143)
    model.addConstr(27 * x1 + 25 * x2 + x3 <= 174)
    model.addConstr(9 * x1 + 26 * x3 <= 345)
    model.addConstr(9 * x1 + 31 * x2 <= 365)
    model.addConstr(31 * x2 + 26 * x3 <= 373)
    model.addConstr(9 * x1 + 31 * x2 + 26 * x3 <= 314)

    # Optimize the model
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.OPTIMAL:
        print('Objective: ', model.objval)
        print('x1: ', x1.x)
        print('x2: ', x2.x)
        print('x3: ', x3.x)
    else:
        print('The model is infeasible')

solve_optimization_problem()
```