## Step 1: Define the symbolic representation of the variables
The variables are 'black beans', 'protein bars', 'sashimi', and 'rotisserie chickens'. Let's denote them as $x_0$, $x_1$, $x_2$, and $x_3$ respectively.

## Step 2: Convert the objective function into symbolic notation
The objective function to minimize is $8x_0 + 3x_1 + 9x_2 + 9x_3$.

## Step 3: Define the resources/attributes for each variable
The resources/attributes given are:
- $r_0$: sourness index with $x_0 = 6$, $x_1 = 5$, $x_2 = 13$, $x_3 = 14$
- $r_1$: umami index with $x_0 = 9$, $x_1 = 12$, $x_2 = 1$, $x_3 = 4$

## 4: Convert the constraints into symbolic notation
The constraints are:
1. $5x_1 + 14x_3 \geq 14$
2. $6x_0 + 5x_1 \geq 5$
3. $6x_0 + 13x_2 \geq 10$
4. $5x_1 + 13x_2 \geq 14$
5. $6x_0 + 14x_3 \geq 14$
6. $6x_0 + 5x_1 + 14x_3 \geq 9$
7. $6x_0 + 5x_1 + 13x_2 \geq 9$
8. $6x_0 + 5x_1 + 14x_3 \geq 12$
9. $6x_0 + 5x_1 + 13x_2 \geq 12$
10. $6x_0 + 5x_1 + 13x_2 + 14x_3 \geq 12$
11. $x_2 + 4x_3 \geq 15$
12. $9x_0 + x_2 \geq 19$
13. $9x_0 + 4x_3 \geq 21$
14. $9x_0 + 12x_1 + x_2 + 4x_3 \geq 21$
15. $-9x_2 + 3x_3 \geq 0$
16. $2x_1 - 3x_2 \geq 0$
17. $13x_2 + 14x_3 \leq 57$
18. $5x_1 + 13x_2 \leq 52$
19. $6x_0 + 13x_2 \leq 41$

## 5: Determine the variable types
- $x_0$ (black beans) must be an integer
- $x_1$ (protein bars) can be a non-integer
- $x_2$ (sashimi) can be a fractional number
- $x_3$ (rotisserie chickens) does not have to be an integer

## 6: Create the symbolic representation of the problem
```json
{
    'sym_variables': [
        ('x0', 'black beans'),
        ('x1', 'protein bars'),
        ('x2', 'sashimi'),
        ('x3', 'rotisserie chickens')
    ],
    'objective_function': '8*x0 + 3*x1 + 9*x2 + 9*x3',
    'constraints': [
        '5*x1 + 14*x3 >= 14',
        '6*x0 + 5*x1 >= 5',
        '6*x0 + 13*x2 >= 10',
        '5*x1 + 13*x2 >= 14',
        '6*x0 + 14*x3 >= 14',
        '6*x0 + 5*x1 + 14*x3 >= 9',
        '6*x0 + 5*x1 + 13*x2 >= 9',
        '6*x0 + 5*x1 + 14*x3 >= 12',
        '6*x0 + 5*x1 + 13*x2 >= 12',
        '6*x0 + 5*x1 + 13*x2 + 14*x3 >= 12',
        'x2 + 4*x3 >= 15',
        '9*x0 + x2 >= 19',
        '9*x0 + 4*x3 >= 21',
        '9*x0 + 12*x1 + x2 + 4*x3 >= 21',
        '-9*x2 + 3*x3 >= 0',
        '2*x1 - 3*x2 >= 0',
        '13*x2 + 14*x3 <= 57',
        '5*x1 + 13*x2 <= 52',
        '6*x0 + 13*x2 <= 41'
    ]
}
```

## 7: Write the Gurobi code
```python
import gurobi

def solve_optimization_problem():
    model = gurobi.Model()

    # Define variables
    x0 = model.addVar(name='black_beans', vtype=gurobi.GRB.INTEGER)
    x1 = model.addVar(name='protein_bars')
    x2 = model.addVar(name='sashimi')
    x3 = model.addVar(name='rotisserie_chickens')

    # Objective function
    model.setObjective(8*x0 + 3*x1 + 9*x2 + 9*x3, gurobi.GRB.MINIMIZE)

    # Constraints
    model.addConstr(5*x1 + 14*x3 >= 14)
    model.addConstr(6*x0 + 5*x1 >= 5)
    model.addConstr(6*x0 + 13*x2 >= 10)
    model.addConstr(5*x1 + 13*x2 >= 14)
    model.addConstr(6*x0 + 14*x3 >= 14)
    model.addConstr(6*x0 + 5*x1 + 14*x3 >= 9)
    model.addConstr(6*x0 + 5*x1 + 13*x2 >= 9)
    model.addConstr(6*x0 + 5*x1 + 14*x3 >= 12)
    model.addConstr(6*x0 + 5*x1 + 13*x2 >= 12)
    model.addConstr(6*x0 + 5*x1 + 13*x2 + 14*x3 >= 12)
    model.addConstr(x2 + 4*x3 >= 15)
    model.addConstr(9*x0 + x2 >= 19)
    model.addConstr(9*x0 + 4*x3 >= 21)
    model.addConstr(9*x0 + 12*x1 + x2 + 4*x3 >= 21)
    model.addConstr(-9*x2 + 3*x3 >= 0)
    model.addConstr(2*x1 - 3*x2 >= 0)
    model.addConstr(13*x2 + 14*x3 <= 57)
    model.addConstr(5*x1 + 13*x2 <= 52)
    model.addConstr(6*x0 + 13*x2 <= 41)

    # Solve the model
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.OPTIMAL:
        print('Objective: ', model.objval)
        print('Black beans: ', x0.varValue)
        print('Protein bars: ', x1.varValue)
        print('Sashimi: ', x2.varValue)
        print('Rotisserie chickens: ', x3.varValue)
    else:
        print('No solution found')

solve_optimization_problem()
```