## Step 1: Define the symbolic representation of the problem
The problem involves three variables: 'milligrams of vitamin B1', 'grams of fat', and 'milligrams of vitamin B2'. Let's denote these as $x_0$, $x_1$, and $x_2$ respectively.

## Step 2: Translate the objective function into symbolic notation
The objective function to minimize is $3x_0 + 9x_1 + 5x_2$.

## 3: List the constraints in symbolic notation
1. $6x_0 \leq 69$
2. $3x_0 \leq 64$
3. $4x_0 \leq 50$
4. $8x_0 \leq 57$
5. $x_1 \leq  \infty$ (no upper bound given, but implicitly from $r1$ it has a bound through other constraints)
6. $5x_1 \leq 64$
7. $3x_1 \leq 50$
8. $5x_1 \leq 57$
9. $2x_2 \leq 69$
10. $7x_2 \leq 64$
11. $6x_2 \leq 50$
12. $8x_2 \leq 57$
13. $x_1 + 2x_2 \geq 8$
14. $6x_0 + x_1 + 2x_2 \geq 8$
15. $5x_1 + 7x_2 \geq 7$
16. $3x_0 + 5x_1 + 7x_2 \geq 7$
17. $3x_1 + 6x_2 \geq 12$
18. $4x_0 + 3x_1 + 6x_2 \geq 12$
19. $8x_0 + 5x_1 \geq 9$
20. $8x_0 + 8x_2 \geq 12$
21. $8x_0 + 5x_1 + 8x_2 \geq 12$
22. $3x_1 - 4x_2 \geq 0$
23. $-9x_0 + 9x_1 \geq 0$
24. $4x_0 + 6x_2 \leq 45$
25. $4x_0 + 3x_1 \leq 18$
26. $x_0$ is an integer.

## 4: Provide the symbolic representation in JSON format
```json
{
'sym_variables': [('x0', 'milligrams of vitamin B1'), ('x1', 'grams of fat'), ('x2', 'milligrams of vitamin B2')],
'objective_function': '3*x0 + 9*x1 + 5*x2',
'constraints': [
'6*x0 <= 69',
'3*x0 <= 64',
'4*x0 <= 50',
'8*x0 <= 57',
'5*x1 <= 64',
'3*x1 <= 50',
'5*x1 <= 57',
'2*x2 <= 69',
'7*x2 <= 64',
'6*x2 <= 50',
'8*x2 <= 57',
'x1 + 2*x2 >= 8',
'6*x0 + x1 + 2*x2 >= 8',
'5*x1 + 7*x2 >= 7',
'3*x0 + 5*x1 + 7*x2 >= 7',
'3*x1 + 6*x2 >= 12',
'4*x0 + 3*x1 + 6*x2 >= 12',
'8*x0 + 5*x1 >= 9',
'8*x0 + 8*x2 >= 12',
'8*x0 + 5*x1 + 8*x2 >= 12',
'3*x1 - 4*x2 >= 0',
'-9*x0 + 9*x1 >= 0',
'4*x0 + 6*x2 <= 45',
'4*x0 + 3*x1 <= 18',
'x0 % 1 == 0'  # integer constraint for x0
]
}
```

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

def optimize_problem():
    model = gurobi.Model()
    
    # Define variables
    x0 = model.addVar(name="x0", vtype=gurobi.GRB.INTEGER)  # milligrams of vitamin B1
    x1 = model.addVar(name="x1")  # grams of fat
    x2 = model.addVar(name="x2")  # milligrams of vitamin B2

    # Objective function
    model.setObjective(3*x0 + 9*x1 + 5*x2, gurobi.GRB.MINIMIZE)

    # Constraints
    model.addConstr(6*x0 <= 69)
    model.addConstr(3*x0 <= 64)
    model.addConstr(4*x0 <= 50)
    model.addConstr(8*x0 <= 57)
    model.addConstr(5*x1 <= 64)
    model.addConstr(3*x1 <= 50)
    model.addConstr(5*x1 <= 57)
    model.addConstr(2*x2 <= 69)
    model.addConstr(7*x2 <= 64)
    model.addConstr(6*x2 <= 50)
    model.addConstr(8*x2 <= 57)
    model.addConstr(x1 + 2*x2 >= 8)
    model.addConstr(6*x0 + x1 + 2*x2 >= 8)
    model.addConstr(5*x1 + 7*x2 >= 7)
    model.addConstr(3*x0 + 5*x1 + 7*x2 >= 7)
    model.addConstr(3*x1 + 6*x2 >= 12)
    model.addConstr(4*x0 + 3*x1 + 6*x2 >= 12)
    model.addConstr(8*x0 + 5*x1 >= 9)
    model.addConstr(8*x0 + 8*x2 >= 12)
    model.addConstr(8*x0 + 5*x1 + 8*x2 >= 12)
    model.addConstr(3*x1 - 4*x2 >= 0)
    model.addConstr(-9*x0 + 9*x1 >= 0)
    model.addConstr(4*x0 + 6*x2 <= 45)
    model.addConstr(4*x0 + 3*x1 <= 18)

    # Solve the model
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.OPTIMAL:
        print("Optimal solution found.")
        print(f"milligrams of vitamin B1: {x0.varValue}")
        print(f"grams of fat: {x1.varValue}")
        print(f"milligrams of vitamin B2: {x2.varValue}")
        print(f"Objective: {model.objVal}")
    else:
        print("No optimal solution found.")

optimize_problem()
```