## Step 1: Define the symbolic representation of the problem
The problem involves maximizing an objective function subject to several constraints. The variables are:
- $x_0$ for milligrams of potassium
- $x_1$ for milligrams of vitamin A
- $x_2$ for milligrams of iron
- $x_3$ for milligrams of calcium

The objective function to maximize is: $6x_0 + 3x_1 + 4x_2 + 9x_3$

## Step 2: List all constraints in symbolic notation
Constraints:
1. $2x_0 + 8x_1 + 3x_2 + 9x_3 \geq 31$
2. $5x_0 + 13x_3 \geq 31$
3. $5x_0 + 9x_2 \geq 40$
4. $9x_2 + 13x_3 \geq 27$
5. $5x_0 + 5x_1 \geq 18$
6. $7x_0 + 9x_3 \geq 13$
7. $7x_0 + 4x_1 + 3x_2 \geq 29$
8. $4x_1 + 3x_2 + 9x_3 \geq 29$
9. $7x_0 + 3x_2 + 9x_3 \geq 29$
10. $7x_0 + 4x_1 + 3x_2 \geq 29$
11. $4x_1 + 3x_2 + 9x_3 \geq 29$
12. $7x_0 + 3x_2 + 9x_3 \geq 29$
13. $7x_0 + 4x_1 + 3x_2 \geq 24$
14. $4x_1 + 3x_2 + 9x_3 \geq 24$
15. $7x_0 + 3x_2 + 9x_3 \geq 24$
16. $2x_0 + 3x_2 \leq 53$
17. $2x_0 + 8x_1 \leq 173$
18. $8x_1 + 3x_2 \leq 106$
19. $2x_0 + 9x_3 \leq 135$
20. $3x_2 + 9x_3 \leq 52$
21. $2x_0 + 8x_1 + 3x_2 \leq 59$
22. $2x_0 + 8x_1 + 3x_2 + 9x_3 \leq 59$
23. $5x_0 + 9x_2 \leq 74$
24. $5x_0 + 13x_3 \leq 163$
25. $5x_0 + 5x_1 \leq 84$
26. $9x_2 + 13x_3 \leq 60$
27. $5x_0 + 9x_2 + 13x_3 \leq 145$
28. $5x_1 + 9x_2 + 13x_3 \leq 103$
29. $5x_0 + 5x_1 + 9x_2 \leq 92$
30. $5x_0 + 5x_1 + 9x_2 + 13x_3 \leq 92$
31. $7x_0 + 4x_1 \leq 143$
32. $3x_2 + 9x_3 \leq 111$
33. $7x_0 + 4x_1 + 3x_2 + 9x_3 \leq 111$

## Step 3: Provide the symbolic representation in JSON format
```json
{
    'sym_variables': [
        ('x0', 'milligrams of potassium'),
        ('x1', 'milligrams of vitamin A'),
        ('x2', 'milligrams of iron'),
        ('x3', 'milligrams of calcium')
    ],
    'objective_function': '6*x0 + 3*x1 + 4*x2 + 9*x3',
    'constraints': [
        '2*x0 + 8*x1 + 3*x2 + 9*x3 >= 31',
        '5*x0 + 13*x3 >= 31',
        '5*x0 + 9*x2 >= 40',
        '9*x2 + 13*x3 >= 27',
        '5*x0 + 5*x1 >= 18',
        '7*x0 + 9*x3 >= 13',
        '7*x0 + 4*x1 + 3*x2 >= 29',
        '4*x1 + 3*x2 + 9*x3 >= 29',
        '7*x0 + 3*x2 + 9*x3 >= 29',
        '7*x0 + 4*x1 + 3*x2 >= 29',
        '4*x1 + 3*x2 + 9*x3 >= 29',
        '7*x0 + 3*x2 + 9*x3 >= 29',
        '7*x0 + 4*x1 + 3*x2 >= 24',
        '4*x1 + 3*x2 + 9*x3 >= 24',
        '7*x0 + 3*x2 + 9*x3 >= 24',
        '2*x0 + 3*x2 <= 53',
        '2*x0 + 8*x1 <= 173',
        '8*x1 + 3*x2 <= 106',
        '2*x0 + 9*x3 <= 135',
        '3*x2 + 9*x3 <= 52',
        '2*x0 + 8*x1 + 3*x2 <= 59',
        '2*x0 + 8*x1 + 3*x2 + 9*x3 <= 59',
        '5*x0 + 9*x2 <= 74',
        '5*x0 + 13*x3 <= 163',
        '5*x0 + 5*x1 <= 84',
        '9*x2 + 13*x3 <= 60',
        '5*x0 + 9*x2 + 13*x3 <= 145',
        '5*x1 + 9*x2 + 13*x3 <= 103',
        '5*x0 + 5*x1 + 9*x2 <= 92',
        '5*x0 + 5*x1 + 9*x2 + 13*x3 <= 92',
        '7*x0 + 4*x1 <= 143',
        '3*x2 + 9*x3 <= 111',
        '7*x0 + 4*x1 + 3*x2 + 9*x3 <= 111'
    ]
}
```

## Step 4: Implement the optimization problem using Gurobi
```python
import gurobi

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

    # Define variables
    x0 = model.addVar(name="x0", lb=-gurobi.GRB.INFINITY)  # milligrams of potassium
    x1 = model.addVar(name="x1", lb=-gurobi.GRB.INFINITY)  # milligrams of vitamin A
    x2 = model.addVar(name="x2", lb=-gurobi.GRB.INFINITY)  # milligrams of iron
    x3 = model.addVar(name="x3", lb=-gurobi.GRB.INFINITY)  # milligrams of calcium

    # Objective function
    model.setObjective(6 * x0 + 3 * x1 + 4 * x2 + 9 * x3, gurobi.GRB.MAXIMIZE)

    # Constraints
    model.addConstr(2 * x0 + 8 * x1 + 3 * x2 + 9 * x3 >= 31)
    model.addConstr(5 * x0 + 13 * x3 >= 31)
    model.addConstr(5 * x0 + 9 * x2 >= 40)
    model.addConstr(9 * x2 + 13 * x3 >= 27)
    model.addConstr(5 * x0 + 5 * x1 >= 18)
    model.addConstr(7 * x0 + 9 * x3 >= 13)
    model.addConstr(7 * x0 + 4 * x1 + 3 * x2 >= 29)
    model.addConstr(4 * x1 + 3 * x2 + 9 * x3 >= 29)
    model.addConstr(7 * x0 + 3 * x2 + 9 * x3 >= 29)
    model.addConstr(7 * x0 + 4 * x1 + 3 * x2 >= 29)
    model.addConstr(4 * x1 + 3 * x2 + 9 * x3 >= 29)
    model.addConstr(7 * x0 + 3 * x2 + 9 * x3 >= 29)
    model.addConstr(7 * x0 + 4 * x1 + 3 * x2 >= 24)
    model.addConstr(4 * x1 + 3 * x2 + 9 * x3 >= 24)
    model.addConstr(7 * x0 + 3 * x2 + 9 * x3 >= 24)
    model.addConstr(2 * x0 + 3 * x2 <= 53)
    model.addConstr(2 * x0 + 8 * x1 <= 173)
    model.addConstr(8 * x1 + 3 * x2 <= 106)
    model.addConstr(2 * x0 + 9 * x3 <= 135)
    model.addConstr(3 * x2 + 9 * x3 <= 52)
    model.addConstr(2 * x0 + 8 * x1 + 3 * x2 <= 59)
    model.addConstr(2 * x0 + 8 * x1 + 3 * x2 + 9 * x3 <= 59)
    model.addConstr(5 * x0 + 9 * x2 <= 74)
    model.addConstr(5 * x0 + 13 * x3 <= 163)
    model.addConstr(5 * x0 + 5 * x1 <= 84)
    model.addConstr(9 * x2 + 13 * x3 <= 60)
    model.addConstr(5 * x0 + 9 * x2 + 13 * x3 <= 145)
    model.addConstr(5 * x1 + 9 * x2 + 13 * x3 <= 103)
    model.addConstr(5 * x0 + 5 * x1 + 9 * x2 <= 92)
    model.addConstr(5 * x0 + 5 * x1 + 9 * x2 + 13 * x3 <= 92)
    model.addConstr(7 * x0 + 4 * x1 <= 143)
    model.addConstr(3 * x2 + 9 * x3 <= 111)
    model.addConstr(7 * x0 + 4 * x1 + 3 * x2 + 9 * x3 <= 111)

    # Solve the model
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.OPTIMAL:
        print("Optimal solution found.")
        print(f"Milligrams of potassium: {x0.varValue}")
        print(f"Milligrams of vitamin A: {x1.varValue}")
        print(f"Milligrams of iron: {x2.varValue}")
        print(f"Milligrams of calcium: {x3.varValue}")
        print(f"Objective function value: {model.objVal}")
    else:
        print("No optimal solution found.")

solve_optimization_problem()
```