## Step 1: Define the symbolic representation of the variables
The variables are defined as follows: 
- $x_0$ represents 'milligrams of zinc'
- $x_1$ represents 'milligrams of vitamin B4'
- $x_2$ represents 'milligrams of vitamin C'
- $x_3$ represents 'milligrams of vitamin B12'

## Step 2: Convert the natural language description into a symbolic representation
The objective function to minimize is $4.03x_0 + 8.56x_1 + 7.71x_2 + 6.89x_3$.

## 3: List the constraints in symbolic notation
The constraints are:
- $11x_0 \leq 185$ (digestive support index of zinc)
- $5x_0 \leq 155$ (cognitive performance index of zinc)
- $5x_1 \leq 185$ (digestive support index of vitamin B4)
- $9x_1 \leq 155$ (cognitive performance index of vitamin B4)
- $4x_2 \leq 185$ (digestive support index of vitamin C)
- $3x_2 \leq 155$ (cognitive performance index of vitamin C)
- $7x_3 \leq 185$ (digestive support index of vitamin B12)
- $9x_3 \leq 155$ (cognitive performance index of vitamin B12)
- $11x_0 + 7x_3 \geq 43$ (total digestive support index from zinc and vitamin B12)
- $5x_1 + 4x_2 \geq 46$ (total digestive support index from vitamin B4 and vitamin C)
- $11x_0 + 5x_1 + 4x_2 + 7x_3 \geq 46$ (total digestive support index from all)
- $5x_0 + 9x_3 \geq 27$ (total cognitive performance index from zinc and vitamin B12)
- $3x_2 + 9x_3 \geq 28$ (total cognitive performance index from vitamin C and vitamin B12)
- $5x_0 + 9x_1 + 9x_3 \geq 33$ (total cognitive performance index from zinc, vitamin B4, and vitamin B12)
- $5x_0 + 9x_1 + 3x_2 + 9x_3 \geq 33$ (total cognitive performance index from all)
- $-10x_0 + 5x_1 \geq 0$
- $2x_0 - 7x_3 \geq 0$
- $-4x_1 + x_2 \geq 0$
- $11x_0 + 5x_1 \leq 100$
- $5x_1 + 4x_2 \leq 156$
- $5x_1 + 7x_3 \leq 99$
- $5x_1 + 4x_2 + 7x_3 \leq 124$
- $3x_2 + 9x_3 \leq 68$
- $9x_1 + 3x_2 \leq 137$
- $9x_1 + 9x_3 \leq 98$
- $5x_0 + 3x_2 \leq 38$
- $5x_0 + 9x_1 + 3x_2 \leq 94$
- $5x_0 + 3x_2 + 9x_3 \leq 56$
- $5x_0 + 9x_1 + 9x_3 \leq 78$
- $x_0 \geq 0$ and $x_0$ is an integer
- $x_1 \geq 0$
- $x_2 \geq 0$
- $x_3 \geq 0$

## 4: Provide the symbolic representation in JSON format
```json
{
    'sym_variables': [
        ('x0', 'milligrams of zinc'),
        ('x1', 'milligrams of vitamin B4'),
        ('x2', 'milligrams of vitamin C'),
        ('x3', 'milligrams of vitamin B12')
    ],
    'objective_function': '4.03*x0 + 8.56*x1 + 7.71*x2 + 6.89*x3',
    'constraints': [
        '11*x0 <= 185',
        '5*x0 <= 155',
        '5*x1 <= 185',
        '9*x1 <= 155',
        '4*x2 <= 185',
        '3*x2 <= 155',
        '7*x3 <= 185',
        '9*x3 <= 155',
        '11*x0 + 7*x3 >= 43',
        '5*x1 + 4*x2 >= 46',
        '11*x0 + 5*x1 + 4*x2 + 7*x3 >= 46',
        '5*x0 + 9*x3 >= 27',
        '3*x2 + 9*x3 >= 28',
        '5*x0 + 9*x1 + 9*x3 >= 33',
        '5*x0 + 9*x1 + 3*x2 + 9*x3 >= 33',
        '-10*x0 + 5*x1 >= 0',
        '2*x0 - 7*x3 >= 0',
        '-4*x1 + x2 >= 0',
        '11*x0 + 5*x1 <= 100',
        '5*x1 + 4*x2 <= 156',
        '5*x1 + 7*x3 <= 99',
        '5*x1 + 4*x2 + 7*x3 <= 124',
        '3*x2 + 9*x3 <= 68',
        '9*x1 + 3*x2 <= 137',
        '9*x1 + 9*x3 <= 98',
        '5*x0 + 3*x2 <= 38',
        '5*x0 + 9*x1 + 3*x2 <= 94',
        '5*x0 + 3*x2 + 9*x3 <= 56',
        '5*x0 + 9*x1 + 9*x3 <= 78',
        'x0 % 1 == 0'
    ]
}
```

## Step 5: Write the Gurobi code
```python
import gurobi

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

    # Define variables
    x0 = model.addVar(name='x0', vtype=gurobi.GRB.INTEGER)  # milligrams of zinc
    x1 = model.addVar(name='x1')  # milligrams of vitamin B4
    x2 = model.addVar(name='x2')  # milligrams of vitamin C
    x3 = model.addVar(name='x3')  # milligrams of vitamin B12

    # Objective function
    model.setObjective(4.03 * x0 + 8.56 * x1 + 7.71 * x2 + 6.89 * x3, gurobi.GRB.MINIMIZE)

    # Constraints
    model.addConstr(11 * x0 <= 185)
    model.addConstr(5 * x0 <= 155)
    model.addConstr(5 * x1 <= 185)
    model.addConstr(9 * x1 <= 155)
    model.addConstr(4 * x2 <= 185)
    model.addConstr(3 * x2 <= 155)
    model.addConstr(7 * x3 <= 185)
    model.addConstr(9 * x3 <= 155)
    model.addConstr(11 * x0 + 7 * x3 >= 43)
    model.addConstr(5 * x1 + 4 * x2 >= 46)
    model.addConstr(11 * x0 + 5 * x1 + 4 * x2 + 7 * x3 >= 46)
    model.addConstr(5 * x0 + 9 * x3 >= 27)
    model.addConstr(3 * x2 + 9 * x3 >= 28)
    model.addConstr(5 * x0 + 9 * x1 + 9 * x3 >= 33)
    model.addConstr(5 * x0 + 9 * x1 + 3 * x2 + 9 * x3 >= 33)
    model.addConstr(-10 * x0 + 5 * x1 >= 0)
    model.addConstr(2 * x0 - 7 * x3 >= 0)
    model.addConstr(-4 * x1 + x2 >= 0)
    model.addConstr(11 * x0 + 5 * x1 <= 100)
    model.addConstr(5 * x1 + 4 * x2 <= 156)
    model.addConstr(5 * x1 + 7 * x3 <= 99)
    model.addConstr(5 * x1 + 4 * x2 + 7 * x3 <= 124)
    model.addConstr(3 * x2 + 9 * x3 <= 68)
    model.addConstr(9 * x1 + 3 * x2 <= 137)
    model.addConstr(9 * x1 + 9 * x3 <= 98)
    model.addConstr(5 * x0 + 3 * x2 <= 38)
    model.addConstr(5 * x0 + 9 * x1 + 3 * x2 <= 94)
    model.addConstr(5 * x0 + 3 * x2 + 9 * x3 <= 56)
    model.addConstr(5 * x0 + 9 * x1 + 9 * x3 <= 78)

    # Solve the model
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.OPTIMAL:
        print('Objective: ', model.objVal)
        print('x0: ', x0.varValue)
        print('x1: ', x1.varValue)
        print('x2: ', x2.varValue)
        print('x3: ', x3.varValue)
    else:
        print('No solution found')

solve_optimization_problem()
```