## Step 1: Define the symbolic representation of the variables
The variables are ['milligrams of vitamin B1', 'milligrams of calcium', 'milligrams of vitamin B3', 'milligrams of vitamin B5']. Let's denote them as $x_0$, $x_1$, $x_2$, and $x_3$ respectively.

## Step 2: Convert the natural language description into a symbolic representation
The symbolic representation of the variables is:
- $x_0$ : milligrams of vitamin B1
- $x_1$ : milligrams of calcium
- $x_2$ : milligrams of vitamin B3
- $x_3$ : milligrams of vitamin B5

## Step 3: Define the objective function in symbolic notation
The objective function to minimize is $7x_0 + 5x_1 + 8x_2 + 8x_3$.

## 4: List the constraints in symbolic notation
The constraints are:
1. $8x_0 \leq 125$ (but it's given that the cognitive performance index of $x_0$ is 8, which seems to be an equality or a specific value rather than a constraint in the traditional sense)
2. $x_0$ has a digestive support index of 1: $1x_0$
3. $3x_1$ (cognitive performance index of $x_1$)
4. $8x_1$ (digestive support index of $x_1$)
5. $11x_2$ (cognitive performance index of $x_2$)
6. $3x_2$ (digestive support index of $x_2$)
7. $11x_3$ (cognitive performance index of $x_3$)
8. $5x_3$ (digestive support index of $x_3$)
9. $11x_2 + 11x_3 \geq 16$
10. $8x_0 + 11x_3 \geq 24$
11. $8x_0 + 3x_1 + 11x_2 + 11x_3 \geq 24$
12. $8x_1 + 3x_2 \geq 16$
13. $1x_0 + 8x_1 + 3x_2 + 5x_3 \geq 16$
14. $-8x_1 + 10x_3 \geq 0$
15. $-3x_2 + 6x_3 \geq 0$
16. $-6x_1 + 4x_2 + 6x_3 \geq 0$
17. $8x_0 + 11x_2 + 11x_3 \leq 98$
18. $1x_0 + 8x_1 \leq 23$
19. $8x_1 + 5x_3 \leq 27$
20. $3x_2 + 5x_3 \leq 40$
21. $1x_0 + 5x_3 \leq 48$

## 5: Specify variable bounds and types
- $x_0$ can be fractional
- $x_1$ must be an integer
- $x_2$ can be fractional
- $x_3$ can be fractional

## 6: Formulate the problem in Gurobi
We will use Gurobi to solve this optimization problem.

```python
import gurobi

# Create a new model
model = gurobi.Model()

# Define variables
x0 = model.addVar(lb=-gurobi.GRB.INFINITY, ub=gurobi.GRB.INFINITY, name="x0")  # milligrams of vitamin B1
x1 = model.addVar(lb=0, ub=gurobi.GRB.INFINITY, vtype=gurobi.GRB.INTEGER, name="x1")  # milligrams of calcium
x2 = model.addVar(lb=-gurobi.GRB.INFINITY, ub=gurobi.GRB.INFINITY, name="x2")  # milligrams of vitamin B3
x3 = model.addVar(lb=-gurobi.GRB.INFINITY, ub=gurobi.GRB.INFINITY, name="x3")  # milligrams of vitamin B5

# Objective function
model.setObjective(7 * x0 + 5 * x1 + 8 * x2 + 8 * x3, gurobi.GRB.MINIMIZE)

# Constraints
model.addConstr(8 * x0 <= 125)
model.addConstr(11 * x2 + 11 * x3 >= 16)
model.addConstr(8 * x0 + 11 * x3 >= 24)
model.addConstr(8 * x0 + 3 * x1 + 11 * x2 + 11 * x3 >= 24)
model.addConstr(8 * x1 + 3 * x2 >= 16)
model.addConstr(x0 + 8 * x1 + 3 * x2 + 5 * x3 >= 16)
model.addConstr(-8 * x1 + 10 * x3 >= 0)
model.addConstr(-3 * x2 + 6 * x3 >= 0)
model.addConstr(-6 * x1 + 4 * x2 + 6 * x3 >= 0)
model.addConstr(8 * x0 + 11 * x2 + 11 * x3 <= 98)
model.addConstr(x0 + 8 * x1 <= 23)
model.addConstr(8 * x1 + 5 * x3 <= 27)
model.addConstr(3 * x2 + 5 * x3 <= 40)
model.addConstr(x0 + 5 * x3 <= 48)

# Optimize 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("The model is infeasible")
```

## 7: Symbolic Representation
The symbolic representation is as follows:
```json
{
    'sym_variables': [
        ('x0', 'milligrams of vitamin B1'),
        ('x1', 'milligrams of calcium'),
        ('x2', 'milligrams of vitamin B3'),
        ('x3', 'milligrams of vitamin B5')
    ],
    'objective_function': '7*x0 + 5*x1 + 8*x2 + 8*x3',
    'constraints': [
        '8*x0 <= 125',
        '11*x2 + 11*x3 >= 16',
        '8*x0 + 11*x3 >= 24',
        '8*x0 + 3*x1 + 11*x2 + 11*x3 >= 24',
        '8*x1 + 3*x2 >= 16',
        'x0 + 8*x1 + 3*x2 + 5*x3 >= 16',
        '-8*x1 + 10*x3 >= 0',
        '-3*x2 + 6*x3 >= 0',
        '-6*x1 + 4*x2 + 6*x3 >= 0',
        '8*x0 + 11*x2 + 11*x3 <= 98',
        'x0 + 8*x1 <= 23',
        '8*x1 + 5*x3 <= 27',
        '3*x2 + 5*x3 <= 40',
        'x0 + 5*x3 <= 48'
    ]
}
```