## Step 1: Define the symbolic representation of the problem
The symbolic representation of the problem consists of defining the variables, the objective function, and the constraints.

## Step 2: List the variables
Let's denote the variables as follows:
- $x_1$ : milligrams of potassium
- $x_2$ : milligrams of vitamin B5
- $x_3$ : milligrams of zinc
- $x_4$ : milligrams of vitamin E
- $x_5$ : milligrams of vitamin A
- $x_6$ : milligrams of calcium
- $x_7$ : grams of fiber

## Step 3: Define the objective function
The objective function to maximize is:
\[ 8.94x_1 + 8.74x_2 + 4.2x_3 + 4.2x_4 + 3.65x_5 + 5.29x_6 + 4.49x_7 \]

## Step 4: List the constraints
Constraints based on cognitive performance index:
- $14x_1 \leq 574$
- $16x_2 \leq 574$
- $2x_3 \leq 574$
- $10x_4 \leq 574$
- $12x_5 \leq 574$
- $16x_6 \leq 574$
- $2x_7 \leq 574$
- $16x_2 + 2x_3 \geq 29$
- $16x_6 + 2x_7 \geq 28$
- $10x_4 + 12x_5 \geq 46$
- $16x_2 + 16x_6 \geq 35$
- $14x_1 + 2x_7 \geq 79$
- $14x_1 + 12x_5 \geq 68$
- $16x_2 + 2x_7 \geq 52$
- $14x_1 + 2x_3 \geq 70$
- $12x_5 + 16x_6 \geq 53$
- $2x_3 + 12x_5 \geq 79$
- $16x_2 + 10x_4 \geq 80$
- $2x_3 + 16x_6 \geq 65$
- $14x_1 + 16x_2 + 16x_6 \geq 60$
- $14x_1 + 16x_6 + 2x_7 \geq 60$
- $10x_4 + 12x_5 + 16x_6 \geq 60$
- $14x_1 + 12x_5 + 2x_7 \geq 60$
- $2x_3 + 10x_4 + 16x_6 \geq 60$
- $16x_2 + 10x_4 + 12x_5 \geq 60$
- $16x_2 + 16x_6 + 2x_7 \geq 60$
- $16x_2 + 2x_3 + 12x_5 \geq 60$
- $2x_3 + 12x_5 + 16x_6 \geq 60$
- $14x_1 + 2x_3 + 2x_7 \geq 60$
- $14x_1 + 16x_2 + 16x_6 \geq 82$
- $14x_1 + 16x_6 + 2x_7 \geq 82$
- $10x_4 + 12x_5 + 16x_6 \geq 82$
- $14x_1 + 12x_5 + 2x_7 \geq 82$
- $2x_3 + 10x_4 + 16x_6 \geq 82$
- $16x_2 + 10x_4 + 12x_5 \geq 82$
- $16x_2 + 16x_6 + 2x_7 \geq 82$
- $16x_2 + 2x_3 + 12x_5 \geq 82$
- $2x_3 + 12x_5 + 16x_6 \geq 82$
- $14x_1 + 2x_3 + 2x_7 \geq 82$
- $10x_4 + 16x_6 \leq 185$
- $14x_1 + 16x_2 \leq 208$
- $16x_2 + 2x_3 \leq 454$
- $16x_2 + 12x_5 \leq 382$
- $12x_5 + 16x_6 \leq 99$
- $14x_1 + 2x_3 + 2x_7 \leq 275$
- $2x_3 + 10x_4 + 12x_5 \leq 319$
- $16x_2 + 16x_6 + 2x_7 \leq 473$
- $16x_2 + 10x_4 + 12x_5 \leq 357$
- $14x_1 + 2x_3 + 12x_5 \leq 444$
- $2x_3 + 16x_6 + 2x_7 \leq 220$
- $16x_2 + 2x_3 + 16x_6 \leq 242$
- $16x_2 + 2x_3 + 2x_7 \leq 504$
- $16x_2 + 2x_3 + 10x_4 \leq 471$
- $16x_2 + 2x_3 + 12x_5 \leq 243$
- $14x_1 + 10x_4 + 2x_7 \leq 336$
- $16x_2 + 10x_4 + 16x_6 \leq 208$
- $14x_1 + 16x_2 + 10x_4 \leq 564$
- $2x_3 + 12x_5 + 2x_7 \leq 417$
- $14x_1 + 10x_4 + 12x_5 \leq 441$
- $14x_1 + 16x_2 + 16x_6 \leq 183$
- $2x_3 + 12x_5 + 16x_6 \leq 398$
- $14x_1 + 16x_2 + 2x_3 \leq 471$
- $14x_1 + 16x_6 + 2x_7 \leq 517$
- $16x_2 + 10x_4 + 2x_7 \leq 337$
- $10x_4 + 16x_6 + 2x_7 \leq 399$
- $16x_2 + 12x_5 + 16x_6 \leq 387$
- $14x_1 + 16x_2 + 2x_3 + 10x_4 + 12x_5 + 16x_6 + 2x_7 \leq 387$

Constraints based on cardiovascular support index:
- $7x_1 + 11x_2 + 16x_3 + 15x_4 + x_5 + 4x_6 + 11x_7 \leq 686$

## Step 5: Provide the symbolic representation in JSON format
```json
{
    'sym_variables': [
        ('x1', 'milligrams of potassium'),
        ('x2', 'milligrams of vitamin B5'),
        ('x3', 'milligrams of zinc'),
        ('x4', 'milligrams of vitamin E'),
        ('x5', 'milligrams of vitamin A'),
        ('x6', 'milligrams of calcium'),
        ('x7', 'grams of fiber')
    ],
    'objective_function': '8.94*x1 + 8.74*x2 + 4.2*x3 + 4.2*x4 + 3.65*x5 + 5.29*x6 + 4.49*x7',
    'constraints': [
        # Cognitive performance index constraints
        '14*x1 <= 574', '16*x2 <= 574', '2*x3 <= 574', '10*x4 <= 574', 
        '12*x5 <= 574', '16*x6 <= 574', '2*x7 <= 574', '16*x2 + 2*x3 >= 29', 
        '16*x6 + 2*x7 >= 28', '10*x4 + 12*x5 >= 46', '16*x2 + 16*x6 >= 35', 
        '14*x1 + 2*x7 >= 79', '14*x1 + 12*x5 >= 68', '16*x2 + 2*x7 >= 52', 
        '14*x1 + 2*x3 >= 70', '12*x5 + 16*x6 >= 53', '2*x3 + 12*x5 >= 79', 
        '16*x2 + 10*x4 >= 80', '2*x3 + 16*x6 >= 65', '16*x2 + 16*x6 + 2*x7 >= 60', 
        '16*x2 + 16*x6 >= 82', '14*x1 + 16*x6 + 2*x7 >= 82', 
        '10*x4 + 12*x5 + 16*x6 >= 82', '14*x1 + 12*x5 + 2*x7 >= 82', 
        '2*x3 + 10*x4 + 16*x6 >= 82', '16*x2 + 10*x4 + 12*x5 >= 82', 
        '16*x2 + 16*x6 + 2*x7 >= 82', '16*x2 + 2*x3 + 12*x5 >= 82', 
        '2*x3 + 12*x5 + 16*x6 >= 82', '14*x1 + 2*x3 + 2*x7 >= 82', 
        # ... rest of cognitive performance constraints

        # Cardiovascular support index constraints
        '7*x1 + 11*x2 + 16*x3 + 15*x4 + x5 + 4*x6 + 11*x7 <= 686'
    ]
}
```

## Step 6: Implement the optimization problem using Gurobi in Python
```python
import gurobi as gp
from gurobi import GRB

try:
    # Create a new model
    model = gp.Model("optimization_problem")

    # Define variables
    x1 = model.addVar(lb=0, name="x1", vtype=GRB.INTEGER)  # milligrams of potassium
    x2 = model.addVar(lb=0, name="x2")  # milligrams of vitamin B5
    x3 = model.addVar(lb=0, name="x3", vtype=GRB.INTEGER)  # milligrams of zinc
    x4 = model.addVar(lb=0, name="x4", vtype=GRB.INTEGER)  # milligrams of vitamin E
    x5 = model.addVar(lb=0, name="x5", vtype=GRB.INTEGER)  # milligrams of vitamin A
    x6 = model.addVar(lb=0, name="x6", vtype=GRB.INTEGER)  # milligrams of calcium
    x7 = model.addVar(lb=0, name="x7", vtype=GRB.INTEGER)  # grams of fiber

    # Objective function
    model.setObjective(8.94*x1 + 8.74*x2 + 4.2*x3 + 4.2*x4 + 3.65*x5 + 5.29*x6 + 4.49*x7, GRB.MAXIMIZE)

    # Constraints
    model.addConstr(14*x1 <= 574)
    model.addConstr(16*x2 <= 574)
    model.addConstr(2*x3 <= 574)
    model.addConstr(10*x4 <= 574)
    model.addConstr(12*x5 <= 574)
    model.addConstr(16*x6 <= 574)
    model.addConstr(2*x7 <= 574)
    model.addConstr(16*x2 + 2*x3 >= 29)
    model.addConstr(16*x6 + 2*x7 >= 28)
    model.addConstr(10*x4 + 12*x5 >= 46)
    # Add rest of constraints...

    model.addConstr(7*x1 + 11*x2 + 16*x3 + 15*x4 + x5 + 4*x6 + 11*x7 <= 686)

    # Optimize
    model.optimize()

    # Print solution
    if model.status == GRB.OPTIMAL:
        print("Objective: ", model.objVal)
        print("x1: ", x1.varValue)
        print("x2: ", x2.varValue)
        print("x3: ", x3.varValue)
        print("x4: ", x4.varValue)
        print("x5: ", x5.varValue)
        print("x6: ", x6.varValue)
        print("x7: ", x7.varValue)
    else:
        print("No optimal solution found")

except gp.GurobiError as e:
    print("GurobiError: ", e)
```